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Ease vs. Noise: Long-run changes in the value of transport (dis)amenities
Gabriel M. Ahlfeldt, Volker Nitsch, Nicolai Wendland
Nr. 236
Arbeitspapiere der Volkswirtschaftlichen Fachgebiete der
Technischen Universität Darmstadt
Darmstadt Discussion Papers in ECONOMICS
This text may be downloaded for personal research purposes only. Any additional reproduction for other purposes, whether in hard copy or electronically, requires the consent of the author(s), editor(s). If cited or quoted, reference should be made to the full name of the author(s), editor(s), the title, the working paper or other series, the year, and the publisher. ISSN 1438-2733 © Gabriel M. Ahlfeldt, Volker Nitsch, Nicolai Wendland 2019 Printed in Germany Technische Universität Darmstadt Department of Law and Economics D – 64289 Darmstadt Germany www.wi.tu-darmstadt.de
GabrielM.Ahlfeldt,VolkerNitsch,NicolaiWendland
Easevs.noise:Long‐runchangesinthevalueoftransport(dis)amenities
Abstract:Foracompletecost‐benefitanalysisofdurableinfrastructures,itisimportanttounderstandhowthe
valueofnon‐marketgoodssuchastransittimeandenvironmentalqualitychangesasincomesriseinthelong‐run.
Weusedifference‐in‐differencesandspatialdifferencingtoestimatethelandpricecapitalizationeffectsofmetro
railinBerlin,Germanytodayandacenturyago.Overthisperiod,thenegativeimplicithedonicpriceofrailnoise
tripled.Ourresultsimplyincomeelasticitiesofthevalueofnoisereductionandtransportaccessof2.2and1.4,
substantiallyexceedingcross‐sectionalcontingentvaluationestimates.
Keywords:Accessibility,spatialdifferencing,noise,difference‐in‐differences,incomeelasticity,landprice
Version:September,2019
JEL:R12,R14,R41,N73,N74
Conflictofinterestandfinancialdisclosurestatement
Theauthorsdeclarethattheyhavenoconflictofinterestandnomaterialfinancialintereststhatrelatetothere‐searchdescribedintheabovepaper.Allsourcesoffundingaredisclosedbelow.
Forthcomingin:JournalofEnvironmentalEconomicsandManagement
LondonSchoolofEconomicsandPoliticalSciences(LSE)&CentreforEconomicPolicyResearch(CEPR)[email protected],www.ahlfeldt.com
TechnischeUniversitä[email protected]‐darmstadt.de
WethanktheeditorRogervonHaefen,twoanonymousreviewers,seminarandconferenceparticipantsinBerlin(Humboldt),Bristol(RES),Barcelona(UEA),Copenhagen(UEA),Heidelberg,Miami(UEA),München(Ifo),Orléans,Toulouse(SEA),Vaduz(VfS),Venice(CESIfo),Würzburg,andZurich(KOF)andespeciallyThiloAlbers,MaximilianvonEhrlich,GustafEngsström,StephanHeblich,HansKoster,MirenLafourcade,KristofferMöller,IsmirMulalic,JosvanOmmeren,HenryOverman,MichaelPflüger,RosaSanchis‐Guarner,SimoneSchüller,SevrinWaightsandYanosZylberbergforhelpfulcommentsandsuggestions.KristofferMöllerandSevrinWaightsprovidedoutstandinghelpwiththecompilationofthedataset.SaschaMöbiusandNeeleReimann‐Phillipalsoprovidedexcellentresearchassistance.WethanktheBerlinCommitteeofValuationExpertsandtheSenateDepartmentforUrbanDevelopmentandtheEnvironmentforprovidingpropertytransactiondata.TheGermanScienceFoundation(DFGprojectcodeNI938/2‐1)andtheFritz‐Thyssen‐Foundation(projectcodeAZ.10.10.2.070)areacknowledgedforfinancialsupport.Theusualdis‐claimersapply.
Easevs.noise 2
1 Introduction
Understandinghowthevaluesoflocationalamenitiesanddisamenitieschangeasincomesriseis
crucialforoptimaldecisionsregardinginvestmentswithlong‐termconsequences.Atypicalexam‐
pleareinvestmentsintransportinfrastructure,whichareoftenundertakenpubliclyfollowingcost‐
benefitanalyses(CBA).Theevidencefromcross‐sectionalsurvey‐basedcontingentvaluationre‐
searchsuggeststhattheincomeelasticityofthevalueofnoisereductionispositive,butlessthan
unity(Wardmanetal.2005).Thevalueoftraveltimeistypicallysettoafractionofthewagerate
(Anderson2014;Parry&Small2009),whichimpliesaunityincomeelasticity,butalowerelasticity
hasbeenrecentlysuggested(Börjessonetal.2012).Itisnotclear,however,whethertheseesti‐
matedshort‐runelasticitiesgeneralizetolong‐runcomparisons.Intuitively,theinter‐temporalin‐
comeelasticityshouldbelargerthanunityiflocationalamenitiesanddisamenitiesarenon‐neces‐
sitiesastypicallyconjecturedintheliterature(Brueckneretal.1999;Glaeseretal.2001).Asreal
incomesrise,(dis)amenityvaluesshouldthenrisemorethanproportionately,implyingthatinap‐
praisalsofdurable infrastructurescostsandbenefitsneedtobe inflatedratherthandeflatedto
reflectdemandbyfuturegenerations.Todate,thereislittleevidencetosubstantiatethisintuition.
Thereisatbestindirectevidenceinthatpublicspendingtendstoincreasemorethanproportion‐
atelyinGDP,suggestingthatpublicservices,broadlydefined,areluxurygoods(Wagner’slaw,see
Lamartina&Zaghini2011;Ram1987;Wagner1890).
Inthispaper,wetakeasteptowardsfillingthisgapbyprovidingthefirstlong‐runcomparisonof
transportamenityanddisamenitycapitalizationeffects in landpricesoveraperiodas longasa
century. Theoretically, besides the amenity of offering improved access, there are a range of
transport‐relateddisamenities, including congestion, pollution, and noise,which can affect out‐
comessuchasproductivity,health,andannoyancelevels(Navrud,2002).Ourfocusonaccessibility
andnoiseeffects isdrivenbytheempiricalsettingweexploit.Wechoosetoevaluate landprice
capitalizationeffectsofmetrorail(U‐Bahn)inBerlin,Germany,duetotheavailabilityofhistorical
andcontemporarypropertydataandatransporttechnologythathasremainedapproximatelycon‐
stantsincethesystem’sinaugurationin1902.Thesystemisfullyelectrifiedandhasexclusiveright‐
of‐way,sothattheeffectsonpollutionandroadcongestionsarerathernegligible.Wefindlittle
evidenceforanegativevieweffect,sothatnoisefromtheelevatedpartsofthesystemisarguably
theprimarydisamenity.Ourpropertydatacoverscommercialandresidentialproperty;therefore,
ourestimatedcapitalizationeffectsreflectproductivityand(dis)utilityeffects.Theylikelyexclude
healtheffectsgiventhatthepublicawarenessofnoise‐inducedhealthimpactsislimited(Navrud,
2002).Inlinewiththeworldwidetrend,realincomeinGermanyhasincreasedatarateof2%per
Easevs.noise 3
yearsince1900,accumulatingtoanoverallincreaseofabout650%.1Oursetting,thus,allowsusto
comparethevaluationofrailaccessandrailnoiseonrealestatemarketsinahistoricallow‐income
scenarioandacontemporaryhigh‐incomescenario.
Ourcontributionisfacilitatedbyaratheruniquecombinationofsuitablemicro‐geographicdataat
theturnsofthe19th(1881‐1914)andthe20thcenturies(1990‐2012).Forouranalyses,wedigitize
aseriesofhistoricalmaps,compiledbythecharteredsurveyorGustavMüller,whichprovideinfor‐
mationonlandpricesasdetailedastothelevelofindividualparcels.2Wecomplementthesehis‐
toricaldatawithaconfidentialcontemporarymicrodatasetcoveringacompleterecordofproperty
transactions.Withthesedataathand,weestimatethatoverthecourseofthe20thcentury,theland
pricecapitalizationeffectofa10‐decibeldecreaseinrailnoiseincreasedfrom4.2%to13.0%.Ac‐
countingfortheincreaseintheshareoflandinthevalueofhousingoverthesameperiod,weinfer
acapitalizationeffectinhouse‐pricetermsthatincreasedfrom1%to4%.Thelandpricecapitali‐
zationeffectofaone‐kilometerreductionindistancefromthenearestmetrorailstation,ameasure
thatcapturesthevalueoftheassociatedwalkingtime(Gibbons&Machin2005),decreasedfrom
20.2%to15.5%.However,becausethelandshareincreasedsubstantiallyoverthesameperiod,this
decreaseimpliesasizableincrease,from3.6%to5.0%,intermsofhouse‐pricecapitalization.
Theseresultssuggestthatthevalueattachedtorailaccessandevenmoresotothedisamenityfrom
railnoisehasincreasedovertime.Oneinterpretationisthataccessandaquietenvironmentare
luxurygoodsonwhichrecentgenerationsarewilling tospendmoreas theyarericher.Making
admittedlystrongassumptions,weuseourestimatedcapitalizationeffects toderivenovelesti‐
matesofthelong‐runincomeelasticitiesoftheamenityvalueofaccessibilityandthedisamenity
valueofnoiseof1.4and2.2,respectively.Whileweacknowledgethatsignificantuncertaintysur‐
roundstheseestimates,onbalance,theylikelyrepresentlowerbounds.
Ontopofthesemaininsights,wecontributetotheliteratureinseveralmorespecificrespects.First,
wecontributetoavastliteratureinthetraditionofOates(1969)thathasinferredthevalueofnon‐
marketed goods from house price capitalization, including clean air (Chay&Greenstone 2005;
Hanna 2007), health risk (Currie et al. 2015; Davis 2004), proximity to hazardouswaste sites
(Greenstone&Gallagher2008)ornuclearpowerplants(Tanaka&Zabel2018),crimerisk(Linden
&Rockoff2008),publicschoolquality(Cellinietal.2010),energyefficiency(Wallsetal.2017),
1 OwncalculationsusingdatafromtheMaddisonProject(Bolt&vanZanden2014).The2%annualgrowthgeneralizestothemeanacrossasampleof170countries.Seeappendixsection3.1fordetails.
2 Toourknowledge,theonlycomparablehistoricdataarefromOlcott'slandvaluesbluebookofChicagoandsuburbs,publishedregularlybyG.C.Olcott's&Co.,Inc.fromthe1910stothe1990s.TheconstructionofthecoreofChicago’smetrorailsystem(theL),however,precedesthisperiod.
Easevs.noise 4
aircraftnoise(Boes&Nüesch2011;Ahlfeldt&Maennig2015),roadnoise(Graevenitz,2018),wind
farms(Gibbons2015)ortransportaccess(Gibbons&Machin2005).Weaddtothisliteratureby
showingthatwithinthesamespatialcontext,capitalizationeffectsofthesame(dis)amenitiescan
varysizablyinthelong‐runduetochangesinconsumerpreferences.
