Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
SchoolFinanceReformandtheDistributionofStudentAchievement
November2015
JulienLafortune
UniversityofCaliforniaBerkeleyjulieneconberkeleyedu
JesseRothstein
UniversityofCaliforniaBerkeleyandNBER
rothsteinberkeleyedu
DianeWhitmoreSchanzenbachNorthwesternUniversity
andNBERdwsnorthwesternedu
ABSTRACT
Westudytheimpactofpost-1990schoolfinancereformsduringtheso-calledldquoadequacyrdquoeraonthedistributionofschoolspendingandstudentachievementbetweenhigh-incomeandlow-incomeschooldistrictsUsinganeventstudydesignwefindthatreformeventsndashcourtordersandlegislativereformsndashleadtosharpimmediateandsustainedincreasesinmeanschoolspendingandinrelativespendinginlow-incomeschooldistrictsUsingtestscoredatafromtheNationalAssessmentofEducationalProgresswealsofindthatreformscausegradualincreasesintherelativeachievementofstudentsinlow-incomeschooldistrictsconsistentwiththegoalofimprovingeducationalopportunityforthesestudentsTheimpliedeffectofschoolresourcesoneducationalachievementislarge
ThisresearchwassupportedbyfundingfromtheSpencerFoundationandtheWashingtonCenterforEquitableGrowthWearegratefultoApurbaChakrabortyEloraDittonandPatrickLapidforexcellentresearchassistanceWethankTomDownesKiraboJacksonRuckerJohnsonandconferenceandseminarparticipantsatAPPAMAEFPandBrookingsforhelpfulcommentsanddiscussions
2
Introduction
Schoolsareakeylinkinthetransmissionofeconomicstatusfromgeneration
togenerationChildrenfromlow-incomefamilieshavelowertestscoreslower
ratesofhighschoolandcollegecompletionandeventuallylowerearnings2The
achievementgapbetweenrichandpoorchildrenhaswidenedinrecentyearseven
asracialgapshaveshrunk(Reardon2011)Onepotentialcontributingfactorto
gapsineducationaloutcomesisinequityinschoolresourcesUSschoolsare
traditionallyfundedoutoflocalpropertytaxesandbecausewealthierfamiliestend
toliveinrichercommunitieswithlargertaxbasestheirchildrenhavetendedto
attendschoolsthatspendmorethandothoseattendedbythechildrenoflow-
incomefamilies
Theproductivityofadditionalschoolresourcesisthesubjectoflongstanding
debateintheeducationpolicyliterature(seeegHanushek2003Krueger2003
Burtless1996)Timeseriesandcross-districtobservationalcomparisonstendto
showsmallorzeroeffectsofspendingonacademicachievement(Hanushek2006
Colemanetal1966)thoughstate-levelcomparisons(CardandKrueger1992a)and
randomizedexperiments(Krueger1999Chettyetal2011)aremorepositive
Compensatoryfundingndashadditionalstateaidfordisadvantagedschool
districtsndashwouldcreateadownwardbiasintheestimatedeffectofschoolresources
fromobservationaldesignsButitisexactlythistypeofprogramthatisofinterest
forpolicyevaluationasthestatefundingformulaisthemainpolicytoolavailableto
addressinequitiesinacademicoutcomesIndeedstatefundingformulashavebeen2SeeBarrowandSchanzenbach(2012)forareviewofthisliterature
3
alocusforreformeffortsBeginningwiththe1971SerranovPriestdecisionin
whichafederalcourtfoundCaliforniarsquosschoolfinancesystemunconstitutional
manyUSstateshavemovedawayfromlocalfundingtomorecentralizedsystems
aimedatincreasingopportunityforlow-incomestudents3
Financereformsarearguablythemostimportantpolicyforpromoting
equalityofeducationalopportunitysincetheturnawayfromschooldesegregation
inthe1980sAlongliteratureexaminestheimplicationsofthesereformsforthe
distributionofschoolspending(seeegLaddandFiske2015Hanushekand
Lindseth2009CorcoranandEvans2015)MostrelevantforourstudyCorcoran
andEvans(2015seealsoCorcoranetal2004)findthatplaintiffcourtvictories
reduceinequalityofspendingacrossdistrictsFischel(1989)andHoxby(2001)
arguethatpoorlydesignedreformssometimesledtoldquolevelingdownrdquoofthetopof
thedistributionratherthantoabsoluteincreasesinspendinginlow-income
districtsNeverthelessCorcoranandEvans(2015)findthatplaintiffvictorieslead
toincreasesatthebottomofthespendingdistributionwhileCardandPayne
(2002)findincreasedrelativespendingindistrictswithlowfamilyincomes(which
mayormaynotbelow-spendingdistricts)
Levelingdownwaspossiblebecausereformsinthe1970sand1980swere
focusedonreducinggapsinfundingbetweendistrictsAnewwaveofreformsinthe
1990swasbasedonadifferentlegaltheoryThatstateconstitutionsrequirednot
justequitableeducationspendingbutanadequatelevelofeducationalqualityIn
3CascioandReber(2013)andCascioGordonandReber(2013)examineanearlierformofschoolfinancereformtheintroductionoffederalTitleIfundingtolow-incomeschoolsviathe1965ElementaryandSecondaryEducationAct
4
judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso
therewaslessscopetoleveldowninresponsetoanadverseruling
Althoughattentionhasshiftedinrecentyearstoaccountabilityandother
processreformsasmoreimportantleversforeducationalopportunityfinance
policychangesremainquiteimportantwithatleast20schoolfinancereformcases
decidedsince2000Severalauthorshaveexaminedindividualadequacy-based
reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans
(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa
grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle
knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending
Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance
reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature
attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut
schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence
spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso
discreteeventswithtimingduemoretolegalprocessesthantopotentially
endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem
attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof
spendingonoutcomesThebarriertothishasbeentheabsenceofnationally
comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby
examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing
ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan
5
andPayne2002)orbyexamininglessproximateoutcomeslikeeventual
educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand
PersicoforthcomingCandelariaandShores2015)
Weprovidethefirstevidencefromnationallyrepresentativedataregarding
theimpactofschoolfinancereformsonstudentachievementWerelyonrarely
usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also
knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage
studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool
districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof
theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform
Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms
Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative
spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy
frameworkwefindthatfinancereformsleadtosharpimmediateandsustained
increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns
ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally
positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent
reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms
havepositiveeffectsontotalrevenuesforatleastadozenyears
Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem
theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold
5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere
6
incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth
quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore
progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)
followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly
aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity
ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand
persistorevengrowoveratleastthenextdecade
Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe
relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome
intheschooldistrictUsingoureventstudyframeworkwefindthatthe
ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income
districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform
indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused
productivelyThe(local)averageeffectofanextra$1000inper-pupilannual
spendingistoraisestudenttestscorestenyearslaterby018standarddeviations
Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending
intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms
correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies
thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool
6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores
7
districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits
consideredarethoseoperatingthroughsubsequentearnings
Inafinalanalysisweconsidertheimpactoffinancereformsonoverall
educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-
incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno
discernableeffectofreformsoneithergapThereasonisthatlow-incomeand
minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow
meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur
estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-
incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe
averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom
zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective
atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district
resourceandachievementgapswillbeneededtoaddresstheoverallgap
I Schoolfinancereforms7
Americanpublicschoolshavetraditionallybeenlocallymanagedand
financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir
taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources
availabletoachildrsquosschooldependedimportantlyonwhereheorshelives
IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda
novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966
7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
2
Introduction
Schoolsareakeylinkinthetransmissionofeconomicstatusfromgeneration
togenerationChildrenfromlow-incomefamilieshavelowertestscoreslower
ratesofhighschoolandcollegecompletionandeventuallylowerearnings2The
achievementgapbetweenrichandpoorchildrenhaswidenedinrecentyearseven
asracialgapshaveshrunk(Reardon2011)Onepotentialcontributingfactorto
gapsineducationaloutcomesisinequityinschoolresourcesUSschoolsare
traditionallyfundedoutoflocalpropertytaxesandbecausewealthierfamiliestend
toliveinrichercommunitieswithlargertaxbasestheirchildrenhavetendedto
attendschoolsthatspendmorethandothoseattendedbythechildrenoflow-
incomefamilies
Theproductivityofadditionalschoolresourcesisthesubjectoflongstanding
debateintheeducationpolicyliterature(seeegHanushek2003Krueger2003
Burtless1996)Timeseriesandcross-districtobservationalcomparisonstendto
showsmallorzeroeffectsofspendingonacademicachievement(Hanushek2006
Colemanetal1966)thoughstate-levelcomparisons(CardandKrueger1992a)and
randomizedexperiments(Krueger1999Chettyetal2011)aremorepositive
Compensatoryfundingndashadditionalstateaidfordisadvantagedschool
districtsndashwouldcreateadownwardbiasintheestimatedeffectofschoolresources
fromobservationaldesignsButitisexactlythistypeofprogramthatisofinterest
forpolicyevaluationasthestatefundingformulaisthemainpolicytoolavailableto
addressinequitiesinacademicoutcomesIndeedstatefundingformulashavebeen2SeeBarrowandSchanzenbach(2012)forareviewofthisliterature
3
alocusforreformeffortsBeginningwiththe1971SerranovPriestdecisionin
whichafederalcourtfoundCaliforniarsquosschoolfinancesystemunconstitutional
manyUSstateshavemovedawayfromlocalfundingtomorecentralizedsystems
aimedatincreasingopportunityforlow-incomestudents3
Financereformsarearguablythemostimportantpolicyforpromoting
equalityofeducationalopportunitysincetheturnawayfromschooldesegregation
inthe1980sAlongliteratureexaminestheimplicationsofthesereformsforthe
distributionofschoolspending(seeegLaddandFiske2015Hanushekand
Lindseth2009CorcoranandEvans2015)MostrelevantforourstudyCorcoran
andEvans(2015seealsoCorcoranetal2004)findthatplaintiffcourtvictories
reduceinequalityofspendingacrossdistrictsFischel(1989)andHoxby(2001)
arguethatpoorlydesignedreformssometimesledtoldquolevelingdownrdquoofthetopof
thedistributionratherthantoabsoluteincreasesinspendinginlow-income
districtsNeverthelessCorcoranandEvans(2015)findthatplaintiffvictorieslead
toincreasesatthebottomofthespendingdistributionwhileCardandPayne
(2002)findincreasedrelativespendingindistrictswithlowfamilyincomes(which
mayormaynotbelow-spendingdistricts)
Levelingdownwaspossiblebecausereformsinthe1970sand1980swere
focusedonreducinggapsinfundingbetweendistrictsAnewwaveofreformsinthe
1990swasbasedonadifferentlegaltheoryThatstateconstitutionsrequirednot
justequitableeducationspendingbutanadequatelevelofeducationalqualityIn
3CascioandReber(2013)andCascioGordonandReber(2013)examineanearlierformofschoolfinancereformtheintroductionoffederalTitleIfundingtolow-incomeschoolsviathe1965ElementaryandSecondaryEducationAct
4
judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso
therewaslessscopetoleveldowninresponsetoanadverseruling
Althoughattentionhasshiftedinrecentyearstoaccountabilityandother
processreformsasmoreimportantleversforeducationalopportunityfinance
policychangesremainquiteimportantwithatleast20schoolfinancereformcases
decidedsince2000Severalauthorshaveexaminedindividualadequacy-based
reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans
(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa
grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle
knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending
Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance
reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature
attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut
schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence
spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso
discreteeventswithtimingduemoretolegalprocessesthantopotentially
endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem
attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof
spendingonoutcomesThebarriertothishasbeentheabsenceofnationally
comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby
examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing
ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan
5
andPayne2002)orbyexamininglessproximateoutcomeslikeeventual
educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand
PersicoforthcomingCandelariaandShores2015)
Weprovidethefirstevidencefromnationallyrepresentativedataregarding
theimpactofschoolfinancereformsonstudentachievementWerelyonrarely
usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also
knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage
studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool
districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof
theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform
Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms
Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative
spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy
frameworkwefindthatfinancereformsleadtosharpimmediateandsustained
increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns
ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally
positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent
reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms
havepositiveeffectsontotalrevenuesforatleastadozenyears
Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem
theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold
5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere
6
incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth
quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore
progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)
followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly
aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity
ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand
persistorevengrowoveratleastthenextdecade
Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe
relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome
intheschooldistrictUsingoureventstudyframeworkwefindthatthe
ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income
districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform
indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused
productivelyThe(local)averageeffectofanextra$1000inper-pupilannual
spendingistoraisestudenttestscorestenyearslaterby018standarddeviations
Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending
intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms
correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies
thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool
6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores
7
districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits
consideredarethoseoperatingthroughsubsequentearnings
Inafinalanalysisweconsidertheimpactoffinancereformsonoverall
educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-
incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno
discernableeffectofreformsoneithergapThereasonisthatlow-incomeand
minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow
meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur
estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-
incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe
averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom
zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective
atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district
resourceandachievementgapswillbeneededtoaddresstheoverallgap
I Schoolfinancereforms7
Americanpublicschoolshavetraditionallybeenlocallymanagedand
financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir
taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources
availabletoachildrsquosschooldependedimportantlyonwhereheorshelives
IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda
novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966
7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
3
alocusforreformeffortsBeginningwiththe1971SerranovPriestdecisionin
whichafederalcourtfoundCaliforniarsquosschoolfinancesystemunconstitutional
manyUSstateshavemovedawayfromlocalfundingtomorecentralizedsystems
aimedatincreasingopportunityforlow-incomestudents3
Financereformsarearguablythemostimportantpolicyforpromoting
equalityofeducationalopportunitysincetheturnawayfromschooldesegregation
inthe1980sAlongliteratureexaminestheimplicationsofthesereformsforthe
distributionofschoolspending(seeegLaddandFiske2015Hanushekand
Lindseth2009CorcoranandEvans2015)MostrelevantforourstudyCorcoran
andEvans(2015seealsoCorcoranetal2004)findthatplaintiffcourtvictories
reduceinequalityofspendingacrossdistrictsFischel(1989)andHoxby(2001)
arguethatpoorlydesignedreformssometimesledtoldquolevelingdownrdquoofthetopof
thedistributionratherthantoabsoluteincreasesinspendinginlow-income
districtsNeverthelessCorcoranandEvans(2015)findthatplaintiffvictorieslead
toincreasesatthebottomofthespendingdistributionwhileCardandPayne
(2002)findincreasedrelativespendingindistrictswithlowfamilyincomes(which
mayormaynotbelow-spendingdistricts)
Levelingdownwaspossiblebecausereformsinthe1970sand1980swere
focusedonreducinggapsinfundingbetweendistrictsAnewwaveofreformsinthe
1990swasbasedonadifferentlegaltheoryThatstateconstitutionsrequirednot
justequitableeducationspendingbutanadequatelevelofeducationalqualityIn
3CascioandReber(2013)andCascioGordonandReber(2013)examineanearlierformofschoolfinancereformtheintroductionoffederalTitleIfundingtolow-incomeschoolsviathe1965ElementaryandSecondaryEducationAct
4
judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso
therewaslessscopetoleveldowninresponsetoanadverseruling
Althoughattentionhasshiftedinrecentyearstoaccountabilityandother
processreformsasmoreimportantleversforeducationalopportunityfinance
policychangesremainquiteimportantwithatleast20schoolfinancereformcases
decidedsince2000Severalauthorshaveexaminedindividualadequacy-based
reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans
(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa
grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle
knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending
Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance
reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature
attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut
schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence
spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso
discreteeventswithtimingduemoretolegalprocessesthantopotentially
endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem
attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof
spendingonoutcomesThebarriertothishasbeentheabsenceofnationally
comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby
examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing
ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan
5
andPayne2002)orbyexamininglessproximateoutcomeslikeeventual
educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand
PersicoforthcomingCandelariaandShores2015)
Weprovidethefirstevidencefromnationallyrepresentativedataregarding
theimpactofschoolfinancereformsonstudentachievementWerelyonrarely
usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also
knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage
studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool
districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof
theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform
Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms
Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative
spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy
frameworkwefindthatfinancereformsleadtosharpimmediateandsustained
increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns
ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally
positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent
reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms
havepositiveeffectsontotalrevenuesforatleastadozenyears
Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem
theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold
5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere
6
incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth
quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore
progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)
followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly
aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity
ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand
persistorevengrowoveratleastthenextdecade
Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe
relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome
intheschooldistrictUsingoureventstudyframeworkwefindthatthe
ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income
districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform
indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused
productivelyThe(local)averageeffectofanextra$1000inper-pupilannual
spendingistoraisestudenttestscorestenyearslaterby018standarddeviations
Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending
intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms
correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies
thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool
6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores
7
districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits
consideredarethoseoperatingthroughsubsequentearnings
Inafinalanalysisweconsidertheimpactoffinancereformsonoverall
educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-
incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno
discernableeffectofreformsoneithergapThereasonisthatlow-incomeand
minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow
meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur
estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-
incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe
averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom
zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective
atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district
resourceandachievementgapswillbeneededtoaddresstheoverallgap
I Schoolfinancereforms7
Americanpublicschoolshavetraditionallybeenlocallymanagedand
financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir
taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources
availabletoachildrsquosschooldependedimportantlyonwhereheorshelives
IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda
novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966
7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
4
judgingadequacycourtsfocusedonthelevelofspendinginlow-incomedistrictsso
therewaslessscopetoleveldowninresponsetoanadverseruling
Althoughattentionhasshiftedinrecentyearstoaccountabilityandother
processreformsasmoreimportantleversforeducationalopportunityfinance
policychangesremainquiteimportantwithatleast20schoolfinancereformcases
decidedsince2000Severalauthorshaveexaminedindividualadequacy-based
reformsascasestudies4ButtoourknowledgeSims(2011)andCorcoranandEvans
(2015)aretheonlysystematicstudiesoftheeffectsofthesereformstakenasa
grouponrealizedschoolfinanceandbothsamplesendin2002Thereisthuslittle
knownabouttheeffectofadequacy-basedreformsonrealizedschoolspending
Anevenbiggergapintheliteratureconcernstheimpactofschoolfinance
reformsonstudentoutcomesAsnotedabovealongbutinconclusiveliterature
attemptstoidentifytheeffectsofschoolspendingusingobservationalvariationBut
schoolfinancereformsarethemeansbywhichstatepolicymakerscaninfluence
spendingsorepresenthighlypolicy-relevantvariationinspendingTheyarealso
discreteeventswithtimingduemoretolegalprocessesthantopotentially
endogenoustrendsinotherdeterminantsofstudentoutcomesmakingthem
attractivecandidatesfornaturalexperimentalanalysesofthecausaleffectsof
spendingonoutcomesThebarriertothishasbeentheabsenceofnationally
comparablestudentoutcomedataAfewauthorshavetriedtocircumventthisby
examiningparticularstates(Clark2003Hyman2013Guryan2001)byfocusing
ontheselectedsubsetofstudentswhotaketheSATcollegeentranceexam(Card4SeeegClark(2003)andFlanaganandMurray(2004)onKentuckyandHyman(2013)Papke(20052008)CullenandLoeb(2004)andChaudhary(2009)onMichigan
5
andPayne2002)orbyexamininglessproximateoutcomeslikeeventual
educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand
PersicoforthcomingCandelariaandShores2015)
Weprovidethefirstevidencefromnationallyrepresentativedataregarding
theimpactofschoolfinancereformsonstudentachievementWerelyonrarely
usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also
knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage
studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool
districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof
theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform
Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms
Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative
spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy
frameworkwefindthatfinancereformsleadtosharpimmediateandsustained
increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns
ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally
positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent
reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms
havepositiveeffectsontotalrevenuesforatleastadozenyears
Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem
theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold
5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere
6
incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth
quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore
progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)
followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly
aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity
ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand
persistorevengrowoveratleastthenextdecade
Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe
relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome
intheschooldistrictUsingoureventstudyframeworkwefindthatthe
ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income
districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform
indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused
productivelyThe(local)averageeffectofanextra$1000inper-pupilannual
spendingistoraisestudenttestscorestenyearslaterby018standarddeviations
Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending
intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms
correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies
thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool
6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores
7
districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits
consideredarethoseoperatingthroughsubsequentearnings
Inafinalanalysisweconsidertheimpactoffinancereformsonoverall
educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-
incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno
discernableeffectofreformsoneithergapThereasonisthatlow-incomeand
minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow
meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur
estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-
incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe
averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom
zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective
atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district
resourceandachievementgapswillbeneededtoaddresstheoverallgap
I Schoolfinancereforms7
Americanpublicschoolshavetraditionallybeenlocallymanagedand
financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir
taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources
availabletoachildrsquosschooldependedimportantlyonwhereheorshelives
IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda
novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966
7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
5
andPayne2002)orbyexamininglessproximateoutcomeslikeeventual
educationalattainmenthealthandlabormarketoutcomes(JacksonJohnsonand
PersicoforthcomingCandelariaandShores2015)
Weprovidethefirstevidencefromnationallyrepresentativedataregarding
theimpactofschoolfinancereformsonstudentachievementWerelyonrarely
usedmicrodatafromtheNationalAssessmentofEducationalProgress(NAEP)also
knownasldquotheNationrsquosReportCardrdquotoconstructastate-by-yearpanelofaverage
studentachievementandofdisparitiesbetweenhigh-andlow-incomeschool
districtsConvenientlythebeginningofourNAEPpanelcoincideswiththeonsetof
theadequacyeraofschoolfinancewhichdatestotheKentuckyEducationReform
Act(KERA)of19905Wethusfocusonidentifyingtheeffectsofadequacyreforms
Thefirstpartofouranalysisdocumentsimpactsonabsoluteandrelative
spendinglevelsinlow-andhigh-incomeschooldistrictsUsinganeventstudy
frameworkwefindthatfinancereformsleadtosharpimmediateandsustained
increasesinstateaidandtotalrevenuesinlow-incomedistrictsTherearenosigns
ofnegativeimpactsonhigh-incomedistrictsrathertheseimpactsaregenerally
positiveaswellthoughsmallerAlthoughthereissomeevidenceofsubsequent
reductionsinlocaleffortinhigh-incomedistrictseveninthesedistrictsreforms
