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1 and IZA Bonn Discussion Paper
and IZA Bonn Discussion Paper No. 981 January 2004 Email: iza@iza.org This Discussion Paper is issued within the framework of IZA’s research area Mobility and Flexibility of IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available on the IZA website ( www.iza.org ) or directly from the author. genderdierencesinparticipationandunemploymentrates.Section7concludesandoutlinesashorttermresearchagendainthepathofthismatchingapproach.2MatchingandWageGapDecompositions:ALiteratureRe-viewMatchingcomparisontech

2 niquesaimtondmatchedsampleswith“similar”
niquesaimtondmatchedsampleswith“similar”observablecharacteristics(oralinearcombinationofthem)exceptforoneparticularobservablevariable,the“treatment”,whichisusedtogroupobservationsintotwosets:thetreamentandthecontrolgroup.Havingcontrolledforobservedcharacteristics,thecomparisontechniquesareusedtomeasuretheimpactofthetreatmentonthesegroupsunderdierentsetsofidentifyingassumptions.Thesestudies,concernedwiththecomparisonofgroupswithsimilarcharacteristics,hasbeenofespecialinteresttoexperimentaldesignandstatisticsformanyyears.However,notuntiltheintroductionofpropensityscoresinexperimentaldesignsbyRosenbaumandRubin(1983)didthematchingsubjectenterintothediscussionofestimationofcausaleectsi

3 neconomics.Asaresultoftheirseminalwork,a
neconomics.Asaresultoftheirseminalwork,adebatestartedintheeconomicliteratureaboutthewidespreaduseofmatchingnotonlyinexperimental,butalsoinnon-experimentaldesigns(LaLonde(1986),Meyer(1995),Heckman,IchimuraandTodd(1997),DehejiaandWahba(1998)andSmithandTodd(2000)amongAlmostthirtyyearsago,Blinder(1973)andOaxaca(1973)proposedamethodologytodecomposewagegapsintermsofexplainedandunexplainedcomponents.Themethodisbasedontheseparateestimationofearningsequationsforthetwogroupsbeingcompared,namelyfemalesandmales: F=bF xF M=bM Thus,thewagegapcanbeexpressedas M yF=bM xMbF Then,themethodrequirestheadditionandsubstractionoftheterm (oralternatively, )whichcanbeinterpretedasthecounterfactualsituatio

4 n,“Whatwouldtheearningsforamale(female)w
n,“Whatwouldtheearningsforamale(female)withaverageindividualcharacteristicsbe,inthecasethathe(she)isrewardedforhis(her)characteristicsinthesamewayastheaveragefemale(male)isrewarded?”Aftersomealgebraicmanipulations,thewagegaptakestheform: M yF=bF¡ xM xF¢+³bMbF´ Whichhasanaturalinterpretation:therstcomponentoftheright-handside, xM ,isattributedtodierencesinaveragecharacteristicsbetweenmalesandfemales,whilethesecondcomponent, ,isattributedtodierencesinaveragerewardstotheindividualcharacteristics.Juhn,MurphyandPierce(1993)extendedthedecomposition“characteristics-rewards”intoonethatconsidersthreecomponents:observablecharacteristics,observablerewardsand Theprecisewayinwhichthesesimilari

5 tiescanbecomputedvaries.Theliteraturepro
tiescanbecomputedvaries.Theliteratureprovidespropensityscores,Euclideandistances,andMahalanobisdistancesamongothers.TheprecisetypeofmatchingproposedinthispaperwillbeintroducedinSection3. wagegapdecompositionproposed.3ALinkBetweenMatchingandWageGapDecompositionsinaNon-ParametricSetupdenotetherandomvariablethatmodelsindividualearningsandthen-dimensionalvectorofindividualcharacteristics(suchasage,education,occupationalexperience,occupation,rmsize,etc.)presumablyrelatedtotheseearnings.Furthermore,letdenotetheconditionalcumulativedistributionfunctionsofindividualcharacteristics,conditionalonbeingmaleandfemalerespectively,denotetheimpliedprobabilitymeasures.Foracorrectdenitionofthemeasu