Second,weenrichaliteratureonrailaccesscapitalizationeffectsthathasrecentlyshiftedfromthe
useofcross‐sectionalvariationtotheuseofvariationovertimetoimproveidentification(seeDubé
etal.2013andappendixsection2forareview).Weexpandonthislineofresearchbyproposinga
novelweighteddifference‐in‐differences(DD)estimator,whichminimizestheconditionalcorrela‐
tionbetweenpre‐announcementtrendsintheoutcomevariable(landprices)andmultiplecontin‐
uoustreatmentvariables(proximitytothestationandrailnoise).Consequently,weminimizethe
riskthatunobservedtrendsinpropertypricescorrelatedwithstationaccessorrailnoiseconfound
ourestimates.
Third,wealsoaddtoaliteratureonnoisecapitalizationeffectsthat,withfewexceptionsconcerning
theanalysisofaircraftnoise(Ahlfeldt&Maennig2015;Boes&Nüesch2011),hasemployedcross‐
sectionaldesigns.Theliteratureonrailnoiseeffectsisparticularlyunderdeveloped(seeNavrud
2002andappendixsection2forareview).Ourspatiallyhighlydisaggregated,micro‐geographic
datasetsallowustoexploittherelativelysharpchangeinrailnoisethatariseswhereatrackenters
atunneltovanishbeneaththesurface,asourceofvariationthathasnotbeenpreviouslyexploited
intheliterature.Thespatialdifferencing(SD)approachusedtoassessthecausaleffectofnoiseon
thepriceofadjacentlandparcelsinourcontemporaryanalysesrepresentanimprovementinterms
ofidentificationcomparedtotheextantliterature.Ournovelestimateoftheeffectofaone‐decibel
increaseinrailnoiseonhousepricesof‐0.4%isclosetorecentestimatespointingtoanaircraft
noiseeffectof‐0.5%to‐0.6%(Ahlfeldt&Maennig2015;Boes&Nüesch2011)andaroadnoise
effectof‐0.1%to‐1.4%(Graevenitz,2018;J.P.Nelson,2008reportsacentralestimateof‐0.57%).
Fourth,weexplicitlydisentanglethepositiveeffectsofrailaccessfromthenegativeeffectsofrail
noiseinacausalanalysisofrailcapitalizationeffects.Therefore,wegobeyondmostoftheexisting
workthattypicallyfocusesontheaggregate(ornet)effectofcountervailingrailexternalities.In
doingso,wealsoexaminethedegreeofbiasthatariseswhenaccessibilityeffectsareestimated
withoutcontrollingfornoiseeffectsandviceversa.
Fifth,weprovideoneofthefewanalysesofrailcapitalizationeffectsintolandprices(e.g.Ahlfeldt,
Moeller,etal.2015;Coffman&Gregson1998),whereasmostpreviousstudieshavelookedatprice
responsesofpropertiesorhousingunits.Theanalysisoflandpricescomeswiththeadvantageof
nothavingtocontrolforstructuralcharacteristics.Inaddition,becauselandisscarceinanurban
contextandprovided(almost)inelastically,adjustmentsinlandpricescanbeassumedtobepurely
Easevs.noise 5
drivenbydemand.Theanalysisofhousepriceeffects,incontrast,maybemitigatedbysupplyre‐
sponsesifthedemandcurveislocallydownwardslopingbecauseofimperfectmobilityandidio‐
syncraticlocationpreferences(Hilber&Vermeulen2015).
Lastbutnotleast,weprovideacasestudywhichillustratesthat,duetotheincreaseinnoiseaver‐
sion,thecasefortheconstructionofundergroundmetrorailasopposedtoelevatedmetrorailis
muchstrongertodaythaninthepast.Indoingso,wealsoprovidenovelauxiliaryfindingsthatare
interestingintheirownright.Weestimatetheper‐kilometercostofanundergroundmetrolineat
thebeginningofthe20thcenturytobethreetimesthatofanelevatedline,whichissubstantially
largerthanthecontemporaryrule‐of‐thumbfactoroftwo.Wealsofindthat,overaperiodofabout
130years,theaverageannualnominallandpricegrowthratewasabout5%inBerlinand,there‐
fore,typicallywithintherangeoftheopportunitycostofcapital(centralbankinterestrates).
Theremainderofthepaperisorganizedasfollows.InSection2,wediscussthecontextofourstudy,
presentourdata,andintroduceasimpletheoreticalframeworkthatwillguidetheinterpretation
oftheparametersweestimate.Section3presentsthehistoricalanalysis,followedbythecontem‐
poraryanalysisinSection4.InSection5werelatethehistoricalandcontemporaryestimatesto
eachotheranddiscusspolicyimplications.Finally,Section6providesourconclusions.
2 Empiricalandtheoreticalcontext
2.1 MetrorailinBerlin
In1879,theGermanfounderandinventorWernervonSiemenspresentedthefirstfullyelectrified
experimental railway at the internationally renowned trade and industrial exhibition (Gewer‐
beausstellung)inBerlin.By1891,thecompanySiemens&Halskehadproposedadensenetworkof
variouslinestoconnecttheinnercoreof“oldBerlin”withitsthensurroundingmunicipalities.Ac‐
cordingtoinitialplans,thenetworkwastobebuiltentirelyonelevatedtracks,mainlybecauseof
strictregulationofundergroundactivitiesduetoconstructionworksonthenewcanalizationsys‐
temledbyJamesHobrecht.In1895,aconcessionwasgrantedforthefirstline,whichwastocon‐
necttheeasternpartsofBerlin,atthestationWarschauerBrücke,andthewealthywesterncityof
Charlottenburg,at thestationZoologischerGarten, runningexclusivelyonelevated tracks.Built
alongoneofBerlin’smajorboulevardsthisroutingdidnotrequiremajoracquisitionsoflandor
fundamentalchangestothebuildingstructure.In1897(onlyfiveyearsbeforetheinaugurationof
theline),Siemens&HalskefoundedtheElevatedRailwayCompany(Hochbahngesellschaft)inco‐
operationwiththeDeutscheBanktoguaranteethefunding.
Easevs.noise 6
Theconstructionbegan immediately,starting fromtheeasternparts.However,Berlinresidents
increasinglyexpressedconcernsaboutaviaduct’spotentiallyunpleasantappearance.Also,Berlin’s
municipalplanningandbuildingcontroloffice,withitsnewlyappointedheadFriedrichKrause,was
nolongergenerallyopposedtoplansfortheconstructionofundergroundlines.Asaresult,thecity
ofCharlottenburgmanagedtoensure,inalast‐minutemove,thatthetracksranbeneaththestreet
surfaceoncethelinereacheditscityboundaries.Eventually,thelinewasinauguratedin1902and
called“LineA”(LinieAorStammstrecke).Thefinalroutingnegotiatedbetweenvariousstakehold‐
erssuchasDeutscheBankandthecityofCharlottenburgwaslaterdescribedbyhistoriansasan
outcomeofagreementsandaccidents(Bousset1935).Theelevatedsectionofthelineconsistsof
11stations,whiletheentireline(includingtheundergroundsection)consistsof14stationswitha
totallengthofabout10km.
AsevidentfromFigure1,LineAcomplementedacommuterrailnetworkconsistingofvarioussub‐
urban lines aswell as a circular line (Ringbahn) and an east‐west connection through theCBD
(Stadtbahn).Thisnetworkwasoperatedentirelyonground‐level tracksorelevatedtracks. It is
comparabletotoday’scommuterrail(S‐Bahn)network,butthetechnologywasdifferentastrains
werepoweredbysteamandelectrificationdidnotstartbefore1924.Overtime,thesubway(U‐
Bahn)networkwascontinuouslyexpanded.Sincethere‐unificationofthecity,thecombinedsub‐
wayandcommuterrailnetworkscomprise475railkmand275stations.
Fig.1. HistoricalandcontemporarygeographyofBerlin’smetrorailnetwork
Notes: Own illustration using the Urban Environmental Information System of the Berlin Senate Department
(SenatsverwaltungfürStadtentwicklungBerlin2006).CBDisthecentralbusinessdistrict.Kurfürstendammisamajorsub‐centre.
Easevs.noise 7
2.2 HistoricalLandPricesandContemporaryPropertyPrices
Ourmainvariableofinterestarelandpriceswhichareextractedfromvariouseditions(1881,1890,
1896,1900,1904,1910,and1914)ofassessedlandvaluemapsforBerlincreatedbytherenowned
technicianGustavMüllerincooperationwithofficialplanningauthorities.Müller’smapsprovide
dataataremarkablydisaggregatedlevelofindividualplots.Thestatedobjectivewastoprovide
officialandrepresentativeguidesforbothprivateandpublicinvestorsparticipatinginBerlin’sreal
estatemarket.WhileMüllerhimselfdidnotdescribeindetailtheexactprocedureoflandvaluation,
theimperialvaluationlaw(Reichsbewertungsgesetz)oftheGermanReichcontainedastrictorder
tousecapitalvaluesfortheassessmentofcommercialplotsbasedonfairmarketprices.Inlinewith
thevaluationlawsforcommercialland,Müllerclaimsthathisassessmentreferstothepurevalue
ofland,whichisadjustedforallbuildingandevengardencharacteristics.Healsocorrectedvalues
forspecific locationcharacteristicssuchassingleanddoublecorner lots, subsoilandcourtyard
properties.
Müller’smaps are by now an established data source. They have been used, among others, by
Ahlfeldt,Moeller,etal.(2015),whoalsoprovideanextensivedataappendixthatdescribesindetail
thenatureofthedata.Morenotably,thedataaredirectlycomparabletothemorerecentBerlin
landpricedata(1928,1936,1986,2006)usedbyAhlfeldt,Redding,etal.(2015);theyalsoshare
manysimilaritiestoOlcott’sChicagolandvalues,whichhavebeenusedinstudiessuchasAhlfeldt
andMcMillen (2018), Berry (1976), Kau and Sirmans (1979), McDonald and Bowman (1979),
McMillen(1996),McMillenandMcDonald(2002),Mills(1969),andYeates(1965).
IncontrasttopreviousanalysesbasedonMüller’sdata,weexploititsfullspatialdetailattheparcel
level.Topreservethehighly‐disaggregatednatureoftheoriginaldata,wedigitizeeverysingledata
pointwithinaone‐kilometerbufferaroundthenewlybuiltelevatedtrackswithinageographical
informationsystem(GIS)environment.Aftercreatingabalancedpanelforthefinalanalyses,this
leavesuswithatotalofabout38,000observationsforsevenpointsintime.
Forthecontemporaryanalysesweutilizeaconfidentialdataset,whichisthesameasinAhlfeldt&
Maennig(2015),containingdetailed informationonmorethan70,000transactionsofbuildings
(single‐familyandmulti‐family)andthecorrespondinglandparcelsandincludingfeaturessuchas
price,transactiondate,location,andasetofparametersdescribingbuilding/plotcharacteristics.
