O -B decOmpOsitiOn: methOds applicatiOns. a literature · Oaxaca-Blinder wage decomposition: Methods, critiques and applications. ... independent variables depend on the microeconomic

[237]

* TheauthorsaremembersofGRANECO,researchgroupfromInstitutodeEstudiosEconómicosdelCaribe,UniversidaddelNorte.

Oaxaca-Blinder wage decOmpOsitiOn: methOds, critiques and applicatiOns. a literature review

CarlosG.Ospino*PaolaRoldánVasquezNaciraBarrazaNarváez

Fechaderecepción:noviembrede2009Fechadeaceptación:diciembrede2009

revista de economía del caribe n° 5 issn:2011-2106

artículo de reflexión

LadescomposiciónsalarialdeOaxaca-Blinder:Métodos,críticasyaplicaciones.Unarevisióndelaliteratura

revistadeeconomíadelcaribenº 5(2010)págs.237-274[238]

Oaxaca-Blinderwagedecomposition:Methods,critiquesandapplications.ALiteratureReview

a b s t r a c tThis document outlines a series of works developed over severaldecades–fromtheoriginalandindependentworksofBlinder(1973)andOaxaca(1973)-withtheaimoffacilitatingthecomprehensionof the technique for wage decomposition and its methodologicalimprovements and applications over time. Similarly, the analyzedapplications serveasaguide for thedevelopmentofworkrelatedto theestimationofwagegapsbetweengroupsof individualsandtheircauses.

k e y wO r d s :WageDecomposition,Blinder,Oaxaca,Heckman,GapWage.j e l c O d e s :J33,J71.

r e s umenEstedocumentorevisaunaseriedetrabajosdesarrolladosalolargodevariasdécadas-desdelostrabajosoriginaleseindependientesdeBlinder(1973)yOaxaca(1973)-conelfindefacilitarlacomprensióndelatécnicaparaladescomposiciónsalarial,susmejorasmetodo-lógicasyaplicacionesa lo largodel tiempo. De igualmanera, lasaplicacionesanalizadassirvendeguíaparaeldesarrollodetrabajosrelacionadosconlaestimacióndebrechassalarialesentregruposdeindividuosysuscausas.

p a l a B r a s c l av e :Descomposiciónsalarial,Blinder,Oaxaca,Hec-kman,BrechaSalarial.c l a s i f i c a c i ó n j e l :J33,J71.

revistadeeconomíadelcaribenº 5(2010)págs.237-274 [239]

CarlosG.Ospino,PaolaRoldánVasquez,NaciraBarrazaNarváez

INTRODUCTION

Thewagedifferencesbetweensimilargroupsareaphenom-enonthat isofconcerntothose investigatingtheevolutionof labormarkets; thesedifferencesmaybedue todifferentlevelsofqualificationoftheworkforce-somethingthatisac-ceptableandfair-ortotheexistenceofdiscrimination-caseinwhichthereisnotajustifiedreason-.Itistheunfairnessofthissubjectthatmakesthisproblemworthyofbeingstudiedandunderstood,inordertoidentifythemeanstodevelopandimplementsuitablepublicpolicies.

Thetermdiscriminationappliestonotoriouslyidentifiablegroupsgiventheirreligious,physical-race,age,sex-andsocialpractices.Thereisdiscriminationifpeoplefromaparticulargroupreceiveadifferenttreatmentjustforbeingapartofthatgroup;suchtreatmentgenerallyplacesthematadisadvantage(Tenjo:2009).Thegroupthatisdiscriminatedagainstislabeledminorityorminoritygroupandtherestofthepopulationisreferredtoasthemajorityormajoritygroup.Giventhatlaborincome,isoneofthemainsourcesofincomeformostpeopleindevelopingcountries,thefocusofthecurrentreviewwillbeonwagediscrimination.

In thisorderof ideas, it is said thatwagediscriminationoccurswhenanindividualsimilartoanother,whoonlydiffersinrace,sexorotherpersonalcharacteristics,receivesalowerwageforotherreasonsthantheperformanceintheirwork.Ingeneral,issociallyandeconomicallyimportanttoidentifywhethertherearewagedifferencesbetweenminoritiesandmajoritiesandwhatitscausesare;Therefore,itcomesasnosurprisethatresearchershavedevelopedmethodstoestimatethedifferencesinwagesandhavedevelopedtheoriestoexplaintheoriginofthesedifferentials.



Thepaperconsistofeightsectionsincludingthisintroduc-tion;inthesecondweexposethetheoreticalfoundationsofthemethodologydevelopedindependentlybyOaxacaandBlinderin1973forestimatingwagegaps;wethenexposetheoriginalmethodologydevelopedbytheseauthors.Inthefourthsec-tiontheoriginalimplementationisoutlinedfollowedbythecriticismithasexperienced.Inthesixthsectionweexposesomemethologicalimprovementsthathavebeenappliedtotheoriginalmethodologyfollowedbythereviewofahand-fulofempiricalimplementation;thefinalsectionsconcludesshowingtheimportanceofthistechniqueandaninvitationforfurtherstudyofotherdecompositiontechniques.

1. OAXACA–BLINDERWAGEDECOMPOSITION.

ThestandardmethodforwagedecompositionoftheOaxacaandBlindermethodologyhasbeenwidelyusedtoexaminediscrimination in the labor market.The technique breaksdowntheaveragewagegapexistingbetweentwodemographicgroupsintotwosummands:thefirstoneshows,differencesinqualifications,thedifferencesthatareexplainedbythemodel;andthesecondoneshows,differencesinthestructureofthemodel,i.e,thosedifferencesnotexplained;theunexplaineddifferenceisanestimateofdiscriminationinthelabormarket.(Oaxaca:1999)

a. TheoreticalFoundations

Ingeneral,thereisconsensustosaythatdiscriminationagainstwomen takesplacewhen the relativewageearnedbymenexceedstherelativewagethatwomenwouldhaveobtained



inthecasethatmenandwomenwerepaidonlytakingintoaccountthepersonaltechnicalcharacteristicsthataffectjobperformance.Oaxaca(1973)formalizedthisideaproposingtheconceptofadiscriminationcoefficient(D)asameasureofdiscrimination:

WhereWm/Wfistheobservedrelationshipbetweenthemaleandfemalewages;and(Wm/Wf

)0isthewomentomenwageratiointheabsenceofdiscrimination.Ifthefirmsperforminanondiscriminatinglabormarketfollowingtheprincipleofminimizingcosts,Oaxaca(1973)expressesthat:

WherePMmandPMfarethemarginalproductivityofmenandwomen,respectively;inotherwords,acceptingtheneo-classicalassumptionthatanindividual’swageisequaltohermarginalproductivity.