havepositiveeffectsontotalrevenuesforatleastadozenyears
Weusetwomeasuresoftheprogressivityofastatersquosschoolfinancesystem
theslopeofper-pupilrevenueswithrespecttoadistrictrsquoslogmeanhousehold
5KERAwaspromptedbya1989courtrulinginRosevCouncilforBetterEducation(790SW2d186)TheNAEPtestingprogrambeganintheearly1970sButuntiltheldquostateNAEPrdquowasintroducedin1990withtheaimofprovidingstate-levelestimatessamplesweretoosmalltosupporttheanalysisweundertakehere
6
incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth
quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore
progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)
followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly
aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity
ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand
persistorevengrowoveratleastthenextdecade
Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe
relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome
intheschooldistrictUsingoureventstudyframeworkwefindthatthe
ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income
districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform
indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused
productivelyThe(local)averageeffectofanextra$1000inper-pupilannual
spendingistoraisestudenttestscorestenyearslaterby018standarddeviations
Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending
intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms
correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies
thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool
6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores
7
districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits
consideredarethoseoperatingthroughsubsequentearnings
Inafinalanalysisweconsidertheimpactoffinancereformsonoverall
educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-
incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno
discernableeffectofreformsoneithergapThereasonisthatlow-incomeand
minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow
meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur
estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-
incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe
averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom
zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective
atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district
resourceandachievementgapswillbeneededtoaddresstheoverallgap
I Schoolfinancereforms7
Americanpublicschoolshavetraditionallybeenlocallymanagedand
financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir
taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources
availabletoachildrsquosschooldependedimportantlyonwhereheorshelives
IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda
novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966
7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
6
incomeandthegapinmeanrevenuesbetweendistrictsinthefirstandfifth
quintilesofthestatersquosdistrictmeanincomedistributionEachbecomesmore
progressive(viaareductionintheslopeandanincreaseintheQ1-Q5gap)
followingareformeventTheimpactontheprogressivityoftotalrevenuesisnearly
aslargeas(andstatisticallyindistinguishablefrom)theimpactontheprogressivity
ofstateaidAgaintheseeffectsareimmediatefollowingthereformeventand
persistorevengrowoveratleastthenextdecade
Wenextturntostudentoutcomesfocusingonanalogousmeasuresofthe
relationshipbetweendistrictmeantestscoresandthelogmeanhouseholdincome
intheschooldistrictUsingoureventstudyframeworkwefindthatthe
ldquoprogressivityrdquooftestscoresgrowssignificantlyndashthatscoresriseinlow-income
districtsrelativetohigh-incomedistrictsndashintheyearsfollowingafinancereform
indicatingthattheextraschoolresourcesreceivedbytheformerdistrictsareused
productivelyThe(local)averageeffectofanextra$1000inper-pupilannual
spendingistoraisestudenttestscorestenyearslaterby018standarddeviations
Thisisroughlytwiceaslargeastheeffectimpliedbytheannualadditionalspending
intheProjectSTARclasssizeexperiment(whichtranslatedintotheseterms
correspondstoanapproximately0085SDeffectper$1000perpupil6)Itimplies
thatmarginalincreasesinschoolresourcesinlow-incomepoorlyresourcedschool
6STARraisedcostsbyabout30inK-3andraisedtestscoresby017SDsCurrentspendingperpupilinTennesseeisaround$6700soSTARwouldtodaycostaround$2000perpupilperyearWethusdividetheSTARtestscoreeffectbytwoThiscomparisonimplicitlyassumesthatmaintainingthesmallerSTARclasssizesbeyond3rdgradewouldyieldnoadditionalgrowthintestscores
7
districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits
consideredarethoseoperatingthroughsubsequentearnings
Inafinalanalysisweconsidertheimpactoffinancereformsonoverall
educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-
incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno
discernableeffectofreformsoneithergapThereasonisthatlow-incomeand
minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow
meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur
estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-
incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe
averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom
zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective
atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district
resourceandachievementgapswillbeneededtoaddresstheoverallgap
I Schoolfinancereforms7
Americanpublicschoolshavetraditionallybeenlocallymanagedand
financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir
taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources
availabletoachildrsquosschooldependedimportantlyonwhereheorshelives
IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda
novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966
7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
7
districtsarecosteffectivefromasocialperspectiveevenwhentheonlybenefits
consideredarethoseoperatingthroughsubsequentearnings
Inafinalanalysisweconsidertheimpactoffinancereformsonoverall
educationalequitymeasuredasthegapinachievementbetweenhigh-andlow-
incomestudentsorbetweenwhiteandminoritystudentsinastateWefindno
discernableeffectofreformsoneithergapThereasonisthatlow-incomeand
minoritystudentsarenotveryhighlyconcentratedinschooldistrictswithlow
meanincomessoarenotcloselytargetedbydistrict-basedfinancereformsOur
estimatesindicatethattheaveragereformeventraisesrelativespendinginlow-
incomedistrictsbyover$500perpupilperyearbutraisesrelativespendingonthe
averagelow-incomestudentbyunder$100(notstatisticallydistinguishablefrom
zero)Thuswhileouranalysissuggeststhatfinancereformscanbequiteeffective
atreducingbetween-districtinequitiesotherpolicytoolsaimedatwithin-district
resourceandachievementgapswillbeneededtoaddresstheoverallgap
I Schoolfinancereforms7
Americanpublicschoolshavetraditionallybeenlocallymanagedand
financedoutoflocalpropertytaxrevenueAslocaljurisdictionsvarywidelyintheir
taxbasesandinclinationstofundlocalschoolsthishasmeantthattheresources
availabletoachildrsquosschooldependedimportantlyonwhereheorshelives
IntheSerranovPriest(1971)8theCaliforniaSupremeCourtaccepteda
novellegaltheory(propoundedinvariousformsbyWise1967Horowitz1966
7OurdiscussionheredrawsheavilyonKoskiandHahnel(2015)8487P2d1241
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
8
Kirp1968andCoonsCluneandSugarman1970amongothers)thattheEqual
ProtectionClauseoftheUSConstitutioncreatedarightofequalaccesstogood
schoolsCaliforniarsquoslegislaturerespondedwithahighlycentralizedschoolfinance
systemthatnearlyperfectlyequalizesper-pupilresourcesacrossdistricts
TheUSSupremeCourtrejectedthislegaltheoryinSanAntonioIndependent
SchoolDistrictvRodriguez9in1973ReformeffortsshiftedtostatecourtsUnlike
theUSConstitutionmanystateconstitutionsaddresseducationspecificallyCourts
inmanystatesfoundrequirementsforgreaterequityinschoolfinancewhileother
statesrsquolegislaturesactedwithoutcourtdecisions(perhapstostaveoffpotential
rulings)Thenewfinanceregimescreatedinthissecondwaveofreformstooka
varietyofformsrangingfromCalifornia-stylecentralizationofschoolfinanceto
ldquopowerequalizationrdquoformulasthataimedmerelytoprovidepoordistrictswith
similartradeoffsbetweentaxratesandspendingasarefacedbyrichdistrictsThese
second-wavereformsproceededthroughthe1970sand1980sandhavebeenmuch
studied(seeegHanushekandLindseth2009CorcoranandEvans2015Card
andPayne2002MurrayEvansandSchwab1998)
Wefocusonthemuchlessstudiedthirdwaveofadequacy-basedfinance
reformsThesebeganin1989whentheKentuckySupremeCourtfoundthatthe
stateconstitutionalrequirementforanldquoefficientsystemrdquoofpublicschoolsrequired
thatldquo[e]achchildeverychildhellipmustbeprovidedwithanequalopportunitytohave
anadequateeducationrdquo(RosevCouncilforBetterEducation10emphasisinoriginal)
Thedecisionmadeclearthatadequacyrequiredmorethanequalinputs(eg
9411US1
10790SW2d186
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
9
ldquosufficientlevelsofacademicorvocationalskillstoenablepublicschoolstudentsto
competefavorablywiththeircounterpartsinsurroundingstatesinacademicsorin
thejobmarketrdquo)Toachievethisspendingwouldneedtobeincreasedsubstantially
inlow-incomedistrictsIndeedsubsequentreformshaveoftenaimedathigher
spendinginlow-incomethaninhigh-incomedistrictstocompensatefortheout-of-
schooldisadvantagesoflow-incomestudents11
TheKentuckylegislaturerespondedwiththeKentuckyEducationReformAct
of1990(KERA)whichrevampedthestatersquoseducationalfinancegovernanceand
curriculumKERAledtosubstantialincreasesinspendinginlow-incomedistricts
andthecorrelationbetweendistrictmedianincomeandtotalcurrentexpenditures
perpupilwentfrompositivetonegative(Clark2003FlanaganandMurray2004)
Since1990manyotherstatecourtshavefoundadequacyrequirementsin
theirownconstitutionsWeidentifyreformeventsin27statesoverthisperiod
manyofthemadequacybasedWediscussourtabulationofpost-1990finance
reformeventsndashcourtordersandmajorlegislativechangesndashinSectionII
Aswithearlierequity-basedreformstherehasbeennosingledefinitionof
adequacyandstateshavevariedinthefinancesystemsthattheyhaveadopted
Despitethisheterogeneitythereisreasontobelievethatadequacy-basedreforms
willhavedifferentimplicationsforthelevelanddistributionofschoolfundingthan
didearlierreformspredicatedonequityprinciplesWhereanequity-basedcourt
ordermightpermitlevelingdowntoastingybutequalfundingformulaastate
cannotsatisfyanadequacymandatebylevelingdownManystatesseeminsteadto
11AlongliteraturestudiesthecalculationofspendinglevelsneededtosatisfyanadequacystandardSeeegDownesandSteifel2015andDuncombeNguyen-HoangandYinger2008
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
10
haveleveledalldistrictsupinordertomeetadequacycriteriainlow-income
districtswhilestillallowinghigher-incomedistrictstodifferentiatethemselves
Overallthenonemightexpectthatadequacy-basedreformswouldleadtohigher
spendingacrosstheboardthanwouldequity-basedreformsbutperhapsalsoto
smallerreductionsininequality(BakerandGreen2015DownesandStiefel2015)
Thispointstotheimportanceofexaminingboththeaverageimpactofreformsand
theirdifferentialeffectonlow-incomevshigh-incomeschooldistrictsWedevelopa
frameworktoassessbothinthenextsectionLaterweapplyittostudyimpactson
bothspendinglevels(SectionIV)andstudenttestscores(SectionV)
II Analyticapproach
WedevelopouranalyticapproachinthreepartsFirstweintroduceournew
post-1990reformeventdatabaseSecondwediscussoursummarymeasuresof
schoolfinanceandstudentoutcomesineachstateineachyearThirdwediscuss
ourmethodologyforrelatingreformeventstosubsequentoutcomes
A Characterizingevents
Themostclearcutschoolfinancereformeventsarewhenastatersquossupreme
courtsfindthestateschoolfinancingsystemtobeunconstitutionalandorders
changesinthefundingformulaMuchofthepriorschoolfinancereformliterature
hasfocusedoncourt-orderedreformsweareabletodrawonlistsinJacksonetal
(forthcoming)HanushekandLindseth(2009)andCorcoranandEvans(2015)
supplementingthemwithourownresearchintocasehistoriesWefocusonevents
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
11
in1990andthereaftercorrespondingbothtotheperiodcoveredbyourNAEP
panel(discussedbelow)andtotheadequacyeraofschoolfinancereform12
Weuseaninclusivedefinitionofeventsincludingmanycourtordersthat
weresubsequentlyreversedorwereignoredbythelegislatureWedateeventsto
thecourtjudgmentndashtypicallyasupremecourtorsignificantappellatedecisionndash
nottoactualflowsofmoney(whichmayneveroccur)Incontrasttosomeprior
workwedonotrestrictattentiontoinitialordersbutwealsotrynottolabelevery
singleproceduralrulingaseparateeventInparticularwhenalowercourtdecision
isstayedpendingappealwedonotcounttheeventuntilahighercourtupholdsthe
initialdecisionandliftsthestay
NotallmajorschoolfinancereformeventsresultedfromcourtordersIn
someimportantcases(egCaliforniaColorado)legislaturesreformedfinance
systemswithoutpriorcourtdecisionsperhapstoforestalladversejudgmentsin
threatenedorongoinglawsuitsAsaresultwealsoincludemajorlegislative
reformsthatchangeschoolfinancesystemsinoureventlist
AsshowninFigure1weidentifyatotalof68eventsin27statesbetween
1990and201351arecourtordersand40arelegislativeactionsin9of
casesweidentifyoneofeachinthesameyearandcountthemasasingleeventA
completelistofoureventsalongwithacomparisontothoseusedinotherstudies
ispresentedinAppendixTableA113Therehavebeenmorecourt-orderedfinance
12Notethatthe1990startdateencompassesKERAbutnotthe1989Rosedecision13AppendixTableA3presentsanalysesusingalternativeeventdefinitions(egcountingonlyinitialeventsoronlycourtorders)moresimilartothoseusedelsewhereResultsarequalitativelysimilar
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
12
reformsduringtheadequacyerathaninthepriorequityera14Figure2showsthe
geographicdistributionofeventsusingshadingtorepresentthedateofthefirst
post-1989eventandnumeralstoindicatethenumberofeventsReformeventsare
geographicallydispersedthoughrareinthedeepSouthandupperMidwest
B Measuringschoolfinancesystemsandstudentoutcomes
Nextweturntothemeasurementoftheindependentvariablesofinterest
beginningwiththestatefinanceregimeHereachallengeishowtosummarizethe
distributionofschoolresources15CorcoranandEvans(2015)forexampleexamine
thestandarddeviationofspendingperpupilandothersummariesoftheunivariate
distributionButthisapproachdoesnotaccountfortherelationshipofspendingto
areaeconomicresourcesSincethecentralissuesinschoolfinancereformarethe
equityofresourcedistributionacrossrichandpoordistrictsandtheadequacyof
resourcesavailabletothelowest-incomedistrictswepreferameasurethat
correspondsmoredirectlytotheseconceptsWeconsiderbothabsoluteand
relativemeasuresoffundingindisadvantageddistrictscorrespondingroughlyto
theadequacyandequityofthefundingsystemrespectively
Ourprimarymeasureofschooldistrict(dis)advantageistheaveragefamily
incomeinthedistrictrelativetothestateaverage16Weusetwomeasuresoffinance
14Althoughourdatabasebeginsin1990Jacksonetal(2015)code15court-orderedreformsfrom1971through1989and48sincethen15Someauthorscategorizeschoolfinancesystemsbytheformofthefinanceformulaitself(egminimumfoundationplanpowerequalizationetcndashseeHoxby2001andCardandPayne2002)Butfinanceformulasdonotalwaysconformtothesecategoriesandeventwostateswithformulasofthesametypemayvarysubstantiallyintheextentofintendedoractualredistribution16TheAppendixreportsanalysesusingalternativemeasures(egmeanhomevaluesortheshareoffamiliesunder185ofpoverty)withsimilarresultsMuchschoolfinancelitigationhasfocusedon
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
13
equityThefirstisthedifferenceinaverageper-pupilrevenuendasheitherintotalor