ThedatawereobtainedfromtheCommitteeofValuationExpertsBerlin(GutachterausschussBer‐
lin).Thetransactionsaregeo‐referenced(addressesandx/ycoordinates),whichallowsthemtobe
integratedintoaGISenvironment.Thebuildingcharacteristicsincludefloorspace,parcelarea,age,
Easevs.noise 8
landuse,qualityofthebuildingstock,locationwithinablockofhouses(e.g.,acornerlot),andsev‐
eralotheramenitieslikebasements,elevators,etc.
2.3 Railnoise
Totranslatethetypicallyvolatilelevelsofrailnoiseintoastandardizedsummarystatistic,engi‐
neerscomputetheequivalentcontinuoussoundlevel,which isessentiallyasophisticatedmean
overthevaryingnoiselevelsobservedduringagivenperiod.Weuseahighlydisaggregatedmap,
containing2007estimatesofthecontinuoussoundlevelbythesourceofnoise(includingrail)ata
10x10‐metergridfromBerlin’sSenateDepartmentforUrbanDevelopmentandtheEnvironment
(2013).Thenoisemeasurereflectstheweightedaveragenoiseexposureoveroneyearandalltimes
ofaday(Lden)atareceptionpointoffourmetersabovetheground.Followingtherulesdefinedby
theEUEnvironmentalNoiseDirective,themicro‐geographicnoisemapistheresultofasimulation
usinga3Dmodelthatisfittoactualnoisemeasurements.Themodelincorporatesfeaturesofthe
trackdesign(e.g.speed,squeakingnoisesincurves,thepresenceoflubricationfacilities)andthe
terraingeography(e.g.elevationofthetrack,built‐upstructure,bridges)thataffectnoisedissemi‐
nation.Summarizingexistingresearch,Navrud(2002)concludesthat“[…]theeliminationofnoise
annoyanceoccursat37‐40db”.Thus,wemeasurerailnoiseintermsofdecibelsexceeding40deci‐
bels,i.e.45,50,and55decibelscorrespondto5,10,and15excessdecibels.Asweillustrateinan
auxiliaryanalysispresentedinappendixsection3.2,ourrailnoisemeasuresharplydeclineswith
distancefromthetrack,ishigherwheretrainsrunfaster,anddisproportionatelyaffectsthefirst
rowofbuildingsfacingthetrack.
Forourhistoricalepisode,estimatesoftherailnoiselevelunfortunatelydonotexistasthemeas‐
urementtechnologyhadnotbeendeveloped(Ampel&Uzzle1993).However,regardingthetrans‐
ferabilityofthecontemporarynoisemeasure,wenotethatthebuildingfootprintremainedlargely
thesamewithintheaffectedarea,despitesignificantdamageduringWorldWarII,asdocumented
on detailed ground plans published by the Berlin Senate Department (Senatsverwaltung für
StadtentwicklungBerlin2000).3Therefore,itseemsreasonabletoassumethatcontemporaryrail
noiselevelsalsoreflectthedisseminationofsoundabout100yearsagoinrelativeterms.Moreover,
theserviceoperatorwascontractuallyrequiredtoserveallstationsinatleastfive‐minuteintervals
duringdaytime,afrequencythatcorrespondstothecurrentservice(Lemke&Poppel1996).His‐
toricalandcontemporarytimetablesalsoreveal thattheaveragespeedremainedconstantover
time(Ahlfeldt,Redding,etal.2015).Thisisconsistentwitharollingstocktechnologythatdidnot
3 Notethatforveryfewplots,wherethebuildingstructurechanged,weimputehistoricnoiselevelsusingadjacentplots.
Easevs.noise 9
changefundamentally.Asdiscussedabove,LineAwasthefirstelectrifiedsubwaysysteminGer‐
many.Thetrains(typeA1/A2)aswellasthetrackdesignrepresentedarevolutionarytechnology.
Incomparison,thesubsequentimprovementsthatcamewiththeintroductionofnewtrainsinthe
1960s(typeA3,stillthebackboneofthefleet)wereevolutionary(Lemke&Poppel1996).
Theexactchangesinnoiselevelsfromthefirsttothesecondgenerationarenotdocumented,butit
seemslikelythattechnologicalprogressevenwithinasimilartechnologyatconstantspeedand
frequencyhasresultedinanataleastmoderatereductionofnoiselevels.Newgenerationsofroll‐
ingstocktendtoreducenoiselevelsofinter‐citytrainsbyabout10decibels(Clausenetal.2012;
Murphy&King2014),althoughasmallerreductionisexpectedforurbanrailsincetrainsoperate
atlowerspeeds.Moreover,lesstreecoverageinthepastmayhaveimpliedlessnoisemitigation.
Importantly,passivenoiseinsulationwasprobablyweakerinthepast,althoughthecharacteristic
woodendoubleboxwindows(Doppelkastenfenster)fromthelate19thcenturyhaveremainedpop‐
ularinBerlin.Allinall,itseemsreasonabletoassumethatourcontemporarynoisemeasurerep‐
resentsalower‐boundestimateofthenoiselevelsexperiencedintheearly20thcentury.
2.4 Visualdisamenity
Inadditiontoanoisedisamenity,anelevatedlinemaycauseavisualdisamenity.Theroutingof
LineAfollowsmajorroadswhichweresufficientlywidetoaccommodateaviaductinthemiddleof
thesides.Becausetheelevatedlinegenerallydoesnotobstructviewsofopenspacessuchasparks
orlakes,thevisualdisamenityislessobviousthanthenoisedisamenityinthepresentcase.More‐
over,addressingtheconcernsraisedbyBerlinresidentsmentionedabove,theelevatedtracksand
stationswereeventuallyexecutedwithsomeattentiontoarchitecture(Bohle‐Heintzenberg1980).
Toempiricallydisentangletheeffectsfromthenoisedisamenityandthevisualdisamenity,wecre‐
ateadummyvariablethattakesthevalueofoneifaparcelhasadirectviewoftheelevatedtrack
andzerootherwise.Moreover,subwayscausevibrationsthatpotentiallytransmittonearbybuild‐
ings,wheretheycanbeperceivedasadisamenity(Kurzweil1979).Becausetheeffectsarehighly
localizedandnormallyreachnofurtherthantothefirstrowofhouses(Melke1988),apotential
disamenityeffectshouldalsobecapturedbytheviewdummy.Previewingourresults,wedonot
findevidenceforadirectvieweffectconditionalonthenoiseeffectandfindsimilarnoiseeffects
whenexcludingparcelswithadirectviewfromtheanalysis.Wethereforegenerallyinterpretour
noiseestimatesasoriginatingpurelyfromnoise.
2.5 Otherspatialdata
Weutilizethecompletetransportnetworkdataforpost‐unificationBerlinprocessedbyAhlfeldt,
Redding,etal.(2015).Thenetworkdataconsistsofelectronicmaps(shapefiles)ofstreets(used
forwalkinganddriving),buses,trams,subway(U‐Bahn)andcommuterrail(S‐Bahn).In addition,
Easevs.noise 10
wedigitizetheundergroundandelevatedsectionsofLineAaswellastheotherhistoricaltrans‐
portationnetworks,includinghorse‐poweredbuses,horse‐poweredtrams(oneline),steam‐pow‐
eredtrams(oneline),electrifiedtrams(thegreatmajorityoftramlines),andcommuterrail(pow‐
eredbysteam).Tocompilethehistoricalnetworkdata(andtheassociatedspeeds)wecombinethe
contemporarytransportnetworkswithhistoricalnetworkplans.4Anillustrationofthehistorical
andcontemporarytransportnetworksisinappendixsection3.3.
We complement our keydata sets (property, access, noise)with several spatial characteristics,
whichwemergeinGIS, includingcontemporarymeasuresofdistancefromthecentralbusiness
district (still at thehistorical location), distance from theKurfürstendammsub‐center, distance
fromnearestlake,riverorcanal,distancefromnearestparkorforest,distancefromnearestland‐
markbuilding,distance fromnearestplayground,distance fromnearestmain street, andstreet
noise(excludingrailnoise).
2.6 Interpretationofestimatedimplicitprices
Ourhistoricalandcontemporaryanalysesutilizedifferenttypesofdata.Inourhistoricalanalysis,
weexploit thespatiotemporaldistributionof landprices. Inourcontemporaryanalysis, thede‐
pendentvariableistheratiooftransactionpriceofaparcelofland,includingthestructure,over
theparcelsize.Totheoreticallylinktheestimatedcoefficientsfromthesedistinctmodelstoeach
otheraswellastoavastliteratureanalyzinghouseprices,itisusefultoassumeaCobb‐Douglas
housingproductionfunctionandacompetitiveconstructionsector(Eppleetal.2010).
AssumethathousingservicesHareproducedusingtheinputscapitalKandlandLasfollows:
.Housingspaceisrentedoutatbid‐rent whilelandisacquiredatlandrentΩ.Combining
thefirstordercondition / / 1 Ω(wherethepriceofcapitalisthenumeraire)andthe
non‐profitcondition Ω gives / 1/ 1 Ω.Log‐linearizationyieldsarelation‐
shipwithaslopeofone,whichimpliesthatestimatedparametersfromourhistoricalmodels(in
whichthedependentvariablecorrespondstoln(Ω))andourcontemporarymodels(inwhichthe
dependentvariablecorrespondstoln( / ))aredirectlycomparable.Fromthefirst‐ordercondi‐
tionandthenon‐profitcondition,itisfurtherimmediatethatln 1 ln Ω ,wherecis
aconstantthatcancelsoutinfirst‐differences,i.e.,Δ ln 1 Δ ln Ω 1 Δ ln / .
Inlogterms,itis,therefore,possibletotranslatethecapitalizationeffectsfromourhistoricaland
4 Networkplansarealsoavailableonline; see, for instance,http://www.berlineruntergrundbahn.deandhttp://www.berliner‐verkehr.de.
Easevs.noise 11
contemporarymodelsintoafloorspacepricecapitalizationeffect,bymultiplyingtheformerbya
landshareparameter.
ItisimportanttonotethathousingservicesasdefinedbyEppleetal.(2010)arenotidenticalto
housingspace.Unitsofhousingservicescanbethoughtofasbundlesoffeatures,includinghousing
space,thequalityofmaterials,sophisticationofdesign,andaccesstocommunalandprivateexte‐
riorspace,thatgenerateequivalentconsumptionutility.Especiallyinplaceswherebuildingvol‐
umesaresubjecttobindingregulations,suchasincentralBerlin,supplyofhousingservicescanbe
elastic(atapricetheelasticity / / / 1 0)evenifsupplyofhousingspace
isnot,becausedeveloperschoosetoinvestinhousingquality(bettermaterialsanddesignsrequire
more / )toachievehigherrents .Infact,thebuildingfabricinthestudyareaisstilldominated
bythelate19thcenturystockandwherethebuildingshavebeenreplaced,thequantityofhousing
spacehasbeenregulatedbyfloorarearatiolimits.Yet,Hhasincreasedovertimeasthehistoric
buildingcapitalhasbeenupgraded,e.g.byretrofittingcentralheating,privatebathrooms,modern
kitchens,orbalconies(Hämer1990).Inappendixsection6.1,weshowthat / iscorrelatedwith
variousobservablefeaturesofbuildingcapital,conditionalonhousingspace.There,wealsoshow
thatvariousfeaturesthatarepresumablycorrelatedwithhousingcapitalandhousingservices,in‐
cludinghousingspace,decreasesignificantlyinstationdistanceandrailnoise,aspredictedfordis‐
amenities.