Inthissense,Oaxaca(1973)exposesthatiftherewerenodiscrimination,thewagestructurewhichaffectswomenalsocouldbeappliedtomen,orviceversa.Thesecasesindicatethatwomen,intheabsenceofdiscrimination,onaveragewouldreceivethesamesalarythatmen,howeverdiscriminationtakestheformofwomenthatreceivelessincomethanwhatanon-discriminatorylabormarketcouldgivethem.



IntheparticularcaseoftheUSeconomy-asBlinder(1973)mentioned-wasverywellknownthatwhitesearnedwageshigherthanblacksandmenearnedwagessubstantiallyhigherthan women.Therefore, the assumption that earned wageswereequaltothemarginalproductivitycouldnothold.

b. Methodology

Blinder(1973)proposesthatinordertocalculatedecomposi-tionitmakessensetoestimatefirst.

Thefollowingequationsofincomeformenandwomen:

wheretheHsuperscriptindicatesthehighsalarygroup[al-wayswhitemeninthestudyofBlinder1973]andsuperscriptLindicatesthesetoflowwagesgroup(asalternative,blackmenandwhitewomen).Yi isthelevelornaturallogarithmofprofit, incomeorwagesrateandX1i,…,Xni are thenobservablecharacteristicsusedtoexplain Y1

Asimplewaytocalculatethegenderwagegapanditscausesistosubtractthelow-wagegroupincomeequationfromthehigh-wagegroupincomeequation,assumingthatthedifferencebetweenthe

1Blinder, Alan S (1973), “Wage Discrimination Reduced Form andStructuralEstimates”,JournalofHumanResources.Vol8,N.°4.Pág438.



intercepts of the equation corresponds to discrimination2; how-ever,Blinder(1973)proposesthattheunexplainedportionofthedifferencecomesfromboth:thedifferencesincoefficients,asthedifferencesinaveragecharacteristicsoftheminoritygroup.Blinder(1973)modeleditsproposalasfollows:

Wherethefirsttermrepresentspartofthewagegapthatcanbeexplainedbydifferencesintheobservedcharacteristicsofin-dividuals-endowmentspossessed-andthesecondterm3reflectstheunexplainedportionofthegap,andthereforeisinterpretedastheeffectsofdiscrimination.

Insummary,themeasuresexposedbyBlinder(1973)are:

“R=raw differentials

E = Portion of the differences attributable to differential in endowments

C = Portion of the differences attributable to differentials in the

coefficients

2Asfollows: andthequantitythatiscapturedbytheintercepts ;-thislastexpressionusedbeattributedtodiscrimination.

3InwordsofBlinder(1973)thesecondpartisthedifferencebetweenhowthehighsalariesequationvaluesthefeaturesoflowwagesgroupandhowtheequationoflowwagesreallyvaluesit



U= Unexplained portion of the differential

D = Portion of the differential attributable to discrimination = C +U”4

Duringestimationitmustbetakenintoaccountthatitiscriticaltouselaborincomesofindividualsasthedependentvariable;thisisduetothefactthat,ingeneral,surveysincludeincomesotherthatlaborincomes.Ontheotherhand,selectedindependent variables depend on the microeconomic wagedeterminationmodelchosen.Bearinginmind,ofcourse,thatcorrelationdoesnotimplycausality,andiftheinterestistofindthecausesofthewagegapyoumustspecifyaquiteaccuratemodel.(Blinder:1973)

c. Firstapplications

i. Blinder(1973):

Blinder(1973)inhisarticle,Wage discrimination: reduced form and structural estimates useswageregressionsofwhitemen,blackmenandwhitewomentoanalyzethewagedifferentialbetweenblackandwhitemenandthewagedifferentialbetweenwhitemenandwomen.

Blinder(1973)indicatesthatapartofeachwagedifferentialisduetodifferencesin“objective”characteristicssuchaseduca-tionandexperience,whileanotherpartofthedifferentialisnotexplainedbythesecharacteristics.Itisallaboutansweringquestionsabouthowmuchofthewagegapbetweenwhitesandblacks,isattributabletohighereducationamongwhites;or

4Ibíd.Pág439.



howmuchofthewagedifferentialsbetweenmenandwomenisduetothefactthatmenmayhaveaneasieraccesstobetterpaidjobs.

ToanswerthesequestionsBlinder(1973)estimatedtwoequationsofincome.

First,estimatedastructuralmodeldefinedas:

Wherewisthewageperhour;Edisavectorofsixeduca-tionaldummyvariables;Occisasetofeightdummiesforoccupation;Jisadummyforvocationaltraining;Mis1forthemembersoftradeunionsand0otherwise,Vis1forvet-eransand0otherwise;Tisasetofsixdichotomousvariablesforstayinginthecurrentwork;Bisasetof13variablesoffamilyhistory;Zisasetofotherexogenousvariables,andf,g,h,k,l,mandnarelinearfunctions.Inthismodel,w,Ed,OCC,J,M,VyTaretakenasendogenous,whileByZareexogenous.TheelementsofZthatcomeintotheequationofwageswithnonzerocoefficientsarehealth,age,residenceandthelocallabormarketconditions.Structuralestimates-thathaveabiasunlesstheerrortermsarenotcorrelated-wereobtainedbyordinaryleastsquares5.

Additionally,Blinder(1973)estimatesthereducedform6ofincomesequationusingtheleastsquaresmethod,thereduced

5Ibid,Pág441.6Thereducedequationislogw=F(B,Z)+v1



equationincludesBandZvariablesthatareomitted-explic-itly-inthestructuralequation.Overall,theestimationofthereduced form takes into account individuals’ conditions ofbirthtoshowtheconditionalexpectationofwagesearnedbythem.Foritspart,thestructuralestimatesreflectthecondi-tionalexpectationofincomeearnedbytheindividualtakingintoaccountthecurrentsocio-economicstatus.

Byanalyzingtheincomegapbetweenwhitemenandblackmen,Blinderfindsthatcomparingstructuralcalculationsanoverallwageadvantageof50.5%ofwhitesoverblackswasobserved; another finding revealed that 30.7% of the dif-ference (around60%of the total) is attributable toblacks’lowerendowments.Similarly,Blinder(1973)analyzeswagedifferentialsbetweenwhitemenandwomenandfinds thatmostfamilyhistoryvariablesusedtoestimatethestructuralequationoperate in favorofwomen reflecting its influencethroughthecoefficients.