fromthestatendashbetweendistrictsinthebottomandtopquintilesofthestatefamily
incomedistributionButwhiletheextremesofthedistributionarecertainlyof
particularinterestinequitydiscussionsonemightalsobeinterestedinthe
distributionofresourcesfordistrictsinthemiddlethreequintilesTosummarize
therelationshipbetweenspendingandincomeacrosstheentireincome
distributionoursecondmeasurefollowsCardandPayne(2002)inmeasuringthe
bivariaterelationshipbetweenfinanceandeconomicdisadvantageacrossdistricts
inthestateWeestimatethefollowingregressionseparatelyforeachstateandyear
(1) Rist=αst+θstln(Yi)+Xistrsquoγst+uist
HereRistmeasuresrevenuesperstudentindistrictiinstatesinyeartln(Yi)isthe
meanhouseholdincomeintheschooldistrict(measuredin1990)andXistcontains
controlsforlogenrollmentanddistricttype(elementarysecondaryorunified)17A
morepositiveθstcoefficientmeansagreatergapinfundingbetweenhigh-andlow-
incomedistrictsaswouldgenerallybeexpectedwithlocalfinancewhileanegative
coefficient(observedinabout40ofthestate-yearcellsinoursample)meansthat
revenuesarenegativelycorrelatedwithmeanincomesacrossdistrictsinthestate
Whenweturntoourexaminationofstudentoutcomesweuseparallel
measurestothoseusedinourfinanceanalysisThemeantestscoresofstudentsat
districtsinthebottomquintileofthefamilyincomedistributionthegapbetween
disparitiesinpropertytaxbaseswhichareimperfectlycorrelatedwithfamilyincomesorevenhomevaluesWearenotawareofanationallycomparablemeasureofdistrictpropertytaxbasesthattakesaccountofthevariationinthedefinitionofthetaxbaseorintaxablenon-residentialproperty17WeweightbymeanlogenrollmentinthedistrictacrossallyearsinthesampletoreducevolatilityfromchangingenrollmentovertimeBycontrasttheenrollmentmeasureintheXistvectoristhetime-varyinglogenrollmentfromyearttocapturesensitivityoffundingformulastodistrictscale
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
14
thismeanandthemeanatdistrictsinthetopquintileandtheslopefroma
regressionofmeantestscoresondistrictfamilyincome18Eachisestimated
separatelyforeachavailablestate-year-subject-gradecombination
C OhioCaseStudy
Toillustratethesemeasuresandtheirrelationshipstoschoolfinancereform
eventswepresentOhioasacasestudyFigure3showstherelationshipbetween
districtincomeandstaterevenuesinOhioin1990and2010Onthehorizontalaxis
isthelogoftheaveragehouseholdincomeinaschooldistrictin1990Onthe
verticalaxisweshowstaterevenuesperpupilininflation-adjusted2013dollarsin
1990(leftpanel)and2011(rightpanel)(Wediscussthedatasourcesatgreater
lengthinSectionIII)Ineachpanelweoverlayaregressionlinewithslopeθstas
wellasastepfunctionshowingmeanrevenuesbydistrictincomequintileIn1990
bottomquintileOhiodistrictsreceivedanaverageof$1102perpupilmorethandid
thetopquintiledistrictsbutby2011thishadgrownto$3387Theθstslopeis
negativeinbothyearsindicatingprogressivestatefundingtodistrictsbutismuch
morenegativein2011thanin1990In1990each10increaseinmeanhousehold
incomewasassociatedwithabout$144lessinstateaidperpupilthe
correspondingfigurein2011is$469Thechangeinslopeisdrivenbyadramatic
increaseinstateaidtolow-incomedistrictsHigher-incomedistrictsalsosaw
increasesbuttheirgainsweremuchsmaller
18Thespecificationusedtoestimatetestscoreslopesdropsthecontrolsfordistricttypefrom(1)andusesNAEPsampleweights
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
15
Figure4apresentsthescatterplotofstaterevenue-incomeslopesθstin
1990and2011acrossallstatesItshowsthatOhiohighlightedinthefigureisnot
anoutlierFully39statesarebelowthe45degreelineindicatingsmallerslopes
(moreprogressivedistributions)in2011thanin1990
Figure4bshowsthecorrespondingscatterplotfortheslopeoftotalrevenues
perpupilinclusiveofstaterevenueslocaltaxcollectionsandfederaltransfers
withrespecttodistrictincomeAlthoughtotalrevenueslopesaregenerallylarger
andmoreoftenpositivendashwhilestaterevenueformulasareoftenprogressivelocal
taxcollectionsarenotndashweagainseedeclininggradientsovertimeinmoststates
Figure3showsthatOhiorsquosfinanceformulachangedsubstantiallybetween
1990and2011andFigure4showsthatthisisnotanisolatedcaseButtowhat
extentwerethechangesduetointentionalreformsToanswerthisweneedto
relatethechangesinfinancestothereformeventsdescribedearlierIntheclearest
casesacourtdecisionfindingthestatersquosfinancesystemtobeunconstitutional
resultsinapromptdiscretechangeinspendingOftenhoweverthereisacomplex
interactionbetweenthecourtsandthelegislaturewithmultiplecourtdecisionsand
legislativechangesovermanyyearsandspendingchangesgradually
OhioisagainausefulillustrationThestateSupremeCourtruledfourtimes
ontheDeRolphvStatecasein199720002001and2002The1997ruling
declaredthestatersquosfinancesystemunconstitutionalonadequacygroundsand
specificallyrejectedthestatersquosrelianceonlocalpropertytaxesTheCourtordereda
ldquocompletesystematicoverhaulrdquooftheschoolfundingsystemIn2000theCourt
determinedthatthelegislaturehadfailedtoactandthatfundinglevelsremained
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
16
inadequateThesameyearthelegislaturerevisedthesystemandasubsequent
rulingin2001determinedthatthenewsystemwithafewminorchangessatisfied
constitutionalrequirementsThisdecisionwasreversedbythesameCourtndashwith
newjudgessincethepreviousyearndashin2002Toourknowledgetherehavenot
beensubstantialreformstothefinancesystemsincethenWecodeOhioashaving
judicialreformeventsin1997and2002andajointstatutory-judicialeventin2000
Figure5ashowstheestimatedstaterevenue-incomeandtotalrevenue-
incomeslopesθstovertimeforOhioVerticallinesindicatethereformeventsThe
figureshowsacleareffectofthe1997decisionwithgradualdeclinesineach
gradientbetween1997and2002followingaperiodofstabilitybefore1997There
islessvisualevidenceofaneffectofthe2000eventswhichdonotseemtohave
interruptedtheprevioustrendwhilethe2002rulingseemstocoincidewithanend
tothedeclineinthegradientIndeedtherewassomebackslidingin2002-2005
thoughinbroadtermsthegradientswerestablefrom2002to2011Thereislittle
signthatchangesinstateaidareoffsetthroughchangesinlocaleffortasthetwo
setsofgradientsmoveinparallelthroughouttheperiodFigure5bpresentssimilar
timeseriesevidenceforthedifferencesinmeanstateaidortotalrevenuebetween
districtsinthebottomandtopquintilesoftheOhiodistrictmeanincome
distributionThismirrorstheslopetrendswiththeexpectedverticalflip
D Eventstudymethodology
Tomodeltherelationshipbetweenschoolfinancereformeventsand
measuresofschoolfinanceprogressivityweadoptaneventstudyframeworkOur
strategyisbasedontheideathatstateswithouteventsinaparticularyearforma
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
17
usefulcounterfactualforstatesthatdohaveeventsinthatyearafteraccountingfor
fixeddifferencesbetweenthestatesandforcommontimeeffects
Weestimateparametricandnon-parametricmodelsThenon-parametric
modelspecifiestheoutcomeforstatesinyeartas
(2) = + + 1 = lowast + +
HerenindexesthepotentiallyseveraleventsinastateWediscussthisbelowfor
nowconsiderthecasewhereeachstatehasonlyasingleeventβrrepresentsthe
effectofaneventinyeartsnonoutcomesryearslater(orpreviouslyforrlt0)
Theseeffectsaremeasuredrelativetoyearr=0whichisexcludedWecensorrat
kmin=-5soβ-5representsaverageoutcomesfiveormoreyearspriortoanevent
relativetothoseintheeventyearκtisacalendaryeareffectthatisconstantacross
stateswhileδsnrepresentsafixedeffectfor(eachcopyof)eachstatersquosdata19
Theeventstudyframeworkyieldsestimatesofthecausaleffectsofeventsif
eventtimingisrandomconditionalonstateandyeareffectsThisneednotbetrue
Theinterplaybetweencourtsandlegislaturesmayproducechangesinfinanceor
outcomesintheyearsimmediatelypriortoouridentifiedeventsndashforexample
whenacourtrespondstoaninadequatereformeffortfromthelegislatureasin
Ohioin2000and2002Ourinclusionofβ-khellipβ-1termscapturingpre-event
dynamicsisdesignedtocapturethisNon-zerocoefficientswouldsuggestthatwe
areunabletodistinguishthecausaleffectsofeventsfromthepriordynamicsthat
ledtothemInnoneofthespecificationsthatweexaminedowefindthatthepre-19Whenθsntisthestateortotalrevenue-incomeslope(2)isweightedbytheinverseestimatedsamplingvarianceofθsntWhenthedependentvariableisaquintilemeanorgapinspending(2)isweightedParalleleventstudymodelsfortestscoresareweightedbyNAEPweightsIneachcasestandarderrorsareclusteredatthestatelevel
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
18
eventeffectsaremeaningfullyorsignificantlydifferentfromzeroThissupportsour
relianceonaneventstudyframework
Inspecification(2)theeffectoftheeventisallowedtobeentirelydifferent
ineachsubsequentandprioryearWepresentestimatesfromthisnonparametric
specificationbutwefocusourattentiononamoreparametricspecificationthat
replacestherelativetimeeffectsin(2)withthreeparametricterms
(3) = + + minus lowast $ + 1 gt lowast $ +
minus lowast 1 gt lowast $ +
Hereβjumpcapturesadiscretechangeintheoutcomefollowingtheeventwhile
βphaseincapturesagraduallygrowingeventeffectthatproducesakinkinthelinear
trendonthedateoftheeventβtrendrepresentsalineartrendthatpredatesthe
eventandcontinuesafterwardandisinterpretedasapotentialconfound
analogoustothepre-eventeffectsin(2)ratherthanastheeffectoftheeventitself
AsbeforethiscoefficientisneverpracticallysignificantComparisonsofthe
parametricandnon-parametricestimatesindicatethatthethree-coefficient
structuredoesagoodjobofcapturingdynamicsinoutcomessurroundingevents
thoughthechangecapturedbythepost-eventldquojumprdquocoefficientissometimes
delayedayearorspreadoutovertwotothreeyearsfollowingtheevent
Acomplicationwefaceinimplementingtheeventstudyframeworkisthat
statesmayhavemultipleeventsInourpreferredestimateswetreateachofseveral
eventsinastateseparately20Specificallysupposethatstateshaseventnumbern
20ResultsarequalitativelyunchangedwhenweuseonlythefirsteventinastatewhenwereweightsothatstateswithmultipleeventsarenotoverrepresentedorwhenweuseonepanelperstatewitharunningcountofeventstodateasthekeyvariableSeeAppendixTableA3
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
19
(outofNstotalevents)inyeartsnWecreateNscopiesofthestate-spanellabeling
themn=1hellipNsandwecodecopynashavingasingleeventintsn(Forstates
withouteventswemakeasinglecopyandsetallrelativetimevariablestozero)
Thisyieldsapaneldatasetcharacterizedbythreedimensionsndashstatetimeand
eventnumberwherethefirsttwodimensionsarebalancedbutthenumberof
eventsvariesacrossstatesWeusethispaneldatasettoestimateequations(2)and
(3)withstate-eventandyearfixedeffects
Ourdecisiontotreateachofseveraleventsinastateseparatelyaffectsthe
interpretationofthepost-eventcoefficientsThecoefficientβrrgt0estimatesthe
reduced-formeffectofaneventinyeartsnontheoutcomemeasureintsn+rnot
holdingconstantsubsequentevents21Insomecasesittakesmanyevents(eg
courtrulings)beforethefinancereformisactuallyimplementedThusgradual
increasesinβrmaynotindicatethatstatesareslowtoimplementnewfinance
formulasbutratherthatthetruefinanceformulachangedidnotoccurforseveral
yearsafteroneofourfocaleventsAsweshowbelowthisisnotveryimportant
empiricallyndasheffectsonfinanceoutcomesappearalmostimmediatelyfollowingour
designatedeventsandpersistwithoutgrowingthereafter
Wealsouseequations(2)and(3)toinvestigatestudentoutcomesreplacing
thedependentvariablewithtestscore-incomeslopesorbetween-quintilegapsin
meanscoresandreplacingtheyeareffectsκtwithsubject-grade-yeareffectsWe
expectadifferenttimepatternofeffectshereBecausestudentoutcomesare
cumulativeandasuddeninfusionofresourcesin8thgradeisnotlikelytohaveas
21SeeCelliniFerreiraandRothstein(2010)oneventstudieswithrepeatedevents
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
20
largeaneffectaswouldaflowofresourceseveryyearfromKindergartenonward
weexpecttheprimaryeffectofreformsonstudentoutcomestooccurthroughthe
βphaseincoefficientoralternatelythroughgradualgrowthintheβrs
III Data
OuranalysisdrawsondatafromseveralsourcesWebeginwithourdatabaseof
schoolfinancereformeventsdiscussedaboveWemergethistodistrict-levelschool
financedatafromtheNationalCenterforEducationStatisticsrsquo(NCES)Common
CoreofData(CCD)schooldistrictfinancefiles(alsoknownastheldquoF-33rdquosurvey)
andtheCensusofGovernmentsdemographicsfromtheCCDschooluniversefiles
householdincomedistributionsfromthe1990Censusandstudentachievement
outcomesinreadingandmathin4thand8thgradefromtheNAEP
TheCCDdistrictfinancedatacollectedbytheCensusBureauonbehalfof
NCESreportenrollmentrevenuesandexpendituresannuallyforeachlocal
educationagency(LEA)Censusdataareavailableannuallysinceschoolyear1994-
95aswellasin1989-90and1991-92Wesupplementthiswithsampledatafrom
theCensusBureaursquosAnnualSurveyofGovernmentFinancesfor1992-93and1993-
94Weconvertalldollarfiguresto2013dollarsperpupil22WeusetheCCDannual
censusofschoolsfrom1986-87through2012-13aggregatedtothedistrictlevel
forschoolracialcompositionfreelunchshareandpupil-teacherratios
22Weexcludedistrictswithhighlyvolatileenrollment(year-over-yearchangesof15ormoreinanyyearorwithenrollmentmorethan10offofalog-lineartrendlineinoverone-thirdofyears)andthosewithrevenueperpupilbelow20orabove500ofthe(unweighted)state-yearmean
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
21
Wedrawdistrict-levelmeanhouseholdincomefromthe1990CensusSchool
DistrictDataBookWedropdistrictsbelowthe2ndorabovethe98thpercentileof
theirstatersquos(unweighted)distribution
Finallyourstudentoutcomemeasurescomefromtherestricted-useNAEP
microdataWelimitattentiontotheldquoStateNAEPrdquowhichisdesignedtoproduce
representativesamplesforeachparticipatingstateThisbeganin1990with8th
grademathand42statesparticipatingandhasbeenadministeredroughlyevery
twoyearssince(withsubjectsandgradesstaggeredintheearlyyears)Since2003
therehavebeen4thand8thgradeassessmentsinbothmathandreadinginevery
odd-numberedyearwithallstatesparticipating23Table1showsthescheduleof
assessmentsthenumberofparticipatingstatesandthenumberofstudents
assessedWegenerallyhaveover100000studentspersubject-grade-yearwitha
representativesampleofabout2500studentsin100schoolsperstate
TheNAEPusesaconsistentscoringscaleacrossyearsforeachsubjectand
gradeWestandardizescorestohavemeanzeroandstandarddeviationoneinthe
firstyearthatthetestwasgivenforthegradeandsubjectbutallowboththemean
andvariancetoevolveafterwardWethenaggregatetothedistrict-year-grade-
subjectlevelandmergetotheCCDandSDDB24Weestimateseparatequintilemean
scoresandscore-incomeslopesforeachstate-year-subject-gradeinoursampleOur
eventstudysamplethusconsistsofstate-subject-grade-eventnumber-yearcells
23TheNAEPalsotests12thgradersbuthighschooldropoutmakesthesamplesnonrepresentative
Weuseonlymathandreadingassessmentswhichareadministeredmostfrequently24Thepre-2000NAEPdatadonotusethesamedistrictcodesastheCCDWecrosswalkusingalink
fileproducedforNCESbyWestat(andobtainedfromtheEducationalTestingService)usingdistrict
namestocheckandsupplementthecrosswalk
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
22
Table2apresentsdistrict-levelsummarystatisticspoolingdatafrom1990-
2011Table2bpresentssummarystatisticsforthestate-yearpanel
IV ResultsSchoolFinance
Webeginbyinvestigatingtheeffectsoffinancereformeventsontransfers
fromstatestoschooldistrictsThesolidlineinFigure6presentsestimatesofthe
non-parametriceventstudyspecification(2)takingtheincomegradientofstate
revenuesperpupilasthedependentvariableThisgradientisroughlystableinthe
yearsleadinguptoafinancereformeventbutdeclinesbyroughly$500(scaledas
2013dollarsperpupilperone-unitchangeinlogmeanincome)inthethreeyears
followingtheeventThegradientcontinuestodeclinethereafterreachinga
minimumtotaleffectof-$937inthe11thyearaftertheeventbeforerebounding
somewhatbutisroughlystablefromaboutyearsevenonwardDottedlinesinthe
graphshowpointwise95confidenceintervalsThesearewidebutexcludezeroin
years2-15Atestofthejointsignificantofallthepost-eventeffectshasap-value