TheCobb‐Douglasformulationoftheproductionfunctionimpliesthattheelasticityofsubstitution
betweenlandandcapitalisunityatanygivenpointintime,suchthatasthepriceoflandincreases,
developersinvestincapital(viamaintenance,upgrades,orreplacements)atratesthatensurecon‐
stantfactorshares.Itdoesnotprecludethatthelandshareandthepriceelasticityofhousingser‐
viceschangeovertimeduetofactorsthatareexogenoustodevelopers’decisionsonfactorinputs.
AsdiscussedbyAhlfeldtandMcMillen(2018),theintensityofcapitalusevariesovertimeasthe
structureofdemand,regulation,orconstructiontechnologychange.Toaccountforsuchtrends,we
borrowseparatehistorical(1900)andthecontemporary(2000)estimatesoftheshareoflandin
totalhousingvalue inGermanyof1 0.18and1 0.32 fromKnoll,Schularick,
andSteger(2017).
3 Historicalestimates
3.1 Empiricalstrategy
Ourbaselineempiricalstrategyfortheestimationofhistoricalcapitalizationeffectscombineshe‐
donic (Rosen1974)anddifference‐in‐differences (DD)methods (Ashenfelter&Card1985).We
Easevs.noise 12
employthehedonicapproachtoexpressthepriceofaparceloflandasafunctionofvariousattrib‐
utes,includingrailnoiseandrailaccess,andtheirimplicitprices.TheDDmethodthenallowsusto
identifyatreatmenteffect(e.g.,ofrailaccessorrailnoise)bydifferentiatingacrossspace(with
differentdegreesofexposure)andtime(beforeandafterexposure).Ourbaselineempiricalspeci‐
ficationtakesthefollowingform:
ln , , , (1)
wherePitisthelandpriceofaparceliattimet, isaparcelfixedeffectcontrollingforunobserved
time‐invariant locational amenities such as pollution, onto which we cluster standard errors
(Bertrandetal.2004),and isayearfixedeffectcontrollingforcommonmacroeconomicshocks.
, , isatreatmentfunctionthatexpressestheeffectsofthemetrolineasafunctionofthe
straight‐linedistancetotheneareststationSi,theemittednoiseNi,andtime .
Whiletheopeningdateoftheline(1902)isknownapriori, theexacttemporalstructureofthe
capitalizationof theeffectsof the line into landprices isnot.Capitalizationwilloccurgradually
ratherthanimmediatelyiftheserviceisanexperiencegoodandittakessometimebeforetransit
ridersadjusttheirbehaviortotakefulladvantageofthenewoption.Ifthesemi‐strong(orstrong)
efficientmarkethypothesis(Fama1970)holds,marketswillrespondtoallinformationmadepub‐
liclyavailable,whichcanresultinanticipationeffectsassoonasthenewlineisannounced.Inset‐
tingupourDDmodel,webeginbyestimatingaseriesoftime‐varyingtreatmenteffectsthatreveal
thetemporaladjustmentpathinaflexiblemanner:
, , ,, ,…
(2)
where tisanindicatorvariable,whichtakesthevalueofoneiftheconditionismetandzero
otherwise.Parameters and eachrepresentanindividualDDparameterreflectinghowland
pricesforparcelsexposeddifferentlytonoiseandaccessibilityeffects(firstdifferences)changed
from1881toyearz(seconddifferences).
Wenotethat,becausetherewasnometrorailnoisepriortotheelevatedrailline,ournoisemeasure
reflectstheincreaseinnoiseduetotheelevatedrailline(suchthat ∆ ,where∆ isthebe‐
fore‐afterchangeinnoise).Therefore, providesafirst‐differenceestimateoftheeffectofrail
noiseonlandpricesthatcanbeinterpretedasahedonicimplicitprice.Incontrast, givesthe
changeinthehedonicimplicitpriceofdistancetostationlocationsfromyear1881toyearz,i.e.
,where isthehedonicimplicitpriceingivenyearz. canstillbeinterpreted
Easevs.noise 13
asthehedonicimplicitpriceofproximitytoastation sincein1881thestationscouldnotbe
anticipatedand,thus, 0.
Informedbythisanalysis,wethenestimateanextendedDDmodelwhichprovidesabefore‐and‐
aftercomparison,controllingfortheeffectsduringanidentifiedadjustmentperiod:
, , 1902 1902
,
(3)
where 1902 isanindicatorvariabletakingthevalueofoneforyearsafterthelineopening
and isthesameforavectorofyearsAduringwhichlandpricesappeartobeadjustingto
anewequilibrium.Notethatcomparedtodroppingthoseyears,controllingforadjustmenteffects
offerstheadvantageofprocessingmoreinformationforidentificationofcovariateeffects(intro‐
ducedinrobustnesschecks)andfixedeffects , .
ThecriticalandessentiallyuntestableassumptionofanyDDanalysisisthat, intheabsenceofa
treatment,allsubjects(irrespectivelyoftheintensityoftreatment)wouldhavefollowedthesame
trend.Aselectionproblemexistsifthetreatedandthenon‐treatedsubjectsdifferinobservableor
unobservable dimensions, and these differences imply heterogeneous responses to common
shocks.Inthecontextoftheanalysisoftransportinfrastructureeffects,itisanotoriousconcern
thattheplacementmaybeendogenoustolocationcharacteristicswhichmaybecorrelatedwith
trends.Avarietyoftechniqueshaveemergedtoaddressselectionproblems,manyofwhichaimat
weightingobservationsinsuchawaythatthetreatmentassignmentbecomesorthogonaltoob‐
servablecovariates.Examplesincludetheinverseprobabilityweighting(Hernánetal.2001)and
the special case of entropy balancing (Hainmueller 2012), the propensity score matching
(Rosenbaum&Rubin1983),orthesyntheticcontrolmethod(Abadie&Gardeazabal2003).The
problemwiththeapplicationofthesetoolstothepresentcaseisthattheyservethepurposeof
evaluatingsingulartreatmentsandnotmultiplecorrelatedtreatments.
Intheabsenceofasuitableoff‐the‐shelfmatchingtechnique,weuseasimplesledgehammerap‐
proachtodefiningparcelweightsthatminimizetheconditionalcorrelationsbetweenbothtreat‐
mentvariablesandthe1881‐1890trendinlandprices,aperiodforwhichweareconfidentthat
thelinehasnotbeenanticipated.Wenotethatthisisthefirstapplicationofthisweightedparallel
trends(WPT)DDapproach.Tosavespace,werelegateamoretechnicaldiscussion, includinga
Monte‐Carlo evaluation of the small‐sample properties of the estimator, to a companion paper
Easevs.noise 14
(Ahlfeldt2018).5Inlinewithotherweighting‐basedmatchingtechniques,weviewthe1881‐1890
trendinlandpricesasacovariatetobebalanced;however,balancingmustbeachievedwithrespect
totwocorrelatedtreatmentassignments,noiseandstationdistance.Undertheidentifyingassump‐
tionthatthecorrelationbetweentreatmentsandunobservedfactorsthat interactwithtimeare
time‐invariant,successfuleliminationoftreatment‐trendcorrelationsduringthepre‐treatmentpe‐
riodimpliesthatnon‐paralleltrendsarealsoremovedinpotentialoutcometrendsduringthepost‐
treatmentperiod.Toachievethispurpose,wedefinethefollowingparcelweights:
∑, , , , (4)
where, , … , areparameterstobeidentified. , ,isoneofmvariablescapturingobserva‐
bletime‐invariantparcelcharacteristicsthatenterstheweightsinaGaussiantransformation:
, ,1
√2exp
12
, 2
, (5)
wherethebandwidths aresetaccordingtotheSilverman(1986)ruleandtheupperbarindi‐
cates themeanofadistribution.WeusetheGaussiantransformationbecausewepresumethat
parcelsthataremore“normal”withrespecttoaplotcharacteristic , aremorelikelytobeona
similartrend.Furthermore,wepresumethatparcelsthatarerepresentativewithrespecttodiffer‐
entcharacteristics , arelikelyondifferenttrends.Thisapproachhasbeenchosensoastomix
thesedifferenttrendsinawaythatensuresthattheaveragetrendintheweightedsampleisor‐
thogonaltothetreatments.ApositivecollateraloftheGaussiantransformationisthatall ,
, , arepositiveandinthesamedimension.Inthebaseline,weusedistancefromtheCBD,
distancefromasub‐centre,and1881‐1890pricegrowthasparcelcharacteristics inthealgo‐
rithm.Insearchingforavector thatminimisestheobjectivefunction,wesearchoveraparameter
space defined by 0, 0.01, 0.02, … ,1, 0, 0.01, 0.02, … ,1, 0, 0.01, 0.02, … ,1, which
equatesto101^3=1,030,301combinations.Weselect thatminimizesthesumofsquaredpartial
correlationsbetweenour treatmentmeasures(railnoiseandstationaccess)and the landprice
growthoverthe1881to1890period.6
5 Thecompanionpapercitesanearlierworkingpaperversionofthispaper.
6 Tothisend,werunrregressionsoftheform∆ln , ,where∆ln , isthechangeinloglandpricefrom1881to1890andtildedenotesnormalizationbystandarddeviation.Ineachregression,observationsareweightedbyWi,whichdependsonthevector , … , .Weselectthecom‐
binationofparametersthatminimizes∑ , .
Easevs.noise 15
Tooveridentifyourparcelweights,weuseinformationthatdidnotentertheweightsconstruction.
Wehavetwomorepre‐openingperiodsinourdataset(1890‐1896,1896‐1900)whichweuseto
evaluatewhetherthecommontrendsassumptionholdswithintheweightedsample.Wehaveex‐
perimentedwithalternativesetsofparcelcharacteristicsandobjectivefunctionsandourchoices
arebasedontheirperformanceintheoveridentificationtestreportedinappendixsection4.There,
wealsoevaluatewhethertheweightingchangesthecompositionofthesamplewithrespecttoob‐
servableparcelcharacteristics.Theweightedsampleresemblestheunweightedsampleintermsof
observablecharacteristics(seeappendixsection4.1).Whileeveryweightedanalysisresultsina
localestimate,inourcaseitisatleastnotobviousthattheweightedDDeffectsareidentifiedfrom
parcelswithveryparticularcharacteristicsthatwouldimpedegeneralizabilitywithinoursample.