ThecoefficientsestimatedbyBlindershowedthatwhitewomenearnmoreiftheyhaveeducatedparentsandiftheywereraisedinacityintheSouth,andtheninfacttheyben-efitedalso(whilemalesdidnot)ofhavingpoorparentsandbeingraisedonfarms.Furthermore,apartfromtheage,themainadvantagewhitemenhadwas lessresponsiveto locallabormarketconditions.

According toBlinder, inregressionsdirect labormarketdiscrimination accounts for around two-thirds of the wagedifferentialandaboutonethirdofthedifferenceofthedis-crimination is due to other endogenous variables, such aslaborsituationandlabortenure.Inotherwords,itdoesnotattribute anypart of the labordifferential todifferences inlaborcharacteristics.



Havingsaidthat,itgoesthatoneofthemainconclusionsoftheworkofBlinder(1973)isthat,whilethedifferentialinsalarybetweenwhitesandblacksandbetweenwhitewomenandmenwasverysimilar insize,decompositionshowsthequalitativenatureofthedifferencesbyraceandsexdiffereddrastically.

ii. Oaxaca(1973):

TheincomeequationestimatedbyOaxaca(1973)foreachgroup(byraceandsex)hasa“semi-logarithmic functional form as follows:

Where:

= the hourly wage of the i - th worker, = a vector of individual characteristic,

= a vector of coeficients, = a perturbance term.7

Duetothelackofdataontheactualnumberofyearsofworkexperienceforindividuals,Oaxacadefinedaproxyfortherealworkexperiencethatincorporatesthemodelofin-vestmentinhumancapitaltraining.TheproxyofexperienceproposedbyOaxacaisasfollows:

Xi = Ai – Ei – 6

7Oaxaca,RonaldL(1973),“Male-FemaleWageDifferentialsinUrbanLaborMarkets”,International Economic Review, 9.Pág695.



WhereXiispotentialexperienceAi isthei-thindividual’s

ageandEi thenumberofyearsofstudyapprovedbythei-thindividual. Potential experience and actual experience willmatchonlyifindividualsobtainedtheiremploymentsimme-diatelyaftercompletingtheirstudies;thisdefinitionimpliesthat individuals do not experience unemployment, or thatindividualsdidn’tworkwhiletheystudied.Forwomen,thecalculationofpotentialexperiencehasalimitationassociatedwiththetimespentonhouseholdandchildbearingactivities.Thereforethepotentialexperienceisareasonableapproxima-tiontotherealexperienceofmenbutexaggeratestheactualyearsofworkforwomen.(Oaxaca:1973).

Ingeneral,itisexpectedthatproblemsassociatedwiththedefinitionofpotentialexperiencedon’thaveamajorimpactontheestimationofdiscrimination;however,inanattempttohandletheproblemofthemissingexperience,Oaxaca(1973)includedthenumberofchildrenborntoeachwomanintheanalysis.Thissolutionhasaproblemassociatedwiththecorre-lationbetweenthevariables:numberofchildrenandpotentialexperience,however,it´sintroductionasacontrolmechanismwasconsiderednecessary.

Other explanatory variables used by Oaxaca (1973) aredefinedasfollows:

Education:yearsofschoolingcompleted(linearandquadraticterms);Class of Worker: dummy variables for union membership(privatelyemployedwageandsalaryworker),governmentemployed,andself-employedwithnonunionprivatewageandsalaryworkersasthereferencegroup;



Industry:dummyvariablesforU.S.Censustwodigitindustrieswithretailtradeasthereferencegroup;Occupation:dummyvariablesforU.S.Censustwodigitoc-cupationswithsalesworkersasthereferencegroup;Health Problems:dummyvariable=1iftheindividualreportshealthproblemsthataffectthekindoramountofworkheorshecanperform,and‘0’otherwise;Part-Time:dummyvariable=1iftheindividualworkslessthanthirty-fivehoursaweek,and‘0’otherwise;Migration:a)dummyvariableIiftheindividualhasmaintainedaresidencemorethanfiftymilesfromhisorhercurrentad-dresssincetheageofseventeen,and‘0’otherwise,b)YRSM:numberofyearssincetheindividuallastmigrated(linearandquadraticterms);Marital Status:dummyvariablesforspousepresent,spouseabsent,widowed, anddivorced (or separated)withnevermarriedindividualsasthereferencegroup;Size of Urban Area:dummyvariablesforresidenceinStandardMetropolitanStatisticalAreaslessthan250,000(SMSA<250),greaterthanorequalto250,000butlessthan500,000(SMSA250-500),greaterthanorequalto500,000butlessthan750,000(SMSA500-750), and greater than or equal to 750,000 (SMSA750+)withurban,non-SMSA’sasthereferencegroup;andRegion:dummyvariablesforU.S.CensusregionsNorthEast,NorthCentral,andWestwithSouthasthereferencegroup8.

Themagnitudeoftheestimatedeffectsofdiscriminationwilldependonthechoiceofcontrolvariablesforthewageregressionsperformedbytheresearcher;therefore,thiselec-

8Ibid,pág698.



tion reveals researcher’s attitude towards what constitutesdiscriminationinthelabormarket(Oaxaca:1973).

ThedatausedbyOaxaca(1973)camefromtheSurveyofEconomic Opportunity of 1967.The used sub-sample wasformedbytheintersectionof:individualswhoreceivedasalaryperhourintheweekprevioustothesurvey;adultsaged16orolder,thoselivinginurbanareas,andthosewhoreportedtheirraceaswhiteorblack.

Theresultsshowachronicgapbetweenworkingmenandwomen’sfulltimeincome:

• Calculations based on the wage regressions showed58.4%discriminationamongwhitemenandwomenand55.6%amongblackmenandwomen.