lessthan0001whilethetestthatallpre-eventeffectsequalzerohasp=022
Figure6alsoshowstheparametricspecification(3)asadashedlineNot
surprisinglygiventhenonparametricresultsthisshowsasmallandstatistically
insignificantpre-eventtrendasharpdownwardjumpfollowingtheeventanda
slowcontinueddeclineinthestaterevenuegradientinsubsequentyearsThis
three-parametermodelfitsthenon-parametricpatternquitewell
Columns1-3ofTable3presentestimatesfromvariousversionsofthe
parametricspecification(3)Incolumn1weincludeonlystateandyeareffectsand
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
23
thepost-eventindicator(ieweconstrainβtrend=βphasein=0)Column2addsthe
phase-ineffectwhilecolumn3alsoaddsthetrendterm(Thisthirdspecificationis
showninFigure6)Thetablealsoreportstestsofthejointhypothesisthatβjump=
βphasein=0Thesehavep-valuesof003incolumns2and3Incolumn3boththe
trendandphase-ineffectsaresmallandneitherapproachesstatisticalsignificance
Onlythepost-eventeffectisstatisticallysignificantoreconomicallymeaningfulWe
thusfocusonthesimplerspecificationinColumn1Herethepost-eventjump
coefficientindicatesthatreformeventsleadtoanimmediatedeclineinthegradient
ofstateaidperpupilwithrespecttologdistrictincomeofabout$500perpupilor
about5ofmeantotalrevenuesperpupilinoursample
Figure7showseventstudyanalysesformeanstaterevenuesinthefirstand
fifthquintilesofthedistrictmeanincomedistributioninthestate(panelsAandB)
andforthedifferencebetweenthese(PanelC)Inthefirstquintiledistrictsstate
revenuesincreasesharplyaftereventsfifthquintiledistrictsseesmallerbutstill
substantialincreasesTheformereffectsgrowovertimewhilethelattererodeAsa
resulttheeffectonthebetween-quintilegapissmallatfirstbutgrowsovertime
Closerinspectionindicatesthatrevenuesaretrendingupinfirstquintiledistricts
beforetheeventsandthatthereislittlechangeinthetrendfollowinganevent
EstimatesfromtheparametricmodelinTable4AconfirmthisNoneofthe
trendorpost-eventtrendchangecoefficientsaresignificantineitherquintilesowe
focusonthemodelswithoutthesetermsinColumns13and5Theyimplythat
staterevenuesriseby$1023perpupilinfirstquintiledistrictsafteraneventThe
increaseinfifthquintiledistrictsissmaller$510(notsignificantlydifferentfrom
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
24
zero)thedifferentialeffectonfirstquintiledistrictsisthus$518Thegapinmean
logincomesbetweenthefirstandfifthquintiledistrictsisonlyabout06sothisisa
largerincreaseinprogressivitythanisimpliedbytheslopecoefficientsinTable3
Manyofourreformeventsdonotndashbecauseofsubsequentjudicialreversals
orlegislativefoot-draggingndasheverleadtoimplementedchangesinschoolfinance
Wethusviewourestimatesasintention-to-treat(ITT)effectsrepresentingan
averageoftheeffectsofimplementedfinancereformswithnulleffectsofevents
thatdidnotleadtochangesinfundingformulasTheeffectsofimplementedfinance
reformsarealmostcertainlylargerthanthosethatweestimate
Districtsmayrespondtochangesinstatetransfersbychangingtheirlocal
taxratesandchangesinthestateaidformulamayinducepropertyvaluechanges
thataffectlocalrevenuesevenwithfixedrates(Hoxby2001)Wethusturnnextto
modelsfortotalrevenuesperpupilinclusiveofstateandlocalcomponentsModels
forthedistrictincomeslopesarepresentedinFigure8andinColumns4-6ofTable
3Thefigureshowsthateventsareassociatedwithadiscretedownwardjumpin
thetotalrevenuegradientThoughnoindividualcoefficientisstatistically
significantinthenon-parametricmodelwedecisivelyrejectthehypothesisthatall
post-eventeffectsarezero(plt0001)Theparametricmodelshowsafallinthe
gradientofabout$320perpupilfollowinganeventaboutone-thirdsmallerthanin
thestaterevenuemodelsbutthisisstatisticallyinsignificant(Table3)
Figure9panelsA-CandTable4Brepeatthequintilemeananalysesfortotal
revenuesThesearemuchmoreprecisethanthesloperesultsWefindstatistically
significantincreasesof$500perpupilinrelativetotalrevenuesinfirstquintile
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
25
districtswithpointestimatesslightlylargerthanforstaterevenuesThisisabout
twiceaslargeisimpliedbythe(insignificant)totalrevenue-incomesloperesults
AsdiscussedinSectionIacentralconcernintheschoolfinancereform
literatureiswhetherreformsleadtovoterrevoltsandultimatelytoreductionsin
totaleducationalspendingToassessthisweexamineaveragestaterevenueand
totalrevenueperpupilacrossalldistrictsinthestateinFigures7Dand9Dand
Table5Averagestaterevenuesperpupilrisebyabout$760followinganevent
withnosignofmeaningfulpre-eventtrendsorphase-ineffectsTheincreaseintotal
revenuesissmalleraround$550butequallysharpandalsohighlysignificant
Takentogetheroureventstudymodelsindicatelargeincreasesinthe
progressivityofstateandtotalrevenuesfollowingfinancereformeventsdrivenby
increasesinlow-incomedistrictsandwithnosignofdeclinesinhigh-income
districtsorinoverallmeansTheincomegradientandquintilemeananalysesare
broadlysimilarthoughthelattersuggestlargerincreasesinprogressivityAverage
totalrevenuesperpupilinfirstquintiledistrictsarearound$11500sothe
approximately$1000averageabsoluteincreasethattheyseefollowinganevent
representsabitunder10oftheirtotalrevenuestherelativeincreasecompared
tohigherincomedistrictsisabouthalfaslarge
Ourestimatedrevenueimpactsarenotablylargerthaninthecomparable
specificationsinCardandPaynersquos(2002)studyoffinancereformsinthe1980s
perhapsreflectingextraldquobiterdquoofadequacyreforms25CardandPaynealsoestimate
25CorcoranandEvans(2015)findthatadequacyreformshavelargereffectsonspendinglevelsthanequityreformsbutsmallereffectsonbetween-districtinequalityTheirinequalitymeasureshoweverdonottakeaccountofdistrictincomeorothermeasuresoflocalresourcesmoreovertheir
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
26
theimpactofstateaidontotalrevenuesusingfinancereformsasinstrumentsfor
theformerandfindthatabout$050ofeachdollarofstateaidldquosticksrdquoWhileour
slopeestimatesareroughlyconsistentwiththisourquintileanalysesimplythata
muchlargershareofthestateaidincreasepersistsintotalrevenuesperhapsin
partbecauseatleastsomeadequacyreformshaveinvolvedstateorjudicial
oversightoflocaltaxratesinadditiontochangesinthedistributionofstateaid
V ResultsStudentOutcomes
Theaboveresultsestablishthatreformeventsareassociatedwithsharp
immediateincreasesintheprogressivityofschoolfinancewithabsoluteand
relativeincreasesinrevenuesinlow-incomeschooldistrictsIfadditionalfundingis
productivewemightexpecttoseeimpactsonstudentoutcomes
Figure10presentsparametricandnon-parametriceventstudyestimatesof
theeffectofreformsonthegradientofmeanstudenttestscoreswithrespecttolog
meanincomeintheschooldistrictThepatternisnotablydifferentthaninthe
financeanalysesThereisnosignofanimmediateeffectherebutthereisaclear
changeinthetrendfollowingreformeventsThenonparametricestimatesindicate
asmoothnearlylineardeclineinthetestscoregradientfollowinganevent
indicatinggradualincreasesinrelativescoresinlow-incomedistrictsThisisexactly
thepatternonewouldexpectastestscoresarecumulativeoutcomesthat
presumablyreflectnotonlycurrentinputsbutalsoinputsinearliergrades
sampleendsin2002InasimilarsampleSims(2011)findsthatadequacyreformsleadtohigherrelativerevenuesindistrictswithgreaterstudentneed
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
27
ThepatterndeviatesfromexpectationsinonerespecthoweverThereisno
indicationthatthephase-inoftheeffectslowsfiveornineyearsaftertheevent
whenthe4thand8thgradersrespectivelywillhaveattendedschoolsolelyinthe
post-eventperiodOurestimatesoftheout-yeareffectsareimprecisehoweverso
wecannotruleoutthissortofslowing26
EstimatesoftheparametricmodelarepresentedinTable6Asdiscussedin
SectionIIDwetreateachstate-subject-grade-eventcombinationasaseparate
panel(butclusterstandarderrorsatthestatelevel)Columns1-3includestate-
eventandsubject-grade-yeareffectswhilecolumns4-6includestate-subject-grade-
eventandyeareffectsThischoicehaslittleimportfortheresultsThereisno
evidenceofapre-reformtrendorajumpfollowingeventsinanyspecificationso
wefocusonthemodelswithjustaphase-ineffectinColumns1and4These
indicatethatthetestscore-incomegradientfallsbyabout0009peryearaftera
reformeventforatotaldeclineovertenyearsof009
Figure11andTable7repeatthetestscoreanalysisthistimeusingthegap
inscoresbetweenfirstandfifthquintiledistrictsResultsarequitesimilarThereis
noimmediateeffectbutrelativemeanscoresinfirstquintiledistrictsbegintorise
linearlyfollowingtheeventaccumulatingto007standarddeviationsoverten
yearsEffectsaredrivenbyincreasesinlow-incomedistrictswithessentiallyno
changeinmeanscoresinhigh-incomedistrictsRecallthatthebetween-quintilegap
26Weobserveoutcomesryearsaftertheeventonlyforeventsin2011-randearlierTheresultingimbalanceispartlyoffsetbytheincreasingfrequencyofNAEPassessmentsovertime(Table1)FigureA1intheAppendixshowsthedistributionofrelativeeventtimeinouranalyticalsampleSamplesarequitelargeforeffectsuptotenyearsoutbutstarttodropoffthereafter
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
28
inlogmeanincomesisabout06sothe0007coefficientinTable7isquite
consistentwiththe0009coefficientinthetestscoreslopemodelinTable6
Thedivergenttimepatternsofimpactsonresourcesandonstudent
outcomescombinedwiththecumulativenatureofthelatterpreventsasimple
instrumentalvariablesinterpretationofthereduced-formcoefficientsintermsof
theachievementeffectperdollarspentndashitisnotclearwhichyearsrsquorevenuesare
relevanttotheaccumulatedachievementofstudentstestedryearsafteraneventIn
SectionVIIIwepresentestimatesthatdividetheimpactonstudentachievementten
yearsfollowinganeventbytheimpactontotaldiscountedrevenuesoverthoseten
yearsTheten-yeareffectcanbeinterpretedastheimpactofachangeinschool
resourcesforeveryyearofastudentrsquoscareer(through8thgrade)aninterpretation
thatisfacilitatedbytheapparentlackofdynamicsintherevenueeffects
Neverthelessthefocusonther=10estimateisarbitraryWewouldobtainlarger
estimatesoftheachievementeffectperdollarifweusedestimatesformorethan
tenyearsafterevents(perhapsreflectingthetimeittakestoimplementsuccessful
newprogramsafterfundingincreases)orsmallereffectswithashorterwindow
Table8presentsestimatesofthekeycoefficientsfromseparatemodelsby
gradeandsubjectusingthesamespecificationsasColumn1inTable6andColumn
5ofTable7Effectsaresomewhatlargerformaththanforreadingscoresandfor4th
thanfor8thgradescoresbutneitherofthesedifferencesisstatisticallysignificant27
27Inseparatenon-parametricmodelsforscoresbygradeakintoFigure10wefindnoindicationthattheeffecton4thgradescoresstopsgrowingfiveyearsaftertheeventndashboth4thand8thgradeeffectsappeartogrowroughlylinearlythroughtheendofourpanelsSeeAppendixFigureA3
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
29
VI Mechanisms
Ourresultsthusfarshowthatschoolfinancereformsleadtosubstantial
increasesinrelativerevenuesinlow-incomeschooldistrictsachievedthrough
absoluteincreasesinbothhigh-andlow-incomedistrictsthatarelargerinthelatter
thantheformerOvertimetheyalsoleadtoincreasesintherelativeandabsolute
achievementofstudentsinlow-incomedistrictsInanefforttounderstandthe
mechanismsthroughwhichincreasedrevenuesaretranslatedintoimproved
studentoutcomesweanalyzeintermediatefactorssuchaspupil-teacherratios
teacherandstudentcharacteristicsandsubcategoriesofspending
Firstweinvestigatestudentcharacteristicstodeterminewhetherchangesto
enrollmentorthecompositionofthestudentbodyarelikelytocontributeto
improvementsintestscoresWeestimatethesametypeofevent-studyanalysis
showninTables3-4butfocusingondistrictdemographiccompositionResultsare
showninTable9Wefindnoevidenceofeffectsoffinancereformeventsonthe
shareofstudentswhoareminorityorlow-incomeeitherwhenexamininggradients
withrespecttodistrictincome(firstpanel)orfirst-fifthquintilegaps(second
panel)Thissuggeststhatcompositionalchangesinthestudentbodyarenotlikely
tobethemechanismfortheriseinachievement28
OtherrowsofTable9showproxiesforclassroomqualityTheaveragepupil-
teacherratioandteachersalaryTherearenosignificanteffectsoneitherPoint
estimatesindicatereductionsintherelativenumberofpupilsperteacherinlow-
incomedistrictsbutthesearequiteimpreciselyestimated28Wealsofindnorelationshipbetweeneventsandthechangeindistrictincomebetween1990and2011SeeAppendixTableA3
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
30
Table10showsparallelresultsforcomponentsofspendingTotal
expendituresperpupilbecomediscretelymoreprogressiveafteraschoolfinance
reformeventthoughaswithtotalrevenuesthisisstatisticallysignificantonlyinthe
quintileanalysisWhenwedividespendingintoinstructionalandnon-instructional
componentsonlythenon-instructionaleffectisrobustlysignificantandappearsto
accountforabouttwo-thirdsofthetotalWithinthiscategorythereisevidenceof
impactsoncapitaloutlaysandlessrobustlyonstudentsupportservices29Neither
oftheseisobviousasthemostefficientroutetoincreasedlearningbutneitherisit
implausiblethateithercouldbeproductive(seeegCellinietal2010Martorell
StangeandMcFarlin2015andNeilsonandZimmerman2014)
Ourresearchdesignispoorlysuitedtoidentifyingtheoptimalallocationof
schoolresourcesacrossexpenditurecategoriesortotestingwhetheractual
allocationsareclosetooptimalItispossiblethattheachievementeffectswould
havebeenmuchlargerhaddistrictsspenttheirextrarevenuesinsomeotherway
Themostthatwecansayisthattheaveragefinancereformndashwhichweinterpretto
involveroughlyunconstrainedincreasesinresourcesthoughinsomecasesthe
additionalfundswereearmarkedforparticularprogramsortiedtootherreformsndash
ledtoaproductivethoughperhapsnotmaximallyproductiveuseofthefunds30
29Manyofthecourtcasesinoureventdatabasespecificallyconcerninadequacyofschoolfacilitiesinpoorschooldistrictssoitisnotsurprisingthatplaintiffvictoriesleadtocapitalspendingincreases30Strongerschoolaccountabilitymayprovideincentivestoschoolstoallocatetheirresourcesmoreefficiently(Hanushek2006)Weinvestigatedspecificationsthatallowedforinteractionsbetweenfinancereformeventsandthestatersquosaccountabilitypolicybutfoundnoevidenceforthis
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
31
VII EffectsonAchievementGaps
Thefinalquestionthatweinvestigateiswhetherfinancereformsclosed
overalltestscoregapsbetweenhigh-andlow-achievingminorityandwhiteorlow-
incomeandnon-low-incomestudentsinastateTheseareperhapsbettermeasures
thanourslopesandquintilegapsoftheoveralleffectivenessofastatersquoseducational
systematdeliveringequitableadequateservicestodisadvantagedstudents
(KruegerandWhitmore2002CardandKrueger1992b)Howeverbecauseonlya
smallportionofincomeorotherinequalityisbetweendistrictschangesinthe
distributionofresourcesacrossdistrictsmaynotbewellenoughtargetedto
meaningfullyclosethesegaps
Table11presentsestimatesofeffectsonmeantestscoresacrossdifferent
subgroupsofinterestThefirstpanelshowssmallandinsignificanteffectsonmean
(pooled)testscoresandonthe25thand75thpercentilesofthestatedistributions
Theabsenceofameanscoreeffectissomewhatofapuzzlegiventheincreasesin
meanrevenuesdocumentedearlierItmustbenotedhoweverthatourresearch
designismorecrediblefordisparitiesinoutcomesthanforthelevelofoutcomesas
thelatterwouldbeconfoundedbyunobservedshockstoaverageoutcomesina
statethatarecorrelatedwiththetimingofschoolfinancereforms(Hanushek
RivkinandTaylor(1996)
Thesecondandthirdpanelspresentresultsbyraceandfreelunchstatus
respectivelyThereisnodiscernibleeffectonmeanscoresforanygrouporon
achievementgapsbyraceorlunchstatusPointestimatesareroughlyafullorderof
magnitudesmallerthantheearlierestimatesforfirst-quintiledistrictmeanscores
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
32
AppendixTablesA5andA6resolvethediscrepancyWhilenon-whiteand
freelunchstudentsaremorelikelythantheirwhiteandnon-free-lunchpeersto
attendschoolinlow-incomeschooldistrictsthedifferencesarenotverylarge
Roughlyone-quarterofnon-whitestudentsand30offreelunchstudentslivein