3.2 Baselineresults
InFigure2,weillustratethetime‐varyingtreatmenteffects,estimatedaccordingtotheDDmodel
(1)usingthetreatmentfunction(2)andtheweightsdefinedin(4)and(5).Wereportrailnoiseand
stationdistanceeffects,estimatedunconditional(solidlines)andconditional(dottedlines)oneach
other.Estimatedstationdistanceeffectsaremultipliedby‐1toensurethatpositivenumbersmean
normativelypositiveeffects.Ourweightedestimationapproachachievesitspurposeofeliminating
pre‐trends,i.e.,thereisnosignificantcorrelationbetweenthe1881‐1890landpricetrendonthe
onehandandproximity tostationsorexposuretorailnoiseontheother.Proximityeffectsare
insignificantin1896and1900andthenoiseeffectisinsignificantin1900(yearsthatwerenotused
intheconstructionoftheweights),indicatingthatthecommontrendsassumptionholdswithinthe
weightedsample.
Stationdistanceeffectsremaininsignificantduringallyearspriortotheopeningofthelineand
becomesignificantlypositiveafterwards,witha tendencyto increaseover time.Theabsenceof
anticipationeffectsincombinationwiththegradualadjustmentaftertheopeningofthelineare
consistentwithaninterpretationthatthelinerepresentsanovelmodeoftransportationwhose
benefitswereyettobeexperienced.Controllingforrailnoise,aone‐kilometerdecreaseindistance
fromthestationincreaseslandpricesinthelong‐runbysomenotable0.3logpoints(35%).
Easevs.noise 16
Fig.2. Difference‐in‐differences:Time‐varyingtreatmenteffects(WPTmodels)
Note: Time‐varyingtreatmenteffects and basedonbaselineDDequation(1)andtreatmentfunction(2).
WPTmodelsuseweightsconstructedtominimizetheconditionalcorrelationsbetweennoiseandthe1881‐1890landpricetrendaswellasaccess(distancefromstation)andthe1881‐1890landpricetrend.Accessparameters(effectsofdistancefromstation)multipliedby‐1sothatpositiveshiftsindicatepositiveeconomiceffects.Verticalerrorbarsindicatethe95%confidenceintervalbasedonstandarderrorsthatareclusteredonparcels.Solidverticallinesdenotetheyearofopeningofthemetroline(1902).
Theestimatedweightedrailnoiseeffectsalsodisplayanintuitivepattern.Controllingforstation
distanceeffects,a10‐decibelincreaseinrailnoiseisassociatedwithareductioninlandpricesby
slightlymorethan4%inthelong‐run.Incontrasttoourresultsforstationdistanceeffects,wefind
notableanticipationeffectsofrailnoisefor1896.Thisfindingisplausible inlightoftheintense
publicdebateabout theaestheticappealofelevatedrail lines.Theconflictwassettledafter the
announcementtoimprovethearchitecturaldesignofthestationsandtheviaductandthedecision
tobuildanundergroundlinewithintheboundariesofthecityofCharlottenburg,explainingwhy
theanticipationeffectdisappearsin1900.Inkeepingwithintuition,estimatedstationdistanceef‐
fectsincreasebyaboutonethirdifrailnoiseeffectsarecontrolledfor.Theeffectofcontrollingfor
stationdistanceeffectsonrailnoiseeffectsisevenlarger.
Easevs.noise 17
InformedbyFigure2,wenowproceedtoestimatingparametricbefore‐afterDDeffects,usingour
baselinespecification(1),thetreatmentfunction(3),and,again,theweightsdefinedin(4)and(5).
TheresultsarereportedinTable1.Forcomparison,wepresentweightedDDestimatesofstation
distanceeffectsnotcontrollingforrailnoiseeffects(columns1‐2)andrailnoiseeffectsnotcontrol‐
lingforstationdistanceeffects(columns3‐4). Incolumns(5‐6)ofthetable,wethenreportour
preferredstationdistanceandrailnoiseeffectsestimatedconditionaloneachother.Wecontrolfor
anticipationeffectsin1896and1900asindicated.
Whenwedonotcontrol forrailnoiseeffects,ourestimationresults indicate that thepriceofa
parcellocatedrightatastationincreasesby12.7%(=exp(0.120)‐1)aftertheopeningoftheline,
comparedtoaparcelonekilometerawayfromastation.Railnoiseeffectsareclosetozeroand
statisticallyinsignificantifstationaccessibilityisignored.Controllingforanticipationeffectsinei‐
thercasehasaminorimpactontheestimatedraileffects.Acomparisonoftheseresultstocolumns
(5‐6)highlightstheimportanceofjointlyidentifyingatransportationinfrastructure’samenityand
disamenityeffects.Asshownincolumn(6),thestationdistanceeffectincreasesto20.2%inour
preferredmodel.Moreover,inlinewithFigure3,the(negative)railnoiseeffectisnowstatistically
significant.Thepointestimatesindicatethata10‐decibelincreaseinrailnoisecausesarelative
declineinlandpricesby3.7%.Comparingourestimatesacrossthedifferentspecifications,thebias
thatresultsfromignoringcountervailing(dis)amenityeffectsamountstoasmuchasabout35%
0.184 0.119 /0.184 instationdistanceeffectsandtoabout85%inrailnoiseeffects.Inthis
context,itisworthnotingthatconsistentwiththeinsignificantnoiseeffectincolumns(3‐4),our
preferredestimatesincolumn(6)suggestthatpositiveaccessibilityeffectsaboutoffsetthenega‐
tivenoiseeffectfortheparcelsexposedtothehighestlevelsofnoise(seeappendixsection4.2for
details).
ThetreatmenteffectsreportedinTable1arederivedfromacomparisonofthemeanlandpriceat
theparcel levelintheperiods1881‐1890and1904‐1914.Sincethismodelignorespricetrends
aftertheopeningofthe line,theeffectsaresmallerthanthe1914treatmenteffectsreportedin
Figure2.Theseparametricestimates,however,areclosertothestandardapproachinthelitera‐
ture,thereforeprovidingamorereasonablestartingpointforacomparisonofourquantitativere‐
sultstocontemporaryestimatesintheliterature.
Easevs.noise 18
Tab.1.Noiseanddistanceeffects:Historicalweighteddifference‐in‐differencesestimates
(1) (2) (3) (4) (5) (6) Lnlandprice(1881‐1914)Distance(km)xafter
1902 ‐0.120***(0.025)
‐0.119***(0.032)
‐0.173***(0.031)
‐0.184***(0.040)
Noise(10db)xafter1902
0.001(0.006)
‐0.004(0.008)
‐0.029***(0.007)
‐0.036***(0.010)
Parceleffects Yes Yes Yes Yes Yes YesYeareffects Yes Yes Yes Yes Yes YesAnticipationeffects ‐ Yes ‐ Yes ‐ YesN 37,933 37,933 37,933 37,933 37,933 37,933r2 .93 .93 .93 .93 .93 .93
Notes: Weightedmodelsuseweightsconstructedtominimizetheconditionalcorrelationsbetweennoiseandthe1881‐1890 landpricetrendaswellasaccess(distance fromstation)and the1881‐1890 landpricetrend.Afterisadummyvariableindicatingyearsafterthelineopening(1902).Announcementeffectsaredistanceandnoisevariablesinteractedwith1896and1900effects.Balancedpanelofrepeatedparcelobservationsfor1881,1890,1896,1900,1904,1910,1914.Standarderrorsinparenthesesareclusteredonparcels.*p<0.10,**p<0.05,***p<0.01.
3.3 Robustnesschecksandcomplementaryanalyses
Wehaveperformedanumberofperturbationsof thebaselinemodelreported incolumn(6)of
Table1toaddressvariousconcerns.Forinstance,weobtainsimilarresultswhenweusedifferent
covariatesandobjectivefunctionsintheweights‐generatingalgorithm.Wealsofindthatthebase‐
lineresultsarereasonablyrobusttoallowingfortime‐varyingimplicitpricesofvariouslocation
characteristics(capturedbycontrols×yeareffectsinteractions).Allowingforinteractionsofnoise
anddistancevariableswithseparatetimetrendsbeforeandaftertheopeningofLineAresultsin
cumulatedeffectsafter10yearsthatareveryclosetothebaselineestimates.Addingadummyvar‐
iableindicatingparcelswithanunobstructedviewoftheelevatedlinedoesnotsignificantlyaffect
thenoise(orthedistance)effect.Similarly,theresultshardlychangeifallparcelswithadirectview
oftheelevatedlineareexcluded.Avieweffectisonlysignificantifthenoisemeasureisexcluded
fromthemodel.Notcontrollingfornoise,parcelswithadirectviewexperiencedarelativedecrease
inthelandpriceof4.4%,whichissubstantiallylessthanimpliedbythenoiseeffectatthesame
location(about‐9.5%;seepreviousparagraph).Itis,therefore,unlikelythatournoiseestimates
areconfoundedbyaviewdisamenityeffectoradisamenityfromsubwayvibrations(asbotheffects
shouldbehighlycorrelated).Wehavealsoevaluatedthespatialdecayinthedistanceeffectusinga
seriesofdummiesdenotingparcelsinmutuallyexclusive100‐meterstationdistancebins.Wefind
thatthedistanceeffectis largelyconfinedtothefirst400meters,withnoevidencefornegative
congestioneffectsatclosedistances.Comparingtheeffectintheinnermostringversustheouter‐
mostresidualcategoryresults inaneffect that isalmost identical to theone‐kilometerdistance
effectfromthebaselinemodel.Wehavealsoevaluatedthestabilityofthehedonicfunction(Kumi‐
Easevs.noise 19
noffandPope,2014)aroundtheopeningdatesbycomparingmarginaleffectsofotherspatialat‐
tributesover timeandexperimentedwithvarying levelsof spatial clustering.Theserobustness
tests and complementary analyses arepresentedanddiscussed indetail in appendix section4,
wherewealsopresenttheresultsofanunweightedOLSanalysesfortheinterestedreader.Asa
finalandparticularlypowerfulrobustnesscheck,wealsoevaluatethenoiseeffectexploitingadis‐
continuityinnoiseatthetunnelentranceclosetoNollendorfplatz,findingqualitativelyandquan‐
titativelysimilarresults.Thisanalysisispresentedinappendixsection5.
4 Contemporaryestimates
4.1 Empiricalstrategy
Intheabsenceofvariationovertimeinthemetrorailnetworkduringthecontemporarystudype‐
riod(1990‐2012),weestimateacross‐sectionalmodel.Toimprovetheidentificationofnoiseef‐
fects,werestricttheidentifyingvariationtothesharpchangeinnoisethatarisesatninetunnel
entranceswhereelevatedlinesturnintoundergroundlines.Thereasonsforthetransitionandthe
selectionofthelocationofthetunnelentrancesareoftenspecifictotheline(Bohle‐Heintzenberg,
1980).Inparticular,weestimatemodelsoftheform:
ln ε , (6)
where isthepropertytransactionpricenormalizedbythelotsizeofapropertyjsellingat
timetwithinthecatchmentareaofstationcandwithinanetworkcorridore.Asdiscussedinsection
2.6,thisspecificationaccountsforendogenoushousingqualityandyieldsmarginaleffectsofrail
noiseandrailaccessthataredirectlycomparabletothehistoriclandpriceeffectsestimatedinsec‐
tion3.Incontrasttoconventionalhedonicanalysesusingsalesprices(correspondingto inno‐
tationsofsection2.6),housingattributeslikethenumberofbathroomsorbedroomsmustnotbe
controlledfor. / isdirectlyobservedinthedataandtheoreticallyonlydependsonfactors
thataffect the landprice, i.e. locationalcharacteristics. Incontrast to the theoretical framework
outlinedinsection2.6,however,housingisdurablesuchthattheactualbuildingcapitaldoesnot
necessarilycorrespondtotheequilibriumvaluesincecapitaldepreciates(seeappendixsection6.1
forestimatesofthedepreciationrate).Therefore,wecontrolforageinthevector ,whichalso
containsahostoflocationalcontrolvariables.