6 resandintegralsthatwillbeintroducedlater
resandintegralsthatwillbeintroducedlaterinthissectionitisenoughtoassumethataremeasurablefunctionsfrom(intheBorelsense).Consequently,denotestheprobabilitymeasureofthesetunderthedistribution,thatis,andanalagouslyTherelationshipgoverningtheserandomvariablesismodeledbythefunctionsresentingtheexpectedvalueofearningsconditionaloncharacteristicsandgender.BeingthecasethatthatY|M,XXY|F,XItfollowsthatthatY|M]=ZSMgM(x)dFM(x),E[Y|F]=ZSFgF(x)dFF(x),whereSMdenotesthesupportofthedistributionofcharacteristicsformalesandthesupportofthedistributionofcharacteristicsforfemales.Insuchaway,thewagegap,denedassY|M]−E[Y|F],canbeexpressedas ThisisageneralizationofthelinearmodelinwhichhY|X]=βX,whereisapa

7 rametervectorandisanregressorvector. =Z
rametervectorandisanregressorvector. =Z SFgM(x)(x) µM³ SF´ZSFgM(x)(x) µM(SF)µM³ SF´+ZSMSFgM(x)(x) µM(SF)ZSMSFgF(x)(x) µF(SM)+ZSMgF(x)(x) µF(SM)Z SMgF(x)(x) µF³ SM´µF³ Finally,thesecondpairofintegralsinthisexpression(thosethatarecomputedoverthecommonsupport)canbedecomposedinananalogouswayasisdoneintheBlinder-Oaxacasetupbyaddingandsubtract-ingtheelementthatpermitsthemtoevaluatethecounterfactualmentionedabove, µF(SM),=Z SFgM(x)(x) µM³ SF´ZSFgM(x)(x) µM(SF)µM³ SF´+ZSMSFgM(x) µM(SF) µF(SM)¸(xSMSF£gM(x)gF(x)¤(x) µF(SM)+ZSMgF(x)(x) µF(SM)Z SMgF(x)(x) µF³ SM´µF³ WhichIdenotebyThetypicalinterpretationofthewagegapdecompositionapplies,butinthisnewconstruction,onlyoverthecommonsupport.Inthisc

8 onstruction,twonewadditivecomponentshave
onstruction,twonewadditivecomponentshavebeenincluded,leavinguswithafour-elementdecomposition. Wearedenotingby M(F) themeasure(withsignal)inducedbytheoriginalmeasuresandthecorrespondingarithmeticoperations. atleastonepossiblecombinationofthesetofcharacteristicsthatthepopulationofmalesreach,oralternatively,ifthesefemaleswerepaid,onaverage,asthematchedfemalesarepaid.Itiscomputedasthedierencebetweentheexpectedwageoffemalesinandoutofthecommonsupport,weightedbytheprobabilitymeasure(underthedistributionofcharacteristicsoffemales)ofthesetofcharacteristicsthatmalesdonotreach.Inthiswaythewagegaphasbeenbrokenintofouradditivecomponents:Beingthecasethatthreeofthemcanbeattributedtotheexistenceo

9 fdierencesinindividualscharacteristicsth
fdierencesinindividualscharacteristicsthatthelabormarketrewardsandtheothertotheexistenceofacombinationofbothunobservable(bytheeconometrician)dierencesincharacteristicsthatthelabormarketrewardsanddiscrimination.Inthatsense,itisconvenienttoexpressthewagegapas:andinterpretitasistraditionallydoneinthelinearBOsetup,withtwocomponents:oneattributabletodierencesinobservablecharacteristicsoftheindividualsandtheotherconsideredasanunexplainedcomponentofthegap.Underthisframework,Iwillintroducethematchingprocedureinordertoestimatethesefourcompo-nents.Iwillre-sampleallfemaleswithoutreplacementandmatcheachobservationtoonesyntheticmale,obtainedaveragingthecharacteristicsofallmaleswithexactlythesa

10 mecharacteristicsThematchingalgorithmini
mecharacteristicsThematchingalgorithminitsbasicformcanbesummarizedasfollows:Step1:Selectonefemalefromthesample(withoutreplacement).Step2:Selectallthemalesthathavethesamecharacteristicsasthefemalepreviouslyselected.Step3:WithalltheindividualsselectedinStep2,constructasyntheticindividualwhosecharacter-isticsareequaltotheaverageofallofthemand“match”himtotheoriginalfemale.Step4:Puttheobservationsofbothindividuals(thesyntheticmaleandthefemale)intheirrespectivenewsamplesofmatchedindividuals.Repeatthesteps1through4untilitexhauststheoriginalfemalesample.Asaresultoftheapplicationofthisone-to-many-with-zero-discrepanciesmatchingIgenerateapartitionofthedataset.Thenewdatasetcontainsobservatio