firstquintiledistrictswhilethesharesinfifthquintiledistrictsareabouthalfas
largeThissuggeststhatfinancereformsmaynothavemucheffectontherelative
resourcestowhichthetypicalminorityorlow-incomestudentisexposed
Toassessthismorecarefullyweassignedeachstudentthemeanrevenues
forthedistrictthathesheattendsandestimatedeventstudymodelsfortheblack-
whiteorfreelunchnofreelunchgapintheseimputedrevenuesResultsreported
inAppendixTableA6indicatethatfinanceeventsraiserelativeper-pupilrevenues
intheaverageblackstudentrsquosschooldistrictbyonly$220(SE166)andinthe
averagefreelunchstudentrsquosdistrictbyonly$79(SE166)Evenifthisfundingwas
moreproductivethantheaverageeffectimpliedbyourpooledanalysisitwould
stillnotbeenoughtoyielddetectableeffectsonblackorfreelunchstudentsrsquo
averagetestscoresThuswhilereformsaimedatlow-incomedistrictsappearto
havebeensuccessfulatraisingresourcesandoutcomesinthesedistrictswe
concludethatwithin-districtchangeswouldbenecessarytohaveameaningful
impactontheaveragelow-incomeorminoritystudent
VIII Conclusion
Afterschooldesegregationschoolfinancereformisperhapsthemost
importanteducationpolicychangeintheUnitedStatesinthelasthalfcenturyBut
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
33
whiletheeffectsofthefirst-andsecond-wavereformsonschoolfinancehavebeen
wellstudiedthereislittleevidenceaboutthefinanceeffectsofthird-wave
ldquoadequacyrdquoreformsorabouttheeffectsofanyofthesereformsonstudent
achievementOurstudypresentsnewevidenceoneachofthesequestions
Wefindthatstate-levelschoolfinancereformsenactedduringtheadequacy
eramarkedlyincreasedtheprogressivityofschoolspendingTheydidnot
accomplishthisbylevelingdownschoolfundingbutratherbyincreasing
spendingacrosstheboardwithlargerincreasesinlow-incomedistrictsAlthough
wecannotruleoutthepossibilitythataportionofthisfundingwasoffsetthrough
localdecisionsmuchorallofitldquostuckrdquoleadingtoappreciableincreasesinspending
inlow-incomeschooldistrictsUsingnationallyrepresentativedataonstudent
achievementwefindthatthisspendingwasproductiveReformsalsoledto
increasesintheabsoluteandrelativeachievementofstudentsinlow-income
districtsOurestimatesthuscomplementthoseofJacksonetal(forthcoming)who
examinethelong-runimpactsofearlierschoolfinancereformsandfindsubstantial
positiveimpactsonavarietyoflong-runoutcomes
Toputourresultsintocontextconsidertheimpliedeffectofanaverage-
sizedreformonadistrictwithlogaverageincomeonepointbelowthestatemean
relativetoadistrictatthemeanAccordingtoourestimatesthereformraised
relativestaterevenueperpupilintheformerdistrictby$500immediatelyaneffect
thatpersistedformanyyearsRelativetotalrevenuesrosebyabout$320again
immediatelyandpersistentlyOverthefollowingyearsrelativetestscoresroseas
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
34
wellcumulatingtoa009standarddeviationimpactinthetenthyearafterthe
reformeventthatifanythingcontinuedtogrowthereafter
Thecost-effectivenessofthesereformscanbeassessedbycomparingthe
financeeffectstotheachievementeffectsTodosoweassumethatfinanceeffects
areuniformovertime$320perpupilinspendingeachyearofastudentrsquoscareer
discountedtothestudentrsquoskindergartenyearusinga3ratecorrespondstoa
presentdiscountedcostof$3505Chettyetal(2011)estimatethata01standard
deviationincreaseinkindergartentestscorestranslatesintoincreasedearningsin
adulthoodwithpresentvalueof$5350perpupilOurten-yearreformeffect
estimatesthusimplythattheadditionalspendingyieldsincreasedearningsof
$4815perpupilimplyingabenefit-to-costratioofnearly14
ThisratioisnotwhollyrobustOurquintileanalysisshowslargerrevenue
effectsimplyingabenefit-costratiobelowoneNotehoweverthatthese
comparisonscountonly4thand8thgradetestscoreincreasesasbenefitswhile
countingascostsexpendituresinallgrades(including9-12)Thisbiasesthe
benefit-costratiodownwardAnotherdownwardbiascomesfromouruseof
earningseffectsofkindergartentestscorestovalueincreasesin8thgradetest
scoreswhicharepresumablybetterproxiesforadultearningsJacksonetalrsquos
(forthcoming)analysisoftheeffectsofearlierfinancereformsonstudentsrsquoadult
outcomesimpliesmuchlargerbenefitsperdollarthandoesourcalculationThus
althoughthesesortsofcalculationsarequiteimprecisetheevidenceappearsto
indicatethatthespendingenabledbyfinancereformswascost-effectiveeven
withoutaccountingforbeneficialdistributionaleffects
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
35
Ourresultsthusshowthatmoneycananddoesmatterineducationand
complementsimilarresultsforthelong-runimpactsofschoolfinancereformsfrom
Jacksonetal(forthcoming)Schoolfinancereformsareblunttoolsandsomecritics
(Hanushek2006Hoxby2001)havearguedthattheywillbeoffsetbychangesin
districtorvoterchoicesovertaxratesorthatfundswillbespentsoinefficientlyas
tobewastedOurresultsdonotsupporttheseclaimsCourtsandlegislaturescan
evidentlyforceimprovementsinschoolqualityforstudentsinlow-incomedistricts
ButthereisanimportantcaveattothisconclusionAswediscussinSection
VIItheaveragelow-incomestudentdoesnotliveinaparticularlylow-income
districtsoisnotwelltargetedbyatransferofresourcestothelatterThuswefind
thatfinancereformsreducedachievementgapsbetweenhigh-andlow-income
schooldistrictsbutdidnothavedetectableeffectsonresourceorachievementgaps
betweenhigh-andlow-income(orwhiteandblack)studentsAttackingthesegaps
viaschoolfinancepolicieswouldrequirechangingtheallocationofresourceswithin
schooldistrictssomethingthatwasnotattemptedbythereformsthatwestudy
References
BakerBDampGreenPC(2015)ConceptionsofEquityandAdequacyinSchoolFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
BarrowLampSchanzenbachDW(2012)EducationandthePoorInPJefferson
edTheOxfordHandbookoftheEconomicsofPoverty316-343OxfordOxfordUniversityPress
BurtlessG(1996)DoesMoneyMatterTheEffectofSchoolResourcesonStudent
AchievementandAdultSuccessWashingtonDCBrookingsInstitutionPress
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
36
CardDampKruegerAB(1992a)DoesSchoolQualityMatterReturnstoEducation
andtheCharacteristicsofPublicSchoolsintheUnitedStatesJournalofPoliticalEconomy100(1)1ndash40
CardDampKruegerAB(1992b)Schoolqualityandblack-whiterelativeearningsA
directassessmentQuarterlyJournalofEconomics107(1)151-200
CardDampPayneAA(2002)Schoolfinancereformthedistributionofschool
spendingandthedistributionofstudenttestscoresJournalofPublicEconomics83(1)49-82
CascioEUGordonNampReberS(2013)Localresponsestofederalgrants
evidencefromtheintroductionoftitleIintheSouthAmericanEconomicJournalEconomicPolicy5(3)126-159
CascioEUampReberS(2013)ThePovertyGapinSchoolSpendingFollowingthe
IntroductionofTitleIAmericanEconomicReview103(3)423-427
CelliniSFerreiraFampRothsteinJ(2010)Thevalueofschoolfacility
investmentsEvidencefromadynamicregressiondiscontinuitydesign
QuarterlyJournalofEconomics125(1)215-261
ChaudharyL(2009)Educationinputsstudentperformanceandschoolfinance
reforminMichiganEconomicsofEducationReview28(1)90-98
ChettyRFriedmanJNHilgerNSaezESchanzenbachDWampYaganD(2011)
HowDoesYourKindergartenClassroomAffectYourEarningsEvidence
fromProjectSTARQuarterlyJournalofEconomics126(4)1593-1660
ClarkMA(2003)Educationreformredistributionandstudentachievement
EvidencefromtheKentuckyEducationReformActUnpublishedworking
paperMathematicaPolicyResearchPrincetonNJ
ColemanJSCampbellEQHobsonCJMcPartlandJMoodAMWeinfeldF
DampYorkR(1966)EqualityofeducationalopportunityWashingtonDC1066-5684
CoonsJECluneWHampSugarmanS(1970)PrivateWealthandPublicEducationCambridgeMABelknapPress
CorcoranSPampEvansWN(2015)EquityAdequacyandtheEvolvingStateRole
inEducationFinanceInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndeditionNewYorkNYRoutledge
CorcoranSEvansWNGodwinJMurraySEampSchwabRM(2004)The
changingdistributionofeducationfinance1972ndash1997Socialinequality433-465
CullenJBandLoebS(2004)SchoolfinancereforminMichiganevaluating
ProposalAInJYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquitypp215-50CambridgeMAMITPress
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
37
DownesTandLStiefel(2015)MeasuringequityandadequacyinschoolfinanceInHFLaddampMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
DuncombeWDPNguyen-HoangandJYinger(2008)MeasurementofcostdifferentialsInLaddHFampFiskeEBedsHandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
FischelWA(1989)DidSerranocauseProposition13NationalTaxJournal42(4)465-73
FlanaganAEandMurraySE(2004)ADecadeofReformTheImpactofSchoolReforminKentuckyInJohnYingeredHelpingChildrenLeftBehindStateAidandthePursuitofEducationalEquity165-213CambridgeMAMITPress
GuryanJ(2001)DoesmoneymatterRegression-discontinuityestimatesfromeducationfinancereforminMassachusettsNationalBureauofEconomicResearchWorkingPaperNow8269
HanushekEA(2003)Thefailureofinput-basedschoolingpoliciesTheEconomicJournal113F64-F98
HanushekEA(2006)SchoolresourcesInHanushekEAandFWelchedsHandbookoftheEconomicsofEducationvol2TheNetherlandsNorthHolland
HanushekEAampLindsethAA(2009)SchoolhousesCourthousesandStatehousesSolvingtheFunding-AchievementPuzzleinAmericarsquosPublicSchoolsPrincetonPrincetonUniversityPress
HanushekEARivkinSGampTaylorLL(1996)AggregationandtheestimatedeffectsofschoolresourcesTheReviewofEconomicsandStatistics78(4)611-627
HorowitzH(1966)UnseparatebutunequalTheemergingFourteenthAmendmentissueinpublicschooleducationUCLALawReview131147-1172
HoxbyCM(2001)AllschoolfinanceequalizationsarenotcreatedequalTheQuarterlyJournalofEconomics116(4)1189-1231
HymanJ(2013)DoesMoneyMatterintheLongRunEffectsofSchoolSpendingonEducationalAttainmentUnpublishedmanuscript
JacksonCKJohnsonRCampPersicoC(forthcoming)TheeffectsofschoolspendingoneducationalandeconomicoutcomesEvidencefromschoolfinancereformsForthcomingQuarterlyJournalofEconomics
KirpDL(1968)ThepoortheschoolsandequalprotectionHarvardEducationalReview38635-668
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
38
KoskiWSampHahnelJ(2015)ThepastpresentandfutureofeducationalfinancereformlitigationInHFLaddandMEGoertzedsHandbookofResearchinEducationFinanceandPolicy2ndEditionNewYorkNYRoutledge
KruegerAB(1999)ExperimentalestimatesofeducationproductionfunctionsQuarterlyJournalofEconomics114(2)497-532
KruegerAB(2003)EconomicconsiderationsandclasssizeTheEconomicJournal113F34-F63
KruegerABampWhitmoreDM(2002)Wouldsmallerclasseshelpclosetheblack-whiteachievementgapInJEChubbandTLovelessedsBridgingtheAchievementGapWashingtonDCBrookingsInstitutionPress
LaddHFampFiskeEB(Eds)(2015)HandbookofResearchinEducationFinanceandPolicyNewYorkNYRoutledge
MartorellPStangeKMampMcFarlinI(2015)InvestinginschoolsCapitalspendingfacilityconditionsandstudentachievementNBERWorkingPaper21515September
MurraySEEvansWNampSchwabRM(1998)Education-financereformandthedistributionofeducationresourcesAmericanEconomicReview88(4)789-812
NielsonCampZimmermanS(2014)TheeffectofschoolconstructionontestscoresschoolenrollmentandhomepricesJournalofPublicEconomics120
PapkeL(2005)TheEffectsofSpendingonTestPassRatesEvidencefromMichiganJournalofPublicEconomics89(5)821-839
PapkeL(2008)TheEffectsofChangesinMichigansSchoolFinanceSystemPublicFinanceReview36(4)456-474
ReardonSF(2011)ThewideningacademicachievementgapbetweentherichandthepoorNewevidenceandpossibleexplanationsInGDuncanandRMurane(Eds)Whitheropportunity91-116NewYorkNYRussellSageFoundation
SimsDP(2011)SuingforyoursupperResourceallocationteachercompensationandfinancelawsuitsEconomicsofEducationReview30(5)1034-1044
WiseA(1967)RichSchoolsPoorSchoolsThePromiseofEqualEducationalOpportunityChicagoILUniversityofChicagoPress
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figures
Figure 1 Timing of school finance events
02
46
8E
ven
ts p
er
yea
r
1990 2000 2010Year
Statute amp court
Statute
Court
Notes When multiple events occur in a state in a given year they are combined into a single event for thischart
39
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 2 Geographic distribution of post-1989 school finance events
3
2
͵
23
1
3
3
2
1
ʹ
2
5
3
3
4
3
1
12
2 5
7
2
11
1 No Event
1990-1993
1994-1997
1998-2001
2002-2005
2006-2009
2010-2013
Notes Colors correspond to the date of the first post-1989 school finance event Numbers indicate thenumber of events in that period
40
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 3 State aid vs district income Ohio 1990 and 2011
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
1990
05000
10000
15000
20000
25000
10 1025 105 1075 11 1125
2011
Sta
te a
id p
er
pupil
(2013$)
ln(district avg HH income 1990)
Notes Each point represents one district Circle sizes are proportional to average district enrollment over1990-2011 Solid lines have slope equal to st from equation (1) and correspond to predicted values for aunified district of average log enrollment Dashed lines represent means among districts in each quintile ofthe district mean income distribution
41
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 4 State-level slopes of school finance with respect to ln(district income) 1990 and 2011
AL
AZAR
CA
COCT
DE
FL
GA
ID
IL
IN
IA
KS KYLA
ME
MD
MA
MI
MN
MSMOMT
NENH
NJ
NM
NY
NC
ND
OK
OR
PA
RI
SC
SDTN
TXUT
VT
VA
WA
WVWI
AKNVWY
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(a) State revenue per pupil
ALAZ
AR
CA
CO
CT
DE
FLGAID
IL
IN
IA
KSKY
LA
ME
MDMAMI
MNMS
MO
MT
NE
NV
NH
NJ
NY
NC
NDOKOR
PA
RI
SC
SD
TNTX
UT VT
VA
WA
WV
WIWY
AK
NM
OH
minus1
00
00
minus5
00
00
50
00
10
00
02
01
1 S
lop
e
minus10000 minus5000 0 5000 100001990 Slope
45 degree line Linear fit (unweighted)
(b) Total revenue per pupil
Notes Points indicate st for t = 1990 2011 Slopes are censored below at -10000 for graphical displaybut uncensored values are used in computing the (unweighted) linear fit
42
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 5 Summaries of school finance in Ohio 1990-2011
minus6
00
0minus
40
00
minus2
00
00
20
00
40
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(a) Log income gradients
minus2
00
00
20
00
40
00
60
00
20
13
$ p
er
pu
pil
1990 1995 2000 2005 2010Fiscal year
State aid
Total revenue
(b) Mean dicrarrerence between 1st and 5th quintile of district mean log income
Notes In panel (a) series represent st from equation (1) varying the dependent variable with 95 confi-dence intervals In panel (b) series are the dicrarrerence in the mean of the relevant revenue variable betweendistricts in the first and fifth quintiles of the district mean income distribution Solid vertical lines representplainticrarr victories in the Ohio Supreme Court in De Rolph v state I II and IV in 1997 2000 and 2002 In2000 there was also a statutory reform
43
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 6 Event study estimates of ecrarrects of reform events on state revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
Sta
te A
id S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of state revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column3
44
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 7 Event study estimates of ecrarrects of reform events on mean state revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean state aid per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panel(though the null hypothesis that the jump and the change in trend are jointly zero is not rejected in panelsC and D) Estimates for parametric models are reported in panel a of Table 4
45
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 8 Event study estimates of ecrarrects of reform events on total revenue slope
minus2
00
0minus
10
00
01
00
02
00
0C
ha
ng
e in
To
tal R
eve
nu