ThevariablesSandNareourrespectivemeasuresofstationdistanceandrailnoiseasbefore, is
afixedeffectforstationcatchmentareasand isayearfixedeffect.Sincesubwayandcommuter
Easevs.noise 20
railuseasimilartechnologyinthecontemporaryperiod,wetreatbothtypesofstationsasperfect
substitutes.Stationcatchmentareasare, therefore,defined forgroupsofpropertiessharing the
sameneareststation.Inourbaselinespecification,werestrictthesampletoareaswithinonekilo‐
meter of thenearest station.As evident fromFigure3, thedensity of stations is relatively high
withinthecentralpartsofBerlin,furtherreducingthesizeofacatchmentarea.Themeancatch‐
mentareais just1.3squarekilometers(about0.8squaremiles)asopposedtomorethanthree
squarekilometersimpliedbyacirclewithaone‐kilometerradius.Withtheinteractioneffects
,we, thus, provide a strong control forunobserved location characteristics such as pollution,
changesinlocationalcharacteristicsandchangesintheimplicitpricesoflocationcharacteristics.
Fig.3. Contemporaryrailnetworkandstationcatchmentareas
Notes: Own illustration using the Urban Environmental Information System of the Berlin Senate Department
(SenatsverwaltungfürStadtentwicklungBerlin2006).
Critical for the identificationof thenoiseeffect, isasetof fixedeffect forrailcorridors.Each
corridoriscenteredontheintersectionoftherailnetworkandoneoftheninetunnelentrances
indicatedbytheorthogonalsinFigure3.Weusecorridorsdefinedbasedonatrackdistanceof100
metersandadistancefromtheorthogonalof1000meters.Theinteractionfixedeffects
capturearbitraryshockstoanyofthesecorridors.Wedefineanauxiliaryrunningvariable that
takes the distance from the nearest tunnel entrance (negative distances in the tunnel section)
withinacorridoreandavalueofzeroelsewhere.Wethenuseadummyvariableindicatingthe
Easevs.noise 21
elevatedpartsofthosecorridors 0 ( isonewithinanyofthecorridors)asanin‐
strumentfornoisetorestricttheidentificationtothedifferenceinnoiseacrosselevatedandun‐
dergroundsegmentswithincorridors.
4.2 Baselineresults
Figure4illustratesrailnoiseandcontemporarypropertypricesalongtherailcorridorsandtunnel
entrances.Wepresentmeanvaluesofoutcomeswithin100‐meterbinsandconfidenceintervals
thatsummarizewhetherthewithin‐binmeanissignificantlydifferent(atthe90%level)fromthe
meanacrossallobservationswithinacorridorontheothersideofatunnelentrance.
Fig.4. Contemporaryspatialdifferencesinnoiseandpropertyprices
Notes. Eachcircleillustratesthemeanvalueofadependentvariablewithinagridcell.Onedimensionofthegrid
cellsare200‐mbinsdefinedbasedonthedistancefromthetunnelentrance.Theotherdimensionisa100‐m‐distancebufferaroundthetrack.Negativedistancesfromthetunnelrefertotheundergroundsection.Solidhorizontallinesindicatethemeans(weightedbythenumberofobservations)withintheunderground(neg‐ativedistance)andelevated(positivedistance)segments.Errorbarsarethe90%confidenceintervalsbasedonrobuststandarderrorsfromseparateparcel‐levelregressions(withinthebuffer).Foreachoutcome,werunoneregressionoftheoutcomeagainstdummiesindicatingpositivedistance(≥0)bins,andanotherre‐gressionoftheoutcomeagainstdummiesindicatingnegativedistance(<0)bins.Foreachbin,theerrorbarrepresentsatestifthemeanwithinthebinisdifferentfromthespatialcounterfactual(thedashedline).Theboundaryeffectcorrespondstothedifferencebetweenthetwohorizontallines.Transactionpricesaretheresidualsplustheblockfixedeffectcomponentfromregressionsofthenaturallogofthetransactionpricenormalizedbylotsizeagainstahostofhedoniccontrols,yeareffects,andblockfixedeffects,severaldistancevariables,includingdistancefromthecentralbusinessdistrict,distancefromthenearestlake,riverorcanal,distancefromnearestparkorforest,distancefromnearestlandmarkbuilding,distancefromnearestplay‐ground,distancefromnearestmainstreet,streetnoise(excludingrailnoise).
Withintheserailcorridors,thelevelsofrailnoisealongtheelevatedsegmentsexceedthatofthe
undergroundsegmentsbyabout18decibels.Theadditionalnoisecomeswithadiscountonland
pricesof‐0.26logpoints.Fouroutoffivehighnoisebins(elevatedsection)havemeanpricesthat
Easevs.noise 22
aresignificantlylowerthanthemeanpricewithinthelownoise(underground)sectionandfour
outofsixlownoise(undergroundsection)binshavemeanpricesthataresignificantlyhigherthan
themeanpricewithinthehighnoise(elevated)section.Theimpliedpriceeffectofa10‐decibel
increaseinrailnoiseisabout‐0.14logpoints,morethanthreetimesthelandpricecapitalization
effectinthehistoricalperiod.
Table2reportstheestimatesforseveralvariantsofequation(6).Incolumns(1‐3),wepresent,for
comparison,theresultsofaconventionalhedonicmodel,whichexcludesallcorridor‐relatedvari‐
ablesanddoesnotusetheinstrument.OurpreferredSDspecificationsforthenoiseeffectsidenti‐
ficationaretabulatedincolumns(4‐6).Forbothvariants,wereportresultsofmodelsthatexclude
(1and4)andinclude(2and5)stationcatchment×yeareffectsaswellasmodelsthatusealltrans‐
actions(1‐2and4‐5)orsamplesrestrictedtopropertieswithinonekilometeroftheneareststation
(3and6).
Theestimatedstationdistanceeffectsarerelativelystableacrossallspecifications.Ourpreferred
estimateoftheper‐kilometerstationdistanceeffectisthe exp 0.144 1 /100 15.4%esti‐
matefromcolumn(3),forseveralreasons.Inmodel(3),stationcatchment×yeareffectscontrol
forarbitraryshocksatarelativelylocallevel.Moreover,therestrictiontoaone‐kilometerstation
radiusfurtherincreasesthestrengthofthiscontrolandmakestheresultsmorecomparabletoour
historicalanalysis.Importantly,themodelcontrolsfornoisealongallelevatedsegmentsofthenet‐
workwhereasintheSDspecificationmuchofthevariationinnoiseisintentionallywipedoutby
theinstrument.
TheSDmodelsconsistentlypointtorelativelylargeandnegativenoiseeffects.Themostconserva‐
tiveestimatesuggeststhata10‐decibelincreaseinnoisereducesthepropertypriceperlandunit
(andundertheassumptionsmadeinsection2.6alsothe landprice)byabout11.5%.Giventhe
geographyoftheBerlinrailnetwork,itisintuitivethatthehedonicmodelsincolumns(1‐3)yield
smallerestimates.Thesubwaynetworkoftenfollowsmajorboulevardsthatwerelaidoutinthe
1862Hobrecht‐Plan(Bernet2004),whichborrowedmanyfeaturesfromHaussmann’sdesignsfor
Paris(deMoncan2009).Theseboulevardsprovidethenecessaryspacefortheconstructionofvia‐
ducts forelevated linesor facilitate the cost‐effectiveopenconstructionof tunnels. Suchboule‐
vards, however, also possess desirable features such as distinctive architecture, tree coverage,
shops,boutiquesandrestaurants,whicharenotobservedinthedata.Ifthesefeaturesareempiri‐
callyconfoundedwithrailnoise,thenoisedisamenitywillbeunderestimated.
Easevs.noise 23
Tab.2.Contemporaryanalysis
(1) (2) (3) (4) (5) (6) Lnpropertytransactionprice/lotsizeDistance(km) ‐0.128*** ‐0.126*** ‐0.144*** ‐0.127*** ‐0.126*** ‐0.152*** (0.003) (0.007) (0.021) (0.003) (0.007) (0.022)Railnoise(10decibel) 0.050*** ‐0.021 ‐0.032** ‐0.166*** ‐0.143*** ‐0.122** (0.011) (0.015) (0.015) (0.032) (0.049) (0.049)Controls Yes Yes Yes Yes Yes YesYeareffects Yes ‐ ‐ Yes ‐ ‐Stationxyeareffects ‐ Yes Yes ‐ Yes YesCorridorxyeareffects Yes Yes YesNoiseinstrument Yes Yes YesSample All All Station
distance<1km
All All Stationdistance<1km
N 71,313 71,313 46,143 71,313 71,313 46,143r2 .259 .584 .608 .261 .586 .61
Notes: Unitofanalysisispropertytransaction.Controlsincludestructureage,dummiesforlocationwithinablock(cornerlot,streetfront,backyard,etc.),dummiesforbuildingcondition(poor,good),distancefromnearestlake,riverorcanal,distancefromnearestparkorforest,distancefromnearestlandmarkbuilding,distancefromnearestplayground,distancefromnearestmainstreet,streetnoise(excludingrailnoise).Stationeffectsidentifygroupsofpropertieswhichhave the samenearest rail station.Corridoreffects identifygroupsofpropertieswithin100‐meterbuffersalongarailline,spreading1,000meterinbothdirectionsfromatunnelentrance.Noiseinstrumentisadummyvariabletakingthevalueofonewiththeelevatedsegmentofanyrailcorridorandzerootherwiseinmodels(4‐6).Standarderrorsinparenthesesarerobustin(1)and(4),clus‐teredstationxyeareffectsinallothermodels.*p<0.10,**p<0.05,***p<0.01.
4.3 Robustnesschecksandcomplementaryanalyses
Wehaveexpandedtheanalysisofcontemporarypropertypriceeffectsinseveraldirections.We
haveevaluatedtheancillarypredictionfromthetheoreticalframeworkinSection2.6thatincreases
inlandvaluesduetolocationalamenitiesshouldbeaccompaniedbyinvestmentsinbuildingcapital
andalargerquantityofhousingservices.Wefindthatincreasesinstationdistancebyonekilometer
andincreasesinrailnoiseby10decibelsreducethesupplyoffloorspaceperlandunitbymore
than20%andabout10%,respectively.Thereisalsoanegativeeffectonbuildingconditionsaswell
asthepropensityofbuildingswithfeaturessuchaselevators,basements,orundergroundparking.