11 nsof“matchedfemales”,“matchedmales”,“unm
nsof“matchedfemales”,“matchedmales”,“unmatched tomakethesekindsofassumptions,andadditionally,Iproposeawaytocomputethosecomponentsofthegapthatcorrespondtothenon-overlappingsupports(Aswillbeshownlaterinthispaper,itisanempiricalregularitythattheunmatchedmaleshaveaveragewagesabovetheaveragewagesoftheirmatchedpeers.Hence,runningregressionstoestimateearningsequationsforallmaleswithoutrecognizingthatempiricalregularitytendstoover-estimatetheunexplainedcomponent()intheBOdecomposition.Itisimportanttoemphasizethenatureofgenderdiscriminationinpaycaptures(thatis,thepossibilityofhavingequallyproductivemalesandfemalesthatarepaiddierentlysimplybecauseofgender)anddistinguishitfromothersortsofdisc

12 riminationthatmayplayroleintheaccesstopa
riminationthatmayplayroleintheaccesstoparticularcharacteristics.Theextenttowhichthesedierencesinaccessareendogenousorexogenoustothelabormarketmayvaryaswemaythinkaboutdiscriminationthatpreventspromotiontohighpayingoccupationsasanexampleoftheformeranddierencesineducationas(arguably)anexampleofthelatter.Whilediscriminationinaccessisembodiedinthethreecomponentsattributedtodierencesincharacteristics,Ibelievethatthecomponentaccountsforthepenalizationonaveragewagesthatfemalesexperiencebyencountering“barrierstotheentry”thatblocktheirwaytocertainindividualcharacteristicsthatmalesachieve.Unfortunatelyhowever,duetounobservedheterogeneity,itisnotpossibletodistinguishwhethercomponentisaresulto

13 f“discrimination”or“choice.”Thenextsecti
f“discrimination”or“choice.”Thenextsectionwillexplorethedatasetforwhichthedecompositionjustintroducedisimplemented,analyzinggenderdierencesinsomeoftheobservablecharacteristicsthatthelabormarketrewards.4GenderDierencesinCharacteristicsandtheGenderWageGapinPeru1986-2000ThedataforthisstudycomefromtheNationalHouseholdSurveys(EncuestasNacionalesdeHogares)andtheSpecializedEmploymentSurvey(EncuestaEspecializadadeEmpleo)undertakenbythePeruvianMinistryofLaborandSocialPromotion(MTPS)duringtheperiod1986-1995(except1988)andbytheNationalInstituteofStatisticsandInformatics(INEI)fortheperiod1996-2000.Forhomogenizingpurposes–andtakingintoaccountthatLimaconcentratesalmostonehalfofthePeruvianlaborf

14 orce–onlyworkersfourteenyearsorolderinth
orce–onlyworkersfourteenyearsorolderinthemetropolitanLimaareahavebeenconsideredforthisstudy.Peru,duringthistimeframeisaninterestingcountrytoanalyze.First,labormarketsinPeruaresegmented.Asmentionedearlierintheintroduction,BlauandFerber(1992)drawattentiontothefactthatLatinAmericaistheregionthatreportsthehighestlevelsofoccupationalsegregationbygenderin MeasuredbytheDuncanIndexofOccupationalSegregation. Figure1:EducationalAttainmentbyGender Peru 1986-2000Educational Attainment for FemalesNO EDUCATIONELEMENTARY SCHOOL21%COLLEGE30%HGH SCHOOL46% Peru 1986-2000Educational Attainment for MalesNO EDUCATIONELEMENTARY SCHOOL15%HGH SCHOOL50%COLLEGE34% duringtheperiodofanalysis.Theseaveragegure

15 sfortheperiod1986-2000showanevolutiontha
sfortheperiod1986-2000showanevolutionthatisimportanttonote.Thepercentageofworkingfemaleswithacollegeorhighschooldegreeincreasedfrom68%to81%,whilefortheirmalepeersthesepercentagesmovedfrom78%to84%.Theobservablecharacteristicforwhichthegreatestgenderdierenceisfoundisoccupationalexperienceoftheworkingpeople,measuredasyearsworkinginthesameoccupation,illustratedingraph2.Fortheperiodinconsideration,onaverage,malesregisterbetween1.4and2.7moreyearsofoccu-pationalexperiencethanfemales,whichrepresentsbetween30%and50%dierence.Itshouldbenoted,however,thatthesegenderdierencesinaverageyearsofoccupationalexperiencehavedecreasedsubstan-tiallyovertheperiod1986-2000.Regardingtheerencesinthesupports