• Furthermore,theeffectsofdiscriminationcalculatedfromtheregressionofwages,personal9characteristicsreflectedabout77.7%ofdiscriminationforwhitesand93.6%forblacks.

d. Critiques:

TheeconometricregressionanalysistechniqueproposedbyBlinderandOaxacatodeducethecausesofthegenderwagegaphasbeensubject toconsiderablecriticismthatrevolvesaroundthemodelspecificationandthechoiceoftheindepen-dentvariables(RiachandRich:2002).Belowisanoutlineofthesecriticisms:

9Itreferstoasetofequationsthatnotcontrolbyoccupation,industryandtheclassofworkersclass.



i.RosenzweigandMorgan(1976)saidthattheuseofageandagesquaredinsteadofworkexperienceandsquaredexpe-rienceinthestructuralequationdevelopedbyBlinder(1973)createsadifferentialbiasinestimatedreturnstoeducationformenandisthereforelikelythattheBlinderresultsreflectanexaggerationofthesizeofthecomponentofeducationthatexplainsthedifferenceinincomebetweenmenandwomenattributabletodiscrimination.

ii.Jones(1983)showedthatBlinder’s(1973)decomposi-tionmethodtoseparatethecontributionoftheconstanttermdiscriminationwasdefectiveinthepresenceofasetoffictionalvariables,sincethemagnitudeoftheestimatedconstanttermdependsonthereferenceout-of-samplegroup(OaxacaandRansom:1999).Ingeneral,Jones(1983)arguesthatelementsUandCofthedecompositionproposedbyBlinder(1973)areforthemostpartarbitraryandnotinterpretable.

WhattheabovediscussionshowsisthatthedecompositionoftheBlinder’sresidualterm-discrimination-cannotbedeterminedinauniquemannersincethevalueofthediffer-enceininterceptsdependsonthedecisionsofmeasurement.AnyspecificdecompositionusingBlinder’salgebrawillleadtoaseriesofestimates,buttheUandC10valueswillalwaysbearbitraryiftheydependonthearbitrarydecisionsofhowtosetthevariablesinvolvedintheprocessofdiscriminationor,inanysocialprocess11.

10U=Unexplainedportionofthedifferential yC=Portionofthedifferencesattributabletodifferentialsinthecoefficients

11Jones,F.L(1983),“OnDecomposingtheWageGap:ACriticalCom-mentonBlinder’sMethod,”JournalofHumanResources18.Pág130.



Inresponsetothiscriticism,OaxacaandRansom(1999)showedthatthefundamentalproblemsofidentificationlaybehindtheeffortsofresearcherstoestimateseparatelythecontributionsthatasetofvariableshaveonthecomponentofdiscrimination.Asforthedummyvariable,theproblemarisesfromthearbitrarynatureofthereferencegroupsthattheresearcherchooses;fortunatelygeneraldecompositionandtheindividualestimatesoftheeffectsofendow-mentsareinvarianttothechoiceofreferenceout-of-samplegroups.

However, theproblemgoes beyond identifying the interceptcomponent.Ingeneral,conventionaldecompositionmethodologiescannotidentifythesinglecontributionfromadummyvariabletothedecompositionofwages,becauseitisonlypossibletoestimatetherelativeeffectsofadummyvariable.(Oaxacaandransom:1999)Finally, Oaxaca and Ransom (1999) claim that almost all wageregression models contain categorical variables, so it is unlikelythatadetailedapplicationofdecompositionscanescapetheaboveidentificationproblem.

iii. Other criticism that can be made to the Oaxaca -Blinderapproachisthatitonlymeasuresthediscriminationinthelabormarket.Iftherearedifferencesinaccesstoendow-mentsthatarerewardedinthelabormarket,-forexample;ifwomenhaveworseaccess tohighereducationthanmen,orevenif,ceterisparibus,menaremorelikelytoworkthanwomen-thentheOaxaca-Blinderstandardapproachtendstounderestimatethediscriminationdegree(Madden:1999).

iv. Furthermore,Atal,ÑopoandWinder(2009)althoughthe decomposition Blinder - Oaxaca is the approach mostappliedinresearchaboutwagedifferentials,ithasthreenote-worthyflaws:First,thedecompositiononlygivesinformation



abouttheaveragewagegapomittingthedifferentdistributionofthisgapamongindividualsofasamegroup.Secondly,au-thorsmentionthatithasbeenobservedthattherelationshipbetween characteristics and wages is not necessarily linear,andfoundthatrecentdataviolatefundamentalimplicationsoftheMincermodel,whichisthekeyinputofthedecomposi-tions.Finally,thedecompositiondoesn’trestricttheanalysistocomparableindividuals,whichcanleadtoanupwardbiasofthecomponentassociatedwithdiscrimination.

v.Fromanempiricalperspective,themostseriousproblemthatthismethodologyhasisthatsinceestimatesofthecoef-ficientscapturebiasesgeneratedfrominformationproblems,errorsinthevariablesandselectivityprocesses,theinterpre-tationofthisresidualasameansofdiscriminationisdebat-able.However,itisworthmentioningthatnoempiricalworkis without problems and methodological questions. (Tenjo,RiveroandBernat:2002)

e. Methodologicalimprovements

Estimatesofwagesequationsoftencontaina sample se-lectionbias;thisbiasariseswhennon-observedfactorsthatinfluencethelikelihoodofparticipationarecorrelatedwithnon-observedonesaffectingwage.Undersuchcircumstances,theassumptions toensure theconsistencyof theestimatedcoefficientsofwageequationsarenotmet,andsincethecal-culationofthepercentageofdiscriminationisbasedonsuchestimates, itcauses theseresults toproducewrongconclu-sionsaboutthedegreeofwagediscriminationagainstwomen.(HernándezandMéndez:2005)



i. SelectionBias(Heckman:1979)12

Heckman(1979)discussesthebiasresultingfromtheuseofnon-randomlyselectedsamplestoestimatetherelationshipsbetween variables.The author mentions, in contrast to theusualanalysisof“omittedvariables”inEconometrics,thatintheanalysisofsampleselectionbiasissometimespossibletoestimate the variables that give rise to specification errors.Theestimatedvaluesoftheomittedvariablescanbeusedasregressorsallowingestimatebehavioralfunctionswhicharetheinterestobjectoftheinvestigation.

Inhisarticle,Heckman(1979)showedsampleselectionbiasasaspecificationerrorandpresentsasimplemethodofconsistentestimationthateliminatesthespecificationerrorinthecaseofcensoredsampling.Heckmanarguesthatsampleselectionbiasmayariseinpracticefortworeasons:first,theremaybeself-selectionofindividualsorunitsofresearchobjectsintothedata;Secondly,thedecisionsofsampleselectionmadebyresearchersordataprocessorsoperatealmostinthesamewayofself-selection.