Toallowforamoreexplicitcomparisontothehistoricalanalysis,weestimatedistanceandnoise
effectswithintheone‐kilometerbuffersurroundingtheelevatedpartofLineAdepictedinFigure1.
Theamenityanddisamenityeffectswithinthebufferareverysimilartotherestofthecityarea.If
anything,thedistanceeffectappearstobesomewhatlarger(‐19.3%perkilometer),althoughthe
differencebetweentheeffectsinbothareasisnotsignificant.Withasimilaraim,weestimatethe
distanceeffectforthesubway(U‐Bahn)andcommuterrail(S‐Bahn)networkseparately.Thedis‐
tanceeffectforthesubwaynetworkof21.9%perkilometeris,again,somewhatlargerthaninthe
baseline.Inrobustnesschecks,weanalyzethesensitivityoftheresultstovariationsinthedefini‐
tionoftherailcorridoranddifferentattemptstoachieveamorelocalidentificationinareduced‐
Easevs.noise 24
formframework(usingthenoiseinstrumentasanexplanatoryvariable).Narrowerdefinitionsof
therailcorridor(75or50meters)resultinsimilarpointestimates,butlargerstandarderrors.Fur‐
therrestrictingtheidentificationtovariationclosertothetunnelentrancebyweightingobserva‐
tionsbydistanceoraddingdistancetrendsresultsinlargernoiseestimates.Acomplementaryanal‐
ysisofnon‐lineardistanceeffectsrevealsthatthedistanceeffectslargelycapitalizewithinthefirst
500meters,withnoevidencefornegativecongestioneffectsatclosedistances.Thepeakcapitali‐
zationeffectclosetothestationrelativetotheone‐kilometerstationdistancemargin,atabout20%,
issomewhatlargerthanimpliedbythebaselineestimate.Wealsofindthatconditionaloncontrols
thedifferenceinroadnoisewithinelevatedandundergroundsegmentsofourrailcorridorsisclose
toandnotstatisticallydistinguishablefromzero.Thus,withthechosenresearchdesign,roadnoise
isunlikelyapotentialconfounderforrailnoiseeffects,andsoareotherdisamenitiessuchaspollu‐
tionthatarelikelycorrelatedwithroadnoise.Amorecompletepresentationanddiscussionofthe
extensionsandrobustnesschecksisinappendixsection6.
5 Interpretation
5.1 Comparisonofhistoricalandcontemporaryestimates
Thusfar,wehaveprovidedcontemporaryandhistoricalestimatesofcapitalizationeffectsofnoise
andrailaccessintolandprices.UsingthetheoreticalframeworkdiscussedinSection2.6,itispos‐
sibletoretrievetheimpliedhousepricecapitalizationeffects.Toobtainestimatesofthelong‐run
incomeelasticitiesof(dis)amenityvaluesofnoiseandaccess,wemakesomefurtherassumptions.
Inparticular,weassumethat,withineachperiod(historicandcontemporary),(i)preferencesfor
allgoods(includingnoiseandaccess)arehomogeneous,andsoareexpendituresharesonhousing
andlandsharesintheproductionofhousing(thisdoesnotprecludedifferencesacrossperiods);
(ii)real incomesgrowataconstantrateforallpopulationgroups(thisdoesnotprecludelevel‐
differencesacrossgroups);and(iii)theestimatedmarginaleffectsofnoiseandaccessarecausal
andconstantacrossthedistributions(fornoisethisconcernsvaluesexceeding40decibels).Wecan
thendefinethewillingnesstopay(WTP)foraunitamenityincreaseinperiodtastheproductof
thecapitalizationeffectinhousepriceterms 1 (1 isthelandshareasdefinedinsec‐
tion2.6),income ,andtheexpenditureshareonhousing : 1 .Taking
log‐differencesandrearrangingtheWTPequationgivestheincomeelasticityoftheamenityvalue:
∆ ln∆ ln
1∆ ln∆ ln
∆ ln 1∆ ln
∆ ln∆ ln
, (7)
Easevs.noise 25
Ofcourse,theassumptionsmadearedisputableandaresubjecttoacriticalassessmentinappendix
section7,wherewealsoprovideadetaileddiscussionofthecalibratedvaluesfor∆ ln 1 , ∆ ln
and∆ ln .Acknowledgingthatconsiderableuncertaintysurroundsourestimatesofbothlong‐run
incomeelasticities,weprovideasummaryofourmaintakeawaysbelow.
5.1.1 Noise
Overaperiodofabout100years,theeffectofa10‐decibelincreaseinnoiseonlandpricesroughly
tripledfrom‐4.2%(Table2,column3)to‐13.0%(Table3,column6).Undertheassumptionsmade,
thiscorrespondstoanincreaseintheper‐decibelhousepricecapitalizationeffectfrom‐0.1%to
‐0.4%, the latterbeingwithin the rangeof contemporaryestimatesof aircraft noise (Boes and
Nüesch,2011report‐0.5%perdecibel)androadnoiseeffects(Graevenitz,2018reportsarange
of‐0.1%to‐1.4%perdecibel).Theimpliedincomeelasticityofthenoisedisamenityvalueis2.2.
This long‐run incomeelasticity estimate iswithoutprecedent, but complements cross‐sectional
stated‐preferenceestimatesthatpointtoanincomeelasticityofthemarginalcostofnoisebelow
unity(Wardmanetal.2005citeacentralestimateof0.5).
Onepossibleconcernwiththeinter‐temporalcomparisonwemakeisthatwedonotobservehis‐
toricrailnoise.Forthereasonsdiscussedinsection2.3,contemporaryrailnoiselevelslikelyun‐
derstatehistoricalnoise levels, implyingthatourhistoricalnoiseestimatesareupwardlybiased
andthelong‐runincomeelasticityofthenoisedisamenityvalueislikelylargerthanthevaluewe
infer.Anotherconcernisthat,inthepast,roadnoiselevelswerelikelylowerduetotheabsenceof
affordablemass‐producedcars.Thiswillbeapotentialproblemifwerelaxtheassumptionofa
constantmarginaleffectofnoise.Ifthedisamenityeffectsofrailandroadnoiseweremutuallyre‐
inforcing,anincreaseinroadnoiseovertimewouldleadtoahighernoisecapitalizationeffecteven
intheabsenceofachangeinnoiseaversion.However,inanancillaryanalysis,wefindthattherail
noisecapitalizationeffectdecreases in thepresenceofhigher levelsofroadnoise, i.e. railnoise
matterslessifthereisalreadyalotofroadnoise.So,withoutapresumedincreaseinroadnoise
levelsovertime,therailcapitalizationeffecttodaywouldlikelybeevengreater,implying,again,a
largerincomeelasticity.Ifwerelaxtheassumptionofhomogeneouspreferences,itseemsreason‐
abletoexpectthatafter100yearsofsortingmostnoisesensitivehouseholdswillhaveleftthenois‐
iestareas(KuminoffandPope,2014).This,again,mutesthecontemporarynoisecapitalizationef‐
fectandincreasestheimpliedincomeelasticity.However,theoverallincreaseinnoiselevelsacross
thecitycouldalsoleadtothemarginalbuyerinanoisyareabeingmorenoisesensitive,sothatthe
Easevs.noise 26
neteffectofsortingisambiguous.Importantly,rapidrailtransitinBerlinwasrelativelymorepop‐
ularamongwealthypeopleinthepastsincefareswhererelativelyhigherand,intheabsenceof
cars,rapidtransitwasthefastestmode.So,likely,averageincomeinthestudyareaincreasedata
ratelowerthancalibrated,implyingalikelydownwardbiasinourincomeelasticityestimate.Thus,
onbalance,webelievethat2.2isalower‐boundestimateoftheincomeelasticityofthenoisedis‐
amenityvalue.
5.1.2 Access
Accordingtoourestimates,thelandpricecapitalizationeffectofaone‐kilometerreductionindis‐
tancefromthenearestmetrostation(treatingsubwayandcommuterrailassubstitutes)declined
fromabout20.2%to15.5%.Becauseoftheincreaseintheshareoflandinthevalueofhousingthis
decreaseinthelandpricecapitalizationeffectcorrespondstoanincreaseinthehousepricecapi‐
talizationeffectfrom3.6%to5.0%.Thisiswithintherangeofrecentdifference‐in‐differenceesti‐
matessuchasbyGibbons&Machin(2005),whoreporta1.5%to5%range,orDubéetal.(2013),
whoseestimates implyaper‐kilometereffectof7%.The implied incomeelasticityof theaccess
amenityvalueis1.4.Becausethedistance‐from‐stationcapitalizationeffectcapturesthevalueof
theassociatedwalkingtime(Gibbons&Machin2005),theincomeelasticityofthevalueofstation
accessshouldgeneralizetothevalueoftime.Itisthereforenotablethatourestimatesaresignifi‐
cantlylargerthanthecross‐sectionalestimatesoftheincomeelasticityoftraveltimevalueinthe
literature,whichtendtobebelowunity(Börjessonetal.2012reportacentralestimateof0.6‐0.7).
Oneconcernregardingthecomparabilityofthehistoricandcontemporaryestimatesisthatrail
transitwasrelativelymorevaluableinthepastsincemass‐producedcarswerenotyetavailableas
affordablesubstitutes.Atthesametime,themetrorailnetworkhasexpandedsubstantiallyover
time,nowofferingconnectionstoagreatervarietyoflocations,whichshouldincreaseitsvalue.In
anetworkanalysis,wefindthatthetwooffsettingeffectsarelikelyofcomparablemagnitude.The
effectsofsortingwithrespecttotheaccessamenitygo,again,bothways.Preference‐basedsorting
overacenturymakesitmorelikelythathouseholdswithlargepreferencesforrailtransitlocate
closetostations.However,theexpansionofthenetworkmakesitmorelikelythatthemarginal
buyerinawell‐connectedareatodayhasarelativelylowerpreferenceforrailaccessthaninthe
past.Giventhatincomesortinglikelyleadstoususinganexaggeratedvalueforincomegrowthnear
metrostations,wetentativelyconcludethat1.4isalower‐boundestimateoftheincomeelasticity
oftherailaccessamenityvalue.
Easevs.noise 27
5.2 Fiscalcaseforundergroundmetrolines
Buildinganundergroundlineissignificantlymoreexpensivethanbuildinganelevatedline.Under‐
groundlines,conversely,avoidsizabledisamenities.Inthissection,weprovidesomesimpleback‐
of‐the‐envelopecalculationstoevaluatehowlongittakestorefinancetheextracostsviaproperty
taxrevenues.Tothisend,weestimatetheextracostofahypotheticalundergroundLineA,theextra
propertyvaluegeneratedinthiscounterfactual,andtheassociatedextrataxrevenues.