e S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of total revenue per pupil with respect to ln(district income) in thestate-year cell Figure shows parametric and non-parametric estimates of the ecrarrect of a finance event onthis slope by years since (or prior to) the event along with 95 confidence intervals for the non-parametricmodel See text for specification The null hypothesis that all post-event coecients in the non-parametricmodel are zero is rejected (plt0001) Estimates for the parametric model are reported in Table 3 Column6
46
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 9 Event study estimates of ecrarrects of reform events on mean total revenues per pupil by districtincome quintile
minus1
01
23
minus5 0 5 10 15 20
(a) Q1
minus1
01
23
minus5 0 5 10 15 20
(b) Q5
minus1
01
23
minus5 0 5 10 15 20
(c) Q1 - Q5
minus1
01
23
minus5 0 5 10 15 20
(d) Overall
Notes Dependent variable is mean total revenues per pupil in the relevant subgroup of districts In PanelsA and B the mean is for districts in the bottom fifth and top fifth respectively of the district meanincome distribution (unweighted) In Panel C the dependent variable is the dicrarrerence between these Alldistricts are included in the mean in panel D See text for event study specifications In the non-parametricspecifications the null hypothesis that all post-event ecrarrects equal zero is rejected in each panel In theparametric specifications the post-event jump coecient is significantly dicrarrerent from zero in each panelEstimates for parametric models are reported in panel b of Table 4
47
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 10 Event study estimates of ecrarrects of reform events on test score slope
minus3
minus2
minus1
01
Ch
an
ge
in T
est
Sco
re S
lop
e
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Figure shows parametric andnon-parametric estimates of the ecrarrect of a finance event on this slope by years since (or prior to) theevent along with 95 confidence intervals for the non-parametric model See text for specification Thenull hypothesis that all post-event coecients in the non-parametric model are zero is rejected (plt0001)Estimates for the parametric model are reported in Table 6 Column 3
48
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure 11 Event study estimates of ecrarrects of Q1-Q5 dicrarrerence in mean scores
minus1
01
23
Ch
an
ge
in M
ea
n T
est
Sco
res
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate Parametric Estimate
Notes Dependent variable is dicrarrerence in mean NAEP test scores (in student-level standard deviationunits) between the first and fifth quintiles with respect to ln(district income) in the state-year cell Figureshows parametric and non-parametric estimates of the ecrarrect of a finance event on this slope by years since(or prior to) the event along with 95 confidence intervals for the non-parametric model See text forspecification The null hypothesis that all post-event coecients in the non-parametric model are zero isrejected (plt0001) Estimates for the parametric model are reported in Table 7 Column 6
49
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Tables
Table 1 NAEP Testing Years
Year Subject(s) Grade(s) Number of States Number of StudentsTested
1990 Math G8 38 979001992 Math Reading G4 G8 42 3211201994 Reading G4 41 1048901996 Math G4 G8 45 2289801998 Reading G4 G8 41 2068102000 Math G4 G8 42 2011102002 Reading G4 G8 51 2702302003 Math Reading G4 G8 51 6913602005 Math Reading G4 G8 51 6744202007 Math Reading G4 G8 51 7113602009 Math Reading G4 G8 51 7750602011 Math Reading G4 G8 51 749250
Notes Number of students tested is rounded to the nearest 10 to satisfy disclosure prevention rules
50
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 2 Summary statistics
(a) District-Year Panel
mean sd N
Total revenue per pupil $10979 (3376) 208207State revenue per pupil $5155 (2234) 208207Local revenue per pupil $4971 (3184) 208207Federal revenue per pupil $853 (625) 208207Log(Mean income) - 1990 1051 (027) 208207Unfied district 093 (025) 208207Elementary district 005 (021) 208207Secondary district 002 (014) 208207Total expenditure per pupil $11149 (3582) 208212Total instructional expenditure per pupil $5804 (1915) 208212Total non-instructional expenditure per pupil $5346 (2151) 208212Enrollment (student weighted) 70973 (188868) 208207Enrollment (unweighted) 4006 (163782) 208207
(b) State-Year Panel
mean sd N
State revenue slope -3164 (3512) 4116Total revenue slope 326 (3666) 4116Test score slope 095 (036) 1498Dist income Q1 mean state revenue $6430 (2856) 4264Dist income Q1 mean total revenue $11462 (3798) 4264Dist income Q5 mean state revenue $4410 (2278) 4256Dist income Q5 mean total revenue $11554 (3358) 4256Dist income Q1-Q5 mean state revenue $2012 (2094) 4256Dist income Q1-Q5 mean total revenue $-103 (2028) 4256Dist income Q1 mean test scores 008 (037) 1573Dist income Q5 mean test scores 048 (041) 1571Dist income Q1-Q5 mean test scores -040 (030) 1568Num events to date 077 (129) 5100
51
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 3 Event study estimates for slopes of state revenue and total revenue with respect to ln(districtincome)
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event -5014 -4415 -3839 -3212 -3274 -2937(1876) (1800) (1538) (2851) (2704) (2281)
Post Event Yrs Elapsed -1797 -4760 2178 1154(1693) (1925) (3623) (4018)
Trend -2400 -1663(2772) (3990)
Observations 1890 1890 1890 1890 1890 1890p total event ecrarrect=0 0010 0032 0034 0266 0486 0438
Notes In columns 1-3 the dependent variable is the slope of state revenue per pupil with respect toln(district income) in the state-year cell In columns 4-6 the dependent variable is the slope of total revenueper pupil with respect to ln(district income) Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable All specifications include state-event and year fixed ecrarrects Seetext for further specification details P-values from the joint hypothesis test that all after-event coecientsequal zero are shown Standard errors are clustered at the state level
52
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 4 Event study estimates for mean state revenue and total revenues per pupil by district incomequintile
(a) State Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 10227 7728 5102 5281 5175 2457
(2799) (2494) (3286) (2559) (2105) (1193)
Post Event Yrs Elapsed -0815 -2548 2373(4653) (2381) (3461)
Trend 5573 1244 4475(3627) (3251) (2804)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0008 0127 0109 0017 0091
(b) Total Revenue
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event 8380 6747 3075 4178 5344 2577
(2368) (2098) (2209) (1931) (1795) (1230)
Post Event Yrs Elapsed -4258 -7276 2316(5869) (3120) (3873)
Trend 3883 -1968 5962
(3971) (2570) (3092)
Observations 1927 1927 1924 1924 1924 1924p total event ecrarrect=0 0001 0005 0170 0099 0004 0119
Notes The dependent variables are mean state revenue and total revenues per pupil in the in therelevant district income quintile All specifications include state-event and year fixed ecrarrects Regressionsare unweighted See text for further specification details P-values from the joint hypothesis test that allafter-event coecients equal zero are shown Standard errors are clustered at the state level
53
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 5 Event study estimates for mean state aid per pupil and mean total revenues per pupil
(1) (2) (3) (4) (5) (6)St Rev St Rev St Rev Tot Rev Tot Rev Tot Rev
Post Event 7623 7601 6911 5446 5624 5686
(2977) (2771) (2401) (2215) (2126) (1894)
Post Event Yrs Elapsed 0749 -1404 -6079 -4732(2899) (3169) (3873) (4226)
Trend 2477 -2256(3133) (2972)
Observations 1927 1927 1927 1927 1927 1927p total event ecrarrect=0 0014 0029 0021 0017 0036 0014
Notes In columns 1-3 the dependent variable is mean state aid per pupil in the state-year cell Incolumns 4-6 the dependent variable is mean total revenues per pupil All specifications include state-eventand year fixed ecrarrects See text for further specification details P-values from the joint hypothesis test thatall after-event coecients equal zero are shown Standard errors are clustered at the state level
54
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 6 Event study estimates for test score slopes
(1) (2) (3) (4) (5) (6)
Post Event Yrs Elapsed -000882 -000863 -000762 -000875 -000864 -000711
(000313) (000324) (000369) (000357) (000367) (000419)
Post Event -000707 -000253 -000410 000255(00187) (00143) (00211) (00168)
Trend -000168 -000253(000365) (000388)
Observations 2743 2743 2743 2743 2743 2743p total event ecrarrect=0 000700 00210 00555 00180 00546 0205State-Event FEs X X XSt-Ev-Gr-Sub FEs X X XYear FEs X X XSub-Gr-Yr FEs X X X
Notes Dependent variable is the slope of district-level mean NAEP test scores (in student-level standarddeviation units) with respect to ln(district income) in the state-year cell Columns 1-3 show estimates withstate-copy fixed ecrarrects and NAEP exam fixed ecrarrects (ie subject-grade-year) Columns 4-6 show estimateswith joint state-copy-grade-subject fixed ecrarrects and separate year ecrarrects Regressions are weighted by theinverse of the estimated sampling variance of the dependent variable See text for further specification detailsP-values from the joint hypothesis test that all after-event coecients equal zero are shown Standard errorsare clustered at the state level
55
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 7 Event studies for mean subgroup scores
(1) (2) (3) (4) (5) (6)Q1 Q1 Q5 Q5 Q1-Q5 Q1-Q5
Post Event Yrs Elapsed 000761 000472 0000708 -000169 000734 000698
(000264) (000375) (000176) (000191) (000256) (000253)
Post Event -000538 -000400 -000485(00151) (00151) (00121)
Trend 000417 000382 0000740(000459) (000228) (000295)
Observations 2832 2832 2828 2828 2819 2819p total event ecrarrect=0 000585 0374 0689 0644 000600 00263
Notes The dependent variables are district-level mean NAEP test scores (in student-level standarddeviation units) in the state-year cell for the relevant district income quintiles State-copy fixed ecrarrects andNAEP exam fixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the sample sizein relevant subcategory See text for further specification details Standard errors are clustered at the statelevel
56
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 8 Event studies for test score slopes by subject and grade
Test Score Slope Q1-Q5 Mean
Pooled -000882 000734
(000313) (000256)
By Subject Math -00106 000803
(000340) (000304)Reading -000653 000577
(000383) (000244)
By Grade4th -00106 000780
(000396) (000286)8th -000724 000728
(000341) (000295)
Notes Each coecient represents a separate regression In column 1 the dependent variables are theslopes of district-level mean NAEP test scores (in student-level standard deviation units) with respect toln(district income) in the state-year cell for the relevant subject andor grade subgroups In column 2 thedependent variables are the dicrarrerence in mean test scores between quintile 1 and quintile 5 districts Pooledestimates correspond to column 1 of table 6 prior trends and post event indicators are not included None ofthe dicrarrerences in the above coecients are statistically significant State-copy fixed ecrarrects and NAEP examfixed ecrarrects (ie subject-grade-year) are included Regressions are weighted by the inverse of the estimatedsampling variance of the dependent variable See text for further specification details Standard errors areclustered at the state level
57
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 9 Mechanisms Teacher and student variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesShare blackhispanic -000175 -000164 00000824 0728
(000197) (000225) (0000487)Share freereduced price lunch -00204 -00287 000442 0480
(00187) (00239) (000486)Mean teacher salary -2352 -2209 -1158 0990
(9210) (7481) (1470)Pupil teacher ratio 0170 0177 -00277 0415
(0137) (0134) (00338)
Q1-Q5 MeansShare blackhispanic -000455 -000352 -0000696 0718
(000878) (000636) (000147)Share freereduced price lunch 000510 000473 -000139 0796
(00105) (00104) (000210)Mean teacher salary 3092 -4602 9769 0588
(6785) (4292) (9888)Pupil teacher ratio -0105 00614 -000120 0832
(0137) (0103) (00182)
Notes In column 1 estimates of the post-event coecient are shown for parametric event study modelswhich include only parameter (only the post event variable) In columns 2 and 3 estimates of the post-eventcoecients are shown for parametric event study models with 3 parameters (includes a post-event variablean event-time trend variable and a post-event time trend) P-values for the joint test of both post eventcoecients in the 3 parameter model are shown in column 4 The columns in table 10 (following page) areanalogously defined
58
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 10 Mechanisms Revenue and expenditure variables
Post Event (1 para) Post Event (3 para) Post Yrs Elapsed (3 para) p (3 para)
SlopesTotal revenue per pupil -3212 -2937 1154 0438
(2851) (2281) (4018)State revenue per pupil -5014 -3839 -4760 00339
(1876) (1538) (1925)Local revenue pp 4434 -3108 -6270 0896
(2099) (1652) (2045)Federal revenue per pupil 3543 2847 2733 00325
(2151) (1641) (5119)Total expenditures per pupil -3744 -3332 1382 0397
(2845) (2527) (4944)Current instructional expenditure per pupil -4973 -2253 -5128 0909
(1383) (1088) (2104)Teacher salaries + benefits per pupil -3652 -2414 -0303 0975
(1410) (1253) (1993)Non-instructional expenditure per pupil -2360 -2827 2053 0264
(1810) (1708) (2865)Student support per pupil -6977 -4908 -6202 0465
(6741) (5417) (7290)Other current expenditures -0862 -7769 1129 0517
(1196) (9320) (1453)Total capital outlays -7837 -9484 3487 0584
(1022) (9224) (1205)
Q1-Q5 MeansTotal revenue per pupil 5344 2577 2316 0119
(1795) (1230) (3873)State revenue per pupil 5175 2457 2373 00910
(2105) (1193) (3461)Local revenue per pupil -4579 2717 -1439 0548
(1755) (1349) (1337)Federal revenue per pupil 6307 9558 -7025 0795
(3192) (2422) (1130)Total expenditures per pupil 5410 2574 5249 0128
(1614) (1273) (3615)Current instructional expenditure per pupil 1636 -0383 1095 0726
(9927) (6669) (1363)Teacher salaries + benefits per pupil 1035 -9957 1158 0673
(8004) (6005) (1303)Non-instructional expenditure per pupil 3774 2578 -5703 00117
(9210) (8352) (2713)Student support per pupil 1147 4381 2681 0522
(6094) (3822) (1008)Other current expenditures -1924 1493 -3021 00666
(6464) (5535) (1268)Total capital outlays 2000 1564 -1237 00501
(7299) (6279) (2310)
Notes See notes to table 9
59
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table 11 Event studies for mean subgroup scores
Post Event Yrs Elapsed
Pooled 000123 (000210)25th percentile 000153 (000257)75th percentile 0000425 (000167)
By RaceWhite 000159 (000180)Black 0000990 (000266)White-black gap -000103 (000205)
By Free Lunch Status No Free Lunch 000123 (000184)Free Lunch 0000604 (000274)No free lunch-free lunch gap -000192 (000177)
Notes White-black gap corresponds to the mean white score minus mean black score in each state-subject-grade-year cell NAEP sample weights are used in the contruction of these state-subject-grade-yearmeans The no free lunch-free lunch gap is analogously defined Regressions of mean score ecrarrects areweighted by the inverse of the subgroup sample size used to compute the subgroup sample mean in eachstate Regressions with test score gaps as the dependent variable are weighted by the square root of the sum
of the inverse subgroup sample sizes (egq
1Na
+ 1Nb
for subgroups a and b) For this reason the estimated