Tosimplifytheexhibitionofthecharacterizationofselec-tionbias,Heckman(1979)considersthefollowingtwoequa-tionmodel:

whereXjiisavectorof1xKjexogenousregressors,βjisavectorofKjx1parametersand

12We reproduce Heckman’s original exposition in order to facilitatereader’sunderstanding.



The final assumption is a consequence of the randomsamplingscheme.JointdensityofU1i,U2i is (U1i,U2i).Theregressorsmatrixisoffullranksoifalldatawereavailable,eachequationparameterscouldbeestimatedbyOLS.

Heckmanproposesthecaseofestimatingequation(1a)butwheredatadoesnotappearinY1forcertainobservations,inthiscase,thecriticalquestionis¿whyisdatamissing?Theonlycostofhavinganincompletesampleisalossofefficiency.Toestimatetheequationitshouldbeawarethat:

Thepopulationregressionfunctionequation(1a)canbewrittenas:

Theregressionfunctionforthesubsampleoftheavailabledatais:

(i = 1, …, I )wheretheconventionthatthefirstobservations

/1<1haveavailabledataforY1ihasbeenadopted.

IfconditionalexpectationofU1iiscero,theregressionfunc-tionoftheselectedsubsampleisthesameasthepopulationregressionfunction.AnOLSestimatormaybeusedtoestimateβ1fortheselectedsubsample.

Inthegeneralcase



InthecaseofinterdependencybetweenU1iandU2i,wheredataformY1iarerandomlymissing,theconditionalmeanofU1iiscero.Inthegeneralcase,wherethemeanofU1iisdifferentfromcerothesubsampleregressionfunctionis:

TheselectedsimpleregressionfunctiondependsonX1iandX2i.Thefittedparametersestimatorsofequation(1a)inthese-lectedsampleomitthefinalpartofequation(2)asaregressor,sothatbiasresultingfromtheuseofnon-randomlyselectedsampleisconsideredasarisingfromthecommonproblemofomittedvariables.

InthewordsofMaradonaandCalderón(2000)selectionbiascomesinlargepartfromnotobservingwomenthathaveahigherreservationsalaryorthathaveloweropportunitycostsofstayingathome,orwhosecharacteristicsmakeitmoredif-ficulttoobtainemployment.

Tobetterunderstand theeffectsof selectionbiason theestimationofwagedifferentials,itisassumedthattheparticipa-tioninthelabormarketdependsontheindividual’sreservationwages.Forthisreason,ifthewageofferedbythemarketislessthanreservationwageoftheperson,itisexpectedthatpersondecidesnottobepartofthelaborforce,whileifmar-ketwageisgreatertheindividualentertoit.MaradonaandCalderon(2000)arguethatreservationwage(Wt)dependsonindividuals’personalcharacteristicsandhumancapitalstock,whilethemarketwage(WM)dependsonhumancapitalonly;



also,theauthorssupposethatthisdependenceislinearandisexpressedas:

WhereXisavectorofcharacteristicsofhumancapitalandYtoavectorofpersonalcharacteristicsandhumancapital,αandβ areparametersand,u1andu2 arerandomerrorswithzeromeanandconstantvariance.

InwordsofMaradonaandCarlderón(2000),thedifferencebetweenmarketandreservationwagesrepresentsthepropensityofpeopletoparticipateinthelabormarket,andismeasuredbyacontinuousvariablecalledI anddefinedasfollows:

Accordingtothis,awomanwilldecidetojointhelabormarketifthisvariabletakespositivesign.Ifthisisthecase,theexpectedvalueofthemarketwageforwomenwillnotdependonlyonthecharacteristicsofhumancapital(X)butalsoonthepersonalfeaturesincludedinthevectorY,whichareincludedintheconditionalexpectationoftheerrorterm.(MaradonaandCalderón:2000).

MaradonayCalderón(2000)exposedthattheerrortermhas conditional expectation with zero mean, however, nonconditionalexpectation13,whichisusedwhenweuseOLS,hasanon-zeromeanandcorrelateswiththeindependentvariables;

13



thesearethereasonswhytheOLSestimateswillbebiased.(MaradonaandCalderón:2000).

Itcanbeshownthattheerrortermexpectationconditionalontheparticipationdecisionisfeasibletobreakdownintwoterms:

Thefirst corresponds to the ratioof thedensity functionandthecumulativedensityassessedonthevalue foreachindividualfunction.ThistermisknownastheinverseoftheMill’sratioandistheexcludedvariableintheanalysisofthemarketwageequationuncorrected for selectionbias.Thesecondtermisthecoefficientofthetheoreticalregressionequations(A)and(B)errors.Thus,themarketwageequa-tioncorrectedforthepresenceofselectionbiasinempiricaltermsisstatedasfollows:

14

ThelambdavariablecorrespondstotheinverseMill’sratioinparticular:

WhereZ is avectorofcharacteristics thatdetermine theprobabilityoflaborparticipation, isavectorofestimatedparameterinaprobitspecification,sothatθ(.)anθ(.)are

14Maradona,PerlbachyCalderón,Mónica,“Estimacióndelsesgodese-lecciónparaelmercadolaboraldeMendoza”,FacultaddeCienciasEconó-micas,UniversidadNacionaldelCuyo,p.7.



thedistributionanddensityfunctionsofastandardnormalrespectively15.

Theparameterthataccompanieslambdaisrelatedtothestandarddeviationsandcovarianceerrorsinbothwageequa-tions.Theexclusionofthelambdavariablecausesabiasintheestimatesofthevector.Therefore,estimatesarebiasedunlessyouenteravalueforthevariablethatcorrespondstotheprob-abilityofbeingincluded(orexcluded)ofthesampleofpeoplewithincome(MaradonaandCalderón:2000).

Toresolvethisissue,Heckman(1979)developsamethodknownastwo-stepestimationmethodconsistingoffirstesti-matingaparticipationequationwhereaperson’sdecisiontoparticipateornotintheworkforcedependsonasetofper-sonalcharacteristics,incomeandhumancapitalvariables.Thisequationisspecifiedadhoc(MaradonaandCalderón:2000).

Insummary,thefirststageintheHeckmanmethodcon-sistsofalaborparticipationprobitestimationthatallowstheconstructionofthevariableλthatislaterincludedasanad-ditionalregressorinthesecondstagewhereawageequationisestimated(HernándezandMéndez:2005).

Thesecondstageistheestimateofwagesasafunctionofhumancapitalandthelikelihoodtoparticipate inthe labormarketvariables-lambda-.Thelatterisamodelforthede-terminationofincomealaMincer,correctedbythepresenceofselectionbias.(MaradonaandCalderón:2000).