16 thatthispaperpointsoutandaddresses,Ihave
thatthispaperpointsoutandaddresses,Ihavefoundthat30% Figure3:HourlyWagesbyGender(in1994soles) Peru 1986-2000 Hourly Wages by Gender Year1994 Soles Male HourlyWage Female HourlyWage wagegap(representedbythedierencebetweenanypairofadjacentbars).Thenextgureexplicitlyshowsthegapinrelativeterms(averagehourlywagegapasmultiplesofaveragehourlyfemaleearnings)Itcanbefoundthatthegenderwagegapinhourlywagesvariedaroundanaveragevalueof0.45(thatis,onaverage,malesearned45%moreperhourthanfemalesinPeruduringtheperiod1986-2000)buttherearesignicantuctuationsaroundthataveragemeasure.Themeasureofthegapthatisreportedinthissection(multiplesofaveragehourlywagesforfemales,asitiscalledinSection2)shouldbetak

17 enas“raw”inthesensethatitconsidersallmal
enas“raw”inthesensethatitconsidersallmalesandfemalesregardlessoftheirdierencesinobservablecharacteristics,andregardlessofwhetheritispossibletocomparethemornot.Itisnecessarytomaketheappropriateadjustmentstothatgapinordertoobtainameasureofunexplaineddierencesinaverageearningsforcomparablesamplesofmalesandfemales,Thatwillbethepurposeofthenextsub-section,butbeforestartingthatexerciseletusexplorehowthesegenderdierencesinaveragehourlywagesvaryaccordingtoindividualcharacteristics.Startingwithage,noteoncethepopulationhavereached30,astheygetolder,thegenderwagegaptendstoincrease;forpeopleclosetoretirementagethegapreaches128%.Accordingtoeducationalattainment,thegenderwagegapexhibitsanon-mono

18 tonicbehavior.Thegapisbiggerbothforpeopl
tonicbehavior.Thegapisbiggerbothforpeoplewithonlyanelementaryeducationandforpeoplewithcollegedegrees.Itgets Notethatthevariableinwhichthegendergapismeasuredinthispaperisthehourlywageinsteadthelogarithmofthehourlywageasiscommonplaceintheliterature.Insub-section4.2thereisadiscussionontheconvenienceofthelatterovertheformer.Itisimportanttonotethatthisbasiccomputationofaveragewagegapsfordierentagegroupsmixes“ageeects”and“cohorteects.” Figure4:HourlyWageGapbyGender(in1994soles) Peru 1986-2000 Hourly Wage Gap by Gender0.00.20.40.60.8YearMult. of Female Wages Figure5:HourlyWagesandGenderWageGapforDierentAgeGroupsPERU 1986-2000HOURLY WAGES ACCORDING TO GENDER AND AGE(In 1994 Soles)Less Tha

19 n 19 Years20 to 2930 to 4445 to 6060 or
n 19 Years20 to 2930 to 4445 to 6060 or moreFEMALES5.5810.0312.9712.4510.17MALES7.6211.9917.1120.3223.16GAP37%20%32%63%128% Figure6:HourlyWagesandGenderWageGapbyEducationalAttainmentPERU 1986-2000HOURLY WAGES ACCORDING TO GENDER AND EDUCATION(In 1994 Soles)EDUCATIONELEMENTARY SCHOOLHGH SCHOOLCOLLEGEFEMALES6.526.839.5616.32MALES7.7910.2211.8623.81GAP19%50%24%46% smallerfortheno-educationandhighschoolpopulations.ThisfactisinlinewiththegenderdiinthereturntoschoolingforPerufoundinSaavedraandMaruyama(1999).Theprevioustablesrevealedsubstantialdierencesinthedistributionofwagesandthegenderwagegapaccordingtosomeindividualcharacteristics,eachanalyzedindependently.NextIwillanalyzethejointeec