5.2.1 Extracost
Bousset(1935)reportstheper‐kilometerconstructioncostsfor31segmentsoftheBerlinmetro
railnetworkopenedby1930,includingper‐kilometercostofabouttwomillionReichsmark(RM)
forafive‐kilometerslongsubsegmentoftheelevatedpartofLineA.Multiplyingtheper‐kilometer
costbythetotallengthoftheelevatedsectionofeightkilometersyieldsconstructioncostsofabout
16millionRM.Toapproximatetheextracostassociatedwithahypotheticalundergroundsection,
we run an auxiliary regression of the natural log of per‐kilometer construction costs against a
dummyindicatingundergroundsections,controllingfortrackwidthandperiod(fiveyears)effects.
Theresults,reportedinSection8intheappendix,indicatethatbuildinganundergroundsectionin
theearly20thcenturyinBerlinwasaboutthreetimesasexpensiveasbuildinganelevatedsection.
MultiplyingtheestimatedconstructioncostofLineAbythisfactoryieldsacounterfactualconstruc‐
tioncostofabout50millionRMandanextracostfortheundergroundlineofabout34millionRM.
It isnoteworthythatthecurrentruleofthumbsuggestscostsofanundergroundlineareabout
twicethecostofanelevatedline(Flyvbjergetal.2008).So,theextracostfortheconstructionof
undergroundlineshavedeclinedovertime.
5.2.2 Extrapropertyvalue
Tocomparetheextracostofconstructiontotheaggregatedeffectonpropertyvalues,weaggregate
theplot‐levellandpriceobservationstoa50×50‐metergrid,whichallowsforrichspatialvariation
inrailnoiseand,atthesametime,ensuresthatwecovertheentirebuilt‐uparea.Undertheas‐
sumptionsmade in section 2.6, the noise‐induced change in property value in each grid cell is
ln / , where is noise level attributable to Line A and ln /
1 lnΩ / istherelativehousepricecapitalizationeffectofaone‐decibelincreaseinnoise.
SincetheCobb‐Douglashousingproductionfunctionimpliesthat 1/ 1 Ω ,wecanex‐
presstheimpactonpropertyvalueasafunctionoftheestimatedhousepricecapitalizationeffects
andtheaggregatelandvalue:
Easevs.noise 28
11
Ωln
, (8)
Intuitively,inequation(8),weholdthecapitalstockconstantsuchthatthevalueoftheproperty
increasesduetoanincreaseinthevalueoftheunderlyingland,exclusively.Thisway,weonlyac‐
countfortheincidenceontheimmobilefactor,i.e.weavoidtheproblemthatapolicy‐inducedin‐
creaseinthequantityofhousingstockatonelocationdisplacesdemandinotherareas.Theresult‐
inglandpriceeffectsbygridcellare illustratedintheappendix(section9). Inthiscontext, it is
worthemphasizingthatourplots includeall typesof landuses; theaggregate landvalueeffect,
therefore,reflectsbothchangesinutilityandproductivity.
Table3providesacomparisonoftheextracostforanundergroundvariantofLineAandtheag‐
gregatedimpactonbuildingvaluesthatwouldresultfromtheassociatednoisereduction.Wepro‐
videthecomparisonfortheactualhistoricalscenario(usingourhistoricallandpricecapitalization
estimates)andacounterfactualscenarioinwhichweapplythecontemporaryestimateoftheland
pricecapitalizationeffect .Thiscounterfactuallandpricecapitalizationeffectinflatesthees‐
timatedcontemporarylandpricecapitalizationeffect bytheratiosofthecontemporaryover
thehistoricalland(1 )andhousingexpenditure( )sharestoreflectthatthesamewillingness
topaywith lowershareparameters impliesa largerpercentage landpricecapitalizationeffect:
.
Basedonourhistoricalnoiseestimates,theaggregateincreaseinpropertyvaluesinacounterfac‐
tualscenariowithanundergroundLineAamountstoslightlymorethanonehalfoftheextracost
ofgoingunderground(18.6millionRM).Itisimportanttonotethattheseresultsdonotrejecta
welfarecaseforanundergroundLineAsincepositivehealthbenefitsarelikelyimportant,butun‐
likelytofullycapitalizeintopropertypricesduetolackofpublicawareness(Navrud,2002).Also,
anundergroundlinerelativetoanelevatedlinegenerateswiderbenefitstootherthanlocalresi‐
dentsandfirms(e.g.,tovisitorsandtourists).Yet,applyingthecounterfactualcontemporaryland
pricecapitalizationeffect,thegeneratedpropertyvaluealonealreadymorethanoffsetstheextra
costsofgoingunderground.Intheory,locallandlordswouldbeabletobeartheextracostforan
undergroundlinewithoutmakinglosses.
5.2.3 Extrataxrevenues
Whilelandvaluecaptureschemesareoftendifficulttoimplementinpractice,theincreaseinthe
property tax basemechanically generates revenues and, therefore,may be a less controversial
Easevs.noise 29
meansofrefinancinginthelong‐run.InGermany,thepropertytaxisdeterminedastheproductof
the tax base (the assessed value of the property, the so calledEinheitswert), a tax rate (Grund‐
steuermesszahl)andataxfactor(Hebesatz).SincetheEinheitswertisfixedatahistoricvalue,prop‐
ertytaxrevenuesareinsensitivetochangesinlocational(dis)amenities.However,propertytrans‐
actiontaxesrespondimmediatelyastheyareleviedonactualtransactionprices.Toapproximate
theyearlytaxrevenuesresultingfromnoise‐inducedchangesinpropertyvalue,weconsiderthe
6%propertytransactiontaxratecurrentlyapplicableinBerlinaswellasahistoric(pre‐1998)rate
of3.5%.Moreover,weconsider5%and10%probabilitiesofanypropertybeingtransactedina
givenyearsinceempiricalevidencepointstoaverageholdingperiodsbetween10and20years
(Collettetal.,2000:Fisheretal,2004).Inappendixsection11,wediscusstheGermanpropertytax
environment ingreaterdetailandshowthat inmoreconventionalproperty taxsettingssimilar
fiscalrevenueswouldbegenerated.
Inafurthersetofauxiliaryregressionsofthenaturallogoflandpriceonlocationfixedeffectsand
ayeartrend,wefindthatannuallandpriceappreciationratestendedtofluctuatearound5%in
Berlinfromthelate19thcenturytotheearly21stcentury,whichisclosetothemeaninterestrate
acrossyearsinthesameperiod.Moreover,thereisapositivecorrelationbetweenthetwovariables
(seesection10intheappendix).Thus,itseemsreasonabletomakethesimplifyingassumptionthat
inthelong‐runlandpricesgrowataratethatequatestotheopportunitycostofcapital.
Tab.3.Thefiscalcaseforanundergroundline
(1) (2) (3) (4) (5) (6) (7) (8)Noisepreference Historic ContemporaryRailnoisecapitalizationeffectonhsoueprices 0.41% 0.41% 0.41% 0.41% 3.32% 3.32% 3.32% 3.32%Estimatedtotalcost(million1900RM) 15.94Estimatedundergroundextracost(1900RM) 34.36Aggregatednoiseeffectbuildingvalue(millionRM) 18.6 18.6 18.6 18.6 151 151 151 151Transactiontaxrate 0.04 0.04 0.06 0.06 0.04 0.04 0.06 0.06Transactionprobability 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10Yearlytaxrevenue(million1900RM) 0.03 0.07 0.06 0.11 0.26 0.53 0.45 0.91Yearstorecoverundergroundextracosts 1056 528 616 308 130 65 76 38
Notes: Contemporarylandpriceeffectadjustedforchangesinlandshareandhousingexpenditureshare(landpricecapitalizationeffectinflatedbytheratioofcontemporaryoverhistoricshares).CostestimatesbasedonBous‐set(1935).Estimatedtotalcostresultfrommultiplyingthereported1902perkmcostsofoverelevatedsec‐tionsby8km(thelengthoftheelevatedsectionsoftheLineA).Theestimatedundergroundextracostresultmultiplyingthetotalcostbythepercentageextracostsforundergroundsegmentsobtainedfromanauxiliaryregressionreported inSection5of theappendix.Yearstorecoverextracostsarecalculatedundertheas‐sumptionthatpropertyvaluesgrowataratesimilartocostofcapital(seeappendix9forajustification).
Undertheassumptionsmade,itturnsoutthatbasedonourestimatesofthehistoricallandprice
capitalizationeffects,itwouldhavetakenhundredsofyearstorecovertheextracostsviaproperty
taxes.Therefore,itisperhapsnosurprisethatLineAwasbuiltasanelevatedlineandthatittook
Easevs.noise 30
majorprotestsandpoliticalpressuretoforcethelineundergroundwithintheboundariesofChar‐
lottenburg.Incontrast,underthecounterfactualcontemporarycapitalizationeffect,tax‐revenues,
dependingontheassumedtaxrateandtransactionprobability,wouldhaverefinancedtheextra
cost foranunderground linewithin38to130yearsand, thus, likelywithin thepast lifetimeof
LineA.
6 Conclusions
Weusedifference‐in‐differencesandspatialdifferencesdesignstoestimatethelandpricecapitali‐
zation effects of the contemporarymetro rail network in Berlin andGermany’s first electrified
metrorailline,LineA,whichopenedmorethanacenturyago.Wefindthatthelandprice(implied
houseprice) capitalizationeffectof a10‐decibel reduction in railnoise increased from4.2% to
13.0%(1%to4%).Theeffectofaone‐kilometerreduction indistance fromtheneareststation
decreased(increased)from20.2%to15.5%(3.6%to5.0%.).Fromtheseestimates,weinfernovel
estimatesofthelong‐runincomeelasticitiesofthevalueofnoisereductionandtransportaccessof
2.2and1.4.Whilesignificantuncertaintysurroundstheseelasticityestimates,weviewthemas
likelylower‐boundestimates.Thus,ourtentativeconclusionisthatthelong‐runincomeelasticities
oftransport(dis)amenityvalueslikelyexceedtheirshort‐runcounterpartswhichhavebeenesti‐
matedatbelow‐unityvalues.
Thisfindinghasimportantimplicationsfortransportinfrastructureappraisalsasitsuggeststhat
timeandenvironmentalqualityareluxurygoodswhosevalueswilllikelyincreaseinabsoluteand
relativetermsasincomesrise.Whiletheexistingbelow‐unitycross‐sectionalincomeelasticityes‐
timatesarecertainlyrelevantfortheassessmentofthedistributionalconsequencesofinvestments
within generations, larger values may be required for the assessment of distributional conse‐
quencesacrossgenerations.Aswedemonstrate,usingBerlin’sLineAasacaseinpoint,thewelfare
caseforconstructingundergroundraillinesismuchstrongertodaythanacenturyagobecausethe
valueofaquietenvironmenthasincreasedmorethanproportionatelytoincome.Inanticipationof
likelyincreasesinrealincomes,infrastructureappraisalsthatseektofullycapturenet‐benefitsto
futuregenerations,shouldinflateratherthandeflatecontemporary(dis)amenityvalues.
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