15Hernandez,PedroyMendéz,Ildefonso(2005)“Lacorreccióndelses-godeselecciónenlosanálisisdecortetransversaldediscriminaciónsalarialporsexo:estudiocomparativoenlospaísesdelaUniónEuropea”,Estadís-ticaEspañola,Vol.47,Núm.158,p.183.



ii. Theinclusionofcorrectiontermsintowagedecomposition

Sampleselectionbiascorrectionintheestimatesofwageequa-tionsthroughthetwo-stepestimationproposedbyHeckman(1979)assumestheestimationofthefollowingexpressions:

Subscriptmreferstothemalesubsampleandftothefe-male.ThevariablewageWisafunctionofthehourlywage,usuallytheneperian logarithmofthevariable;x isavectorofoccupationalandpersonalcharacteristicsoftheindividualwiththesamecomponentsformenandwomen,βisthevectorofparameterstoestimate,λisthecorrectionterm(inverseMill’sratio),σisthecovarianceofunobservedfactorsaffectinglaborparticipationandthoseaffectingwageanduisarandomperturbationtermwhereE(u)=0.Becausethewagediscrimi-nationstudiesusetheseestimates,selectionbiasextendstothissubject.TheOLSestimatewhichisthesecondstageal-lowsustoexpresstheknownrelationshipbetweenincludedvariablessamplemeansandparameterestimates.(HernándezandMéndez:2005)

Themethodologydevelopedin1973byOaxacaandBlinderallowstobreakdownthewagegapbetweenmenandwomen



intwopartsofwhichoneisthedifferentialcausedbydiffer-encesintheobservedcharacteristicsofindividuals;andtheotherpartcorrespondingtothedifferentialbetweenthewageswhichisnotexplainedbythecharacteristicsofindividualsandthereforeassociatedwithdiscrimination.However,toincludethetermsofcorrection,someauthorsbreakthesalaryaveragedifferenceinthreesummands,thus:

wherethebarsabovevariablesindicatetheestimationofthecoefficientsataveragevaluesofthese.Then,addingandsubtractingtheterm givesthefollowingexpression:

Theterm correspondstothepartofthewagegap that can be explained by differences in the observedcharacteristics of individuals.On theotherhand, the term

reflectstheunexplainedpartofthegap,whichisduetodifferencesinthecoefficientsofXi,thistermisregardedastheeffectsofdiscrimination.Theterm isduetoselectionbiasandisgeneratedbythedifferencesbetweenthe incorporation pattern into the labor market men andwomenhave.

Selectionbiascorrectionhasnotbeenfreeofcriticism.AsinLewis(1986)inmostcasesthereisnotatheoreticalmodeltoexplain the specific selectionprocess, and to specify thevariablestoexplainit.Intheabsenceofthistheory,whatisusuallydoneistoincludeadhocvariableswhicharethought



toberelatedtothatprocess.Thisprocedurecanendupbyintroducingmoreproblemsthanitsolvesintheequationsofincome.Inmostcasesitisnotknowniftheprocedureiscap-turingthenatureofthedecisionsofindividuals,orratherthenon-lineareffectofvariablesincludedintheselectionequation.(Tenjo,RiveroandBernat:2002)

If the only reason for not reporting income is the factthatpeoplearenotinvolved,youmightthinkofapplyingtheHeckmancorrectiontoanequationofalaborparticipation,whosetheoreticalsupportisprettysolid.However,inpractice,nonreportofincomemaybeduetootherthings(otherthannon-participation)suchasopen-wideunemploymentorem-ploymentinoccupationsoffamilyassistantwithoutadefinedremuneration.Thisgeneratesadditionalcomplicationswhicharenotclearlydiscernible.(Tenjo,RiveroandBernat:2002)

f. Applications

i. Genderwagegap

Attheinternationallevel,severalauthorshaveexaminedthewage differential between men and women and its causesthrough wage decomposition a la Blinder–Oaxaca; findingrevealing resultsof theexistenceofdiscrimination inmostcases.Basicallyalloftheseauthorsestimatedmincerianincomeequationsasfollows:

whereWisthehourlywage,Yedurepresentsyearsofedu-cation,Expyearsofexperienceanduisarandomerrorwith



theusualcharacteristics(normaldistribution,expectedvalueofcero,constantvariance,independenceofobservationsandorthogonalitytoregressors).Themajorityofcases,intheab-senceofameasureofactualexperience,ameasureofpotentialexperienceisused.

Expectedcoefficientsderivedfromtheseestimatessignsareconsistentwiththehypothesisofthetheoryofhumancapital;i.e.anincreaseinincomeasyearsofeducationincrease(posi-tivesignforthevariableyedu)andexperience(positivesignforthevariableexp),butthatthiseffectisnonlinear,i.e.thattheincomedoesnotalwaysincreaseproportionally,butforhighlevelsofexperience,thecontributiontotheincreaseinincome,althoughpositive,diminishes(Bernat:2005).TheuseofHeckman’stwo-stepmethodofestimationisverycommontocorrectselectionbias.

We now summarize the findings of research where thegenderwagegapwasestimated,highlightingwherenecessary,papersweremethodologicalchangesintroduced:

• Paz(1998)estimatedincomegendergapforBuenosAiresandtheArgentineNorthwestinMay1997.UseddatacomefromtheEncuestaPermanentedeHogares(EPH),thestudiedpopulationcomprisesallindividualsbetween15and64yearsofage(WorkingAgePopula-tion).Fortheestimationof theregressionshealwaysusedaweightedsample.

Sheusedtwokindsofdependentvariables:a)thelogarithmofthemonthlyincome(Y);b)thelogarithmofthemonthlyincomeevaluatedatfulltime(YFULL).Inthefirstcase,the



matrixofindependentvariables(X)includedasanadditionalregressorthelogarithmofweeklyhoursworked(LNHOR).

ToobtainthevariableYFULLshefirstestimatedthefollowingregressionforbothsexesseparately:

WherePARTisadummyvariabletothepart-time;HRPARTandHRFULLaretermsofinteractionbetweentheweeklyhoursofpart-timeandtotal,respectively.Thisadjustmentisextremelyimportantgiventhestrongprevalenceoffemaleworkersinpart-timelabor.UsingtheestimatedcoefficientsforPART,HRPARTandHRFULL,YFULLwasconstructedaccordingtoequation:

16

Inthewordsoftheauthor,thefundamentalpropertyofthisvariableisthatit“punishes”incomeofthoseworkingmorethan40hoursperweekand“rewards”incomeofpart-timeworkers, i.e., homogenizes the equivalent to 40 hours perweekforthemarketincome.