test score gaps do not necessarily correspond to the dicrarrerence between the estimated coecients for eachsubgroup
60
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Appendix
Overview of Appendix Results
Sample construction
Figure A1 and table A1 give additional background on the sample construction in the event study analysisTable A1 details how the event database used varies from those considered in prior studies A more completediscussion of event classification is given in section IIA of the text Figure A1 shows the distribution ofstate-year (in the finance analyses) or state-grade-subject-year (in the NAEP analyses) observations in eventtime Both the finance and NAEP panels are fairly balanced in event time at least up to 10 years after theinitial event
Number of events
During the period we study many states had several court-ordered and legislative school finance reformswhich complicate analysis and interpretation using traditional event study methods To empirically addressthe magnitude of potential biases from overlapping event-time windows within certain states we considerevent study models where the dependent variable is the total number of events to date in each state FigureA2 shows results from this alternative specification Nonparametric point estimates shown in the figureimply that roughly 10 years after the initial event the average state experiences an additional statutory orcourt ordered finance reform event Parametric versions of the same event study model (not reported here)estimate that a school finance reform event is associated 16 total events in the entire post-event periodThis suggests that the preferred event study estimates of finance reforms on realized financial and studentachievement outcomes are underestimates - these reduced form coecients estimate the ecrarrect of havingapproximately 16 reform events in a given state
Heterogeneity by grade
It is plausible that the timing of school-age years of finance reform exposure would acrarrect the timing ofgains in test scores for 4th relative to 8th grade students One might expect that the increased duration ofadditional state funding would eventually lead to larger impacts on 8th grade NAEP performance than in4th grade Figure A3 addresses this point and shows separate event study estimates on the progressivity of4th and 8th grade NAEP scores with respect to log mean district incomes We find no evidence of dicrarrerentialimpacts or timing between 4th and 8th grade students The nonparametric 4th grade test score estimatesare almost all greater (in absolute value) than the 8th grade estimates and this gap appears to slightly growrather than shrink over time
Change in district incomes
One alternative explanation for rising test scores in low income districts is that finance reforms inducedhigher income families to move into low income districts to benefit from increased state funding Table A2investigates whether the finance reform events are associated with changes in district income compositionThe table reports estimates from models where the dicrarrerence in district incomes between 1990 and 2011(2011 income minus 1990 income) is the dependent variable Independent variables are the number of yearssince the event log of 1990 mean district income and their interaction When the interaction term is notincluded there is a slightly positive and marginally significant relationship between time elapsed since the
61
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
event and log district income changes in states that experienced an event When the interaction term isincluded the years since event coecient is still positive while the interaction is negative Neither coecientis significant whether or not non-event states are included in the estimation as controls When all states areincluded in the analysis (column 3) the sign on the coecients is reversed Both coecients are insignificantin columns 2 and 3 where the interaction term is included This provides suggestive evidence that changesin district incomes do not appear to be substantively associated with finance reform events
Robustness alternative specifications
Tables A3 and A4 report event study results from alternative specifications where the event study sampleis handled dicrarrerently or where the slopes and quintile means of district revenues and NAEP scores areestimated with respect to dicrarrerent independent variables The first panel of table A3 shows estimates frommodels where only the first event in a state is used Concerns over the potential endogeneity of subsequentevents motivate this approach however the results are largely consistent with those estimated using thefull sample Similarly it could be the case that the timing of legislative reforms is correlated with economicconditions in a state (this is less likely to be the case with court ordered reforms which are arguably moreexogenous) As shown in panel (b) of table A3 event study models using only court ordered reform eventsare very similar to our baseline results Focusing on both court ordered and legislative reforms as we do inour baseline specifications does not appear to introduce meaningful biases in our estimates
In table A3 we also consider dicrarrerent weighting conventions and regressing the number of events todate on our progressivity measures in lieu of the event study approach Reweighting each state by 1nwhere n is the number of total events in a state during the sample period places equal weight on each statein the estimation In the baseline estimation each state-event panel is weighted equally meaning stateswith multiple events receive greater weight in the estimation Panel (c) of table A3 reports estimates fromreweighted regressions which are again qualitatively comparable to baseline estimates Panel (d) showsestimates from models where the independent variable is the number of events to date which are slightlysmaller but qualitatively similar to the baseline results
Table A4 reports estimates where the slopes and Q1-Q5 mean dicrarrerences are computed using alternativeincome measures Panels (a) and (b) are computed using 2010 mean incomes and 1990 mean housing values(for owner-occupied housing) respectively Baseline estimates are computed using 1990 mean householdincomes The results are not sensitive to this choice although this is expected as these measures areextremely highly correlated within school districts over time Ideally we could use property tax basesinstead of household income or housing values in a district although to our knowledge there is no suchnationally comparable database that exists for this time period The final panel of table A4 uses the shareof individuals below 185 of the federal poverty lines Estimates computed using these shares in lieu ofmean log incomes are qualitatively consistent with our baseline estimates although none are statisticallysignificant
Income race analysis
Tables A5 examines racial composition between districts in dicrarrerent income quintiles Minorities and studentsfrom low socioeconomic backgrounds are not highly concentrated in low income districts which demonstratesthe limited ability of reforms targeted to low income districts to acrarrect achievement gaps between high andlow income (or minority and non-minority) students Table A6 shows parametric event study estimates offinance reforms on black-white and free lunch - no free lunch funding gaps The coecients suggest smallbut positive post event ecrarrects (ie decreasing gaps) although only the coecient on the black-white statefunding gap is significant and only at the 10 level See section VII in the text for further discussion
62
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Appendix Figures
Figure A1 Number of statesstate-events at each ldquoEvent Yearrdquo
020
40
60
o
f S
tate
minusE
vents
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(a) State-year-event sample for finance analysis
020
40
60
80
100
o
f S
tminusG
rminusS
ubminus
Ev
Cells
minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(b) State-year-event-subject-grade sample for test score analysis
Notes X-axis corresponds to ldquoevent-timerdquo used in event study figures States without events (there are24) are not included in this figure Panel A shows the number of state-event observations in the financeanalysis Panel B shows the number of state-subject-grade-event observations in the test score analysis
63
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Figure A2 Event study of number of events to date
minus1
01
23
4C
hange in
num
ber
of eve
nts
so far
minus5 0 5 10 15 20Years Since Event
Notes Dependent variable is the number of events to date Nonparametric point estimates of event studytime coecients are shown with 95 confidence intervals Sample construction and fixed ecrarrects are identicalto baseline specifications
Figure A3 Event study estimates of ecrarrects of reform events on test score slope (G4 and G8 separately)
minus3
minus2
minus1
01
Change in
Test
Sco
re S
lope
minus5 0 5 10 15 20Years Since Event
NonminusParametric Estimate (G4) Parametric Estimate (G4)
NonminusParametric Estimate (G8) Parametric Estimate (G8)
Notes Dependent variables are slopes of 4th and 8th grade test scores wrt log district income Non-parametric and parametric estimates of event study coecients (identical to specifications in figure 10) areshown for models run separately on 4th and 8th grade test scores
64
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Appendix Tables
HanushekampLindseth(through2005)
JacksonJohnsonampPerisco(through2010)
CorcoranampEvans(results
through2006)
MurrayEvansampSchwab(through1996)
CourtOrder Statute CourtOrder CourtOrder CourtOrder CourtOrderAlaska 2007 _ Equity 1999 _ _Arizona 1994
19971998
1994Equity
1994199719982007
_ 1994
Arkansas 199420022005
19952007
2002Equity
199420022005
20022005
1994
California _ 19982004
Equity 2004 _ _
Colorado _ 2000 _ _ _ _Connecticut 1996 _ Equity 1995
2010_ 1995
Idaho 19932005
1994 _ 19982005
_ _
Indiana 2011 _ _ _ _Kansas 2005 1992
20052005
Equity2005 2005 _
Kentucky (1989) 1990 (1989) (1989) (1989) (1989)Maryland 1996 2002 _ 2005 _ _Massachusetts 1993 1993 1993 1993 1993 1993Missouri 1993 1993
2005Equity 1993 _ _
Montana 2005 19932007
2005Equity
199320052008
2005 1993
NewHampshire 199319972002
19992008
1997 19931997199920022006
19971998199920002002
1993
NewJersey 1990199419982000
1990199619972008
2002Equity
199019911994
1990199419971998
199019911994
NewMexico 1999 2001 Equity 1998 _ _NewYork 2003
20062007 2003 2003
20062003 _
TableA1SchoolFinanceEventsLafortuneRothsteinampSchanzenbach(through
2013)
65
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
NorthCarolina 199720042012
2012 2004 19972004
2004 _
NorthDakota _ 2007 _ _ _ _Ohio 1997
20002002
2000 _ 199720002002
1997200020012002
_
Tennessee 199319952002
1992 Equity 199319952002
199319952002
19931995
Texas 19911992
1993 Equity 199119922004
199119922005
19911992
Vermont 1997 2003 1997Equity
1997 1997 _
Washington 2010 2013 _ 19912007
_ _
WestVirginia 19952000
_ 1995 _ 1994
Wyoming 1995 19972001
1995Equity
19952001
1995 1995
Noyeargivenplantiffvictory
Table A2 Dicrarrerence in log mean district income 1990-2011
(1) (2) (3)
Years Since Event (In 2011) 000237 00313 -00121(000120) (00353) (00299)
log(Dist avg HH income) -00863 -00519 -0114
(00263) (00397) (00320)
log(Dist avg HH income) Years Since Event -000277 000130(000328) (000280)
Observations 12527 12527 15576Event States X XAll States X
Notes Coecients are reported for models with the long dicrarrerence in district income (from 1990-2011)as the dependent variable Standard errors are clustered at the state level
66
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table A3 Alternative ways of handling event sample
(a) First event in each state
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -4608 -1949 4270 6101
(2546) (3950) (3086) (2388)
Post Event Yrs Elapsed -000810 000461
(000332) (000269)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0 0077 0624 0019 0173 0014 0093State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) Court events only
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3128 -6552 8707 1302(1244) (2634) (1491) (1641)
Post Event Yrs Elapsed -000885 000789
(000478) (000360)
Observations 3444 3444 1249 3436 3436 1253p total event ecrarrect=0 0020 0021 0078 0565 0436 0040State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) Reweight states w multiple events by 1n
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -5639 -3177 5590 6946
(2444) (3451) (2631) (2029)
Post Event Yrs Elapsed -000771 000487
(000362) (000266)
Observations 7560 7560 2743 7696 7696 2819p total event ecrarrect=0 0025 0362 0039 0039 0001 0073State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(d) Number of events to date
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Num Events to Date -2896 -1807 -00252 3631 3370 00199(1016) (1647) (00111) (1406) (1263) (00121)
Observations 4116 4116 1498 4256 4256 1568p total event ecrarrect=0State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
67
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table A4 Alternative income measures
(a) 2010 district income
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3844 -2221 4100 3947
(1683) (2205) (2095) (1461)
Post Event Yrs Elapsed -000977 000844
(000286) (000207)
Observations 7560 7560 2743 7696 7696 2827p total event ecrarrect=0 0027 0319 0001 0056 0009 0000State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(b) 1990 housing values
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event -3318 -2141 5590 6946
(1386) (2094) (2631) (2029)
Post Event Yrs Elapsed -000717 000871
(000201) (000248)
Observations 7560 7560 2743 7696 7696 2826p total event ecrarrect=0 0021 0312 0001 0039 0001 0001State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
(c) 1990 share lt 185 poverty line
Slopes Q1-Q5 Means
St Rev Tot Rev NAEP St Rev Tot Rev NAEP
Post Event 0000648 0000123 -1605 -2068(0000498) (0000808) (3431) (3044)
Post Event Yrs Elapsed -840e-09 -000201(120e-08) (000481)
Observations 7560 7560 2743 7644 7644 2787p total event ecrarrect=0 0200 0880 0489 0642 0500 0678State-Event FEs X X X X X XYear FEs X X X XSub-Gr-Yr FEs X X
Notes Tables A3 and A4 report variations on baseline specifications from columns 1 and 4 of tables 3 4(both panels) column 1 of table 6 and column 5 of table 7 State-event and year fixed ecrarrects are included infinance models and state-event and grade-subject-year fixed ecrarrects are included in NAEP models Standarderrors are clustered at the state level See notes to tables 3 4 6 and 7 and the text for further details
68
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69
Table A5 Fraction in each district income quintile
Q1 Q2 Q3 Q4 Q5
Black 0238 0242 0225 0171 0124
BlackHispanic 0237 0232 0243 0171 0117
White 0196 0189 0182 0203 0230
Freereduced-price lunch 0312 0219 0201 0158 0110
Notes Table shows proportion of each racialsocioeconomic group in each district income quintile Thenumbers in each row (ie across the 5 columns) add up to one
Table A6 Event studies for per pupil revenue gaps
St Rev Tot Rev
BlackWhite Free Lunch BlackWhite Free Lunch
Post Event 2784 5199 2201 7941(1474) (2111) (1664) (1656)
Observations 1810 1624 1810 1624
Notes Post event coecient shows estimated post event ecrarrect from parametric event study model withoutcontrolling for prior trends State-event and year fixed ecrarrects are included and standard errors are clusteredat the state level
69