TheobtainedresultsshowedthatthedifferencesinthegapbetweenGranBuenosAiresandtheArgentineNorthwestweresmallanditislikelythattheyrespondmoretotheroundingof numbers rather than economically relevant issues. Ob-servedgapislocatedinnotlessthan0.70ormorethan0.85,dependingonthespecificationofempiricalmodelsusedto

16Paz,Jorge(1998),“Brechadeingresosentregéneros.(ComparaciónentreelGranBuenosAiresyelNoroesteArgentino)”.19p.



estimatethem.Theportionofthegapthatisnotexplainedbytheendowmentsofhumancapitalandoccupationalpositiondoesnotdifferbetweenthetwolabormarketsandissituatedintheorderof90%approximately(Paz:1998).

• InthecaseofLatinAmerica,Tenjo,RiveroandBernat(2002)analyzetheevolutionofwagedifferencesbysexinArgentina,Brazil,CostaRica,Colombia,HondurasandUruguayintheestimationofthemincerianequationsformenandwomen,employeedandunemployed,foreachofthesixcountriesinstudy,usingwagedifferentialsOaxacadecomposition.

The authors estimated Mincer equations for men andwomen,withandwithoutselectioncorrection,foremployedandunemployed,foreachofthesixcountriesinthestudy.Thedependentvariableusedwasthehourly income;tocorrectforselection,anestimationofHeckman’stwo-stepmethodwasused.

Theauthorscometotheconclusionthattherearedifferen-tialsinmonthlysalariesbetweenmenandwomen,thatthesehavedeclinedsignificantlyinfavoroffemaleworkers,andalsothattheimmediatereasonwhywomenhavelowermonthlywagesthanmenisbecausetheyworkfewerhours.

Similarly,Tenjo, Rivero and Bernat (2002) observed asignificant level of job segregation by branch of economicactivityandoccupations.Howevertheymakeclearthatthissegregationisnotreflectedinlowerwagesforwomen.Thus,hourlywagedifferentialsbetweenmenandwomenappeartobeassociatedwithlaborremunerationpatternswithinsectorsandoccupation.



• DiPaolaandBerges (2000),calculated thegenderwage gap estimating income Mincerian functions forbothsexesandapplyingthetechniqueofBlinderandOaxaca.

The dependent variable, the logarithm of the monthlyhours,wascalculated fromthehoursperweekdeclared intheSurvey17bytheworker,dividedby7andmultipliedby30.Theyexpectedthatsignsandapproximatevaluesofthecoefficientsof the income functionmatched thehypothesisofhumancapital.Theauthorsalsostatedthatthecoefficientofthenaturallogarithmofmonthlyhoursworkedshouldbepositiveanditwouldbeinterpretedasanelasticity,indicatinginwhatproportionvariestheincometoapercentagechangeinhoursworked(DiPaolaandBerges).Theycorrectedtheproblem of selection bias by estimating labor participationequationasmentionedabove.

The model suggested by Dipaola and Berges (2000) forselectionbiascorrectionwasasfollows:

Where,Part1isfemalelabormarketparticipation(Dichoto-mousvariable=1ifthewomanreceiveslaborincomeand0=otherwise),Eiiswoman’sage,E1

2isagesquared,Siareyearsofschooling,Est11indicates1ststratum,eEst21indicate2ndstratum,Yjefe

1isheadofhousehold’sincome,Niisthenumber

17TheInformationusedcamefromthewaveofMay1997,ofthePerma-nentSurveyofHomesmadebytheINDECfortheareaofMardelaPlata.



ofhousemembers,πiisaresidualterm,subscriptiindicateswomani=1,........,548.

Theresultsshowthat:ifresultswerenotcorrectedandifwomenwerepaidasmen,thetotaldifferenceofthelogarithmofincomewouldbe0.471.Afterperformingthedifferencedecomposition,28%isexplainedbytheallocationofhumancapitalandtheremaining72%bythemarketstructure.Esti-matesforthisincomeselectionbias-correctedequationyieldeddifferentresults.Thetotaldifferenceofthelogarithmoftheincomeislower,0.196andreversestherelativeimportanceofthecomponentsthatexplain(humancapital78%and22%marketstructure)(DiPaolayBerges,2000).

• Johanson,KatzandNyman(2005)discusstheevolu-tionofwagedifferentialsand the factors thatmayberelated,yearbyyearthroughtheanalysisofcrosssectiondataoftheDepartmentofstatisticsofSweden(HEK)fortheyears1981and1983-98;thereforedecomposethewagedifferentialgenderaccordingtothestandardmethodofOaxaca(1973).

Thedependentvariableonestimatesis(thelogarithmof)imputedhourlywage.Variablesused in thewageequationsareagesquared,fictionalvariablesfor:theleveloftraining,requirementstobeablue-collarorwhite-collarworker,in-dustry,region,thecentralgovernment,theprivatesector,orlocalgovernmentemployeesandtoworkinmen-dominatedorwomen-dominatedoccupations(Johanson,KatzandNyman:2005).Authorsviewageasameasureoftheexperienceoflifeingeneral,thatcanaffectthewages.



Theresultsshowedthatthedifferencebetweenthegeo-metric averagewagesperhourofmenandwomen rankedbetween13and14percentoftheaveragewageofmenduring1983-1987.From1988itwasaround14-16%,exceptforagapof17percentin1990(Johanson,KatzandNyman:2005).

• Bernat(2005)analyzedthewagedifferentialperhourbetweenmenandwomeninsevenmajormetropolitanareasofColombiaintheperiod2000-2004;attemptedtoexplainthechangeinthedifferentialintheseyears,distinguishingtwocomponents:ononeside,thecontri-butionthatcangeneratehumancapitaldifferences,andontheother,adiscriminatorycomponent,understoodasanythingthat isnotexplainedbydifferences inthefirstcontribution(Bernat:2005).

Bernat(2005)estimatedwagedecompositionofOaxaca-Blindercorrectingforselectionbias,therefore,firstestimatesthe participation equation, using variables such as maritalstatus,headofthehousehold,theunemploymentrateofthefamily and the number of children, characteristics whichclearly affect theparticipationof an individual in the labormarket.Theincomefortherestofthefamilyisincludedasanapproximationoftheindividual’sreservationwage.Thehigherthisincome,thehigheritisexpectedthattheindividualhasmoretimetoanalyzeemploymentopportunitiesinthelabormarket,thecrossovereffect(cc)thatitincludesinvestigateswhetherbeingamarriedheadofthehouseholdorunmarriedhouseholdheadaffectsthedecisionoflabormarketparticipa-tion.(Bernat:2005).



Amongcities,thehourlywagedifferentials(onlysalariedworkers)werelowerinManizales,BogotáandMedellín.Forthesevencitiesconsideredtotal,discriminationwasat20%forsalariedand21%inaveragefornon-salaried,intheperiodunder review, althoughwithdifferent aggregate trends andbetweencitiesforthetwogroups(Bernat:2005).

ii. Otherapplications

Thissectionsummarizestheworkofseveralresearcherswhoestimatedwagegapsbyethnicity,nationality,amongothers:

• Johnson(1978)estimatedwagediscriminationbyin-dustryusingabroadsamplingofdataontheindividualcharacteristicsoftheworker,theindustrialemploymentandwages.Thisworkaimstoinvestigatehowcompeti-tivefeaturesofanindustryinfluenceitstendencytoen-gageinwagediscrimination.Johnson(1978)measuredthewagediscriminationduetotheresidualdifferencebetweenthesalariesofblacksandwhitesthatisnotduetotheirpersonalcharacteristics.

Theestimatedequationisasfollows:

Where,Wiisthesalaryforthei-thindividual,Xijarepersonalcharacteristics, α-β-δ-w-b are market determined param-eters,Xij

.Ri areinteractiontermswithraceandagroupofm

≤ncharacteristics,thatrepresenttheinteractionofdummy



employmentvariablesforwhitesandblacksintheindustryk,(k=1…P).

Racial discrimination by industry estimates are calculatedby,meaning;thewagegapbetweenwhitesandblacks inthesame industry,afterdiscountingthedifferences in theindividualcharacteristics18

According to the results found by Johnson, employersclassifiedascostsminimicersdiscriminatemoreinwagesthatemployerswhocanoperatemoreindependentlyofthecom-petitivemarketdiscipline.Theregulatedcompaniesseemtodiscriminatelessthanotherfor-profitemployers.

• Stewart(1983)attemptstoprovideempiricalevidenceaboutthedifferencesinoccupationalpositionsbetweenblackandwhiteimmigrantsbornintheUnitedKingdomthathavethesamepersonalcharacteristicsandonlydifferbytheircountryofbirth.Thisresearch,onlyexaminesthediscriminationinthelabormarketandthereforetheresultsmaybelessthantotaldiscrimination,duetotheoriginoftheindividuals.Also,theauthorindicatesthatdifferencesattributedtodiscriminationaretheresultofacombinationofracediscriminationanddiscriminationonthebasisofthecountryofbirth.

According to the author, estimated results revealed thatbetween75and100%ofthedifferentialaverageincomewascaused by differences in occupational level, indicating the

18Johnson,William(1978),“RacialWageDiscriminationandIndustrialStructure”TheBellJournalofEconomics,Vol.9,No.1.Pág72.



problemreferstothepolicyofentrytoworkinsteadofdif-ferentpaymentswithinasameoccupationlevel. Inspiteofchanging economic conditions, no evidence of movementsontheaveragewagedifferentialintheperiod1970-1975wasfound.Finally,notedthatduringthisperiodblackimmigrantshaveprogressedconsiderablyless,professionally,thanwhitesbornintheUnitedKingdom.(Stewart:1983)

• Reimers(1983)attemptstomeasurethedegreeofwage discrimination against Hispanics and Blacks intheUnitedStates.TheauthorusesmicrodatafromtheSurveyofIncomeandEducationfrom1976toestimateseparate wage functions, selection bias corrected foreach ethnic group -Mexican, Puerto Rican, Cuban,CentralAmericanandSouthAmerican,otherHispanic,non-Hispanicandwhitenon-Hispanicblacks.Samplesconsistofwagesforemployedmalecivilians,14orolder,whowerenotself-employedorfull-timestudents.

Accordingtotheauthor,thedifferencesinaverageincomecanbedecomposedasthis:

WhereIistheidentitymatrixandDisaweightingdiagonalmatrix.

ReimersfoundthatformenofPuertoRico,discrimina-tionmayberesponsiblefor18%ofthewagedifferential,onits part, for“other Hispanics”, discrimination can cause upto12%ofthewagegap.ForMexicans,however,accountsof



discriminationonlyamountto6%,therestofthe34%wagegapisduetodifferencesincharacteristicssuchaseducation(Reimers:1983).

2. CONCLUSIONS

In this article we make an effort to illustrate a techniquefortheanalysisofwagediscrimination.Wefirstexposetheindependent works of Blinder (1973) and Oaxaca (1973),followed by criticism and methodological improvements ithas experienced over time.We also summarize empiricalimplementationsofthetechniquefortheanalysisofgenderandracialdiscrimination.

Estimatesofwagedifferentialsbetweengroupsofindividu-als-minority-majority-hasbeenwellstudied;understandingwhatexplainsthisgapledBlinder(1973)andOaxaca(1973)todevise-independently-awaytobreakdownthewagegapintotwosummands:oneexplainedbythecharacteristicsofindividualsandanotherexplained,allegedlybydiscrimination.

This methodology has been widely used, in spite of itslimitationsanddisadvantages,especiallytocalculatethewagedifferentialbetweenmenandwomenandtodemonstratetheexistenceofdiscriminationasakeycauseofthosedifferences.Amethodologicalimprovementbymanyresearchersistoincludeathirdsummandrepresentingtheexistenceofselectionbiasinthesample;thistermisenteredusingtheestimateproposedbyHeckman’stwo-stepmethodin1979.

Subsequently,severalauthorshavedevelopedafewexten-sionsoftheoriginalmethodproposedbyOaxacaandBlinder;however,theanalysisofthesemethodologieswasnotaddressedinthisarticledueto its lengh.Therefore,ananalysisofthe



methodologiesthatextendtheoriginalconceptionofwagedecompositionofOaxaca-Blinderisproposedasatopicofinterestandwillbecarriedoutinasubsequentpaper,wherewewillreviewtechniquesthatfocusnotonlyonaveragedif-ferences but that also decompose, indexes and distributionfunctions.

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