20 tofthesedierencesincharacteristicsonwage
tofthesedierencesincharacteristicsonwagesbymeansofmatchingandthedecompositionpresentedinSection2.5ExplainedandUnexplainedComponentsoftheGenderWage5.1WageGapDecomposition.TheMatchingApproachRecallingfromequation[6],thewagegap,canbeexpressedasasY|M]−E[Y|F]=∆M+∆X+∆0+∆F.Thatis,theaveragewagedierencebetweenmalesandfemalescanbebrokenintofourcomponents.Threeofthemcanbeattributedtogenderdierencesinobservableindividualcharacteristicsandthefourthcomponenttotheexistenceofbothnon-observablegenderdierencesincharacteristicsthatdeterminewagesandgenderdiscriminationinpayinthelabormarketrepresentsthepartofthegapexplainedbythefactthatmalesandfemalestendtohaveindividualcharacteristicsthata

21 redistributeddierentlyovertheircommonsup
redistributeddierentlyovertheircommonsupport(forinstance,inthePe-ruviandatasetsitispossibletondbothmalesandfemaleswith“MastersorPh.D.degree”,buttheproportionoffemalesunderthatcategoryissubstantiallysmallerthantheproportionofmales). Figure7:GenderWageGapAfterControllingforObservableCharacteristics Peru 1986-1999Relative Gender Gaps and Controlled Diferences YearMultiples of Females Wages Males Relative toFemales Hourly WageGap After Controlling for Age,Education, MaritalStatus and MigratoryCondition thattakesthevalue0forsinglesand1formarriedindividuals)andmigratorycondition(adichotomousvariablethatdistinguishesindividualswhowereborninLimafromthosewhowerenot).Whilethegenderwagegap

22 withoutcontrollingforcharacteristics,has
withoutcontrollingforcharacteristics,hasanaveragevalueof45%duringtheperiodofanalysis,thecontrolledgap,,variesaround28%.Thatis,themixturebetweengendererencesnotconsideredintheanalysis(whichmaycompriseobservableandunobservabledierences)anddiscriminationaccountsforadierentialof28%inhourlywagesformalesrelativetofemales.Thesegurescorrespondtotheuseoftheparticularsetofvariablesspeciedabove.Thatsetdoesnotincludevariablesthataretypicallyconsideredasbeingdeterminedendogenouslyinthelabormarket.Combi-nationsofthesevariablesareconsideredforthefollowingdecompositions.FortheseIconsiderdierentcombinationsofage,education,occupationalexperience(measuredinyears),informality(adichotomousvariablethat

23 distinguishesindividualswithformaljobsfr
distinguishesindividualswithformaljobsfromindividualswithinformaljobs),occupation(thatcomprisessevenoccupationalcategories)andrmsize(withvecategories).Theaverageunexplainedgenderwaggapthatresultsaftercontrollingfortheseendogenouschar-acteristicsisslightlybelowtheaveragethatdoesnotconsiderthem.Itisaround25%,threepercentualpointsbelowthegapestimatedaftermatchingonlyonage,schooling,maritalstatusandmigratorycondi-Interestingly,foralmosteverycombinationofcharacteristicsIconsideredinthepreviousexercises, Aswillbeshowninsub-section5.3,a99%condenceintervalforthisaverageunexplainedgenderdierencesinpayrangesfrom24.92%to31.13%.Ajobisconsideredformalifsatisesatleastoneofthefollowingrequiremen

24 ts:beinginthePublicSectororbeingregister
ts:beinginthePublicSectororbeingregisteredontheSocialSecuritySystemorbeingaliatedtoanyprivateretirementplanorbeingunionized.Familyworkersareconsideredinformalworkers.Adetailedspreadsheetwiththeresultsforallthedecompositionsshowedhere,aswellassomeothercombinationsofindividualcharacteristicsnotreportedinthissection,isavailablefromtheauthor. Figure9:WageGapDecompositionsforDierentSetsofControls(2) Gender Wage Gap and Controlling Components(Controlling for Age, Education and Migratory Condition)-0.1YearsMult. of Female Wages Delta-F Delta-X Delta-M Delta-0 Gender Wage Gap and Controlling Components(Controlling for Age, Educ., Marit. Status and Mig. Cond.)-0.1YearsMult. of Female Wages

25 Delta-F Delta-X Delta-M Delta-0 Figure1
Delta-F Delta-X Delta-M Delta-0 Figure11:WageGapDecompositionsforDierentSetsofControls(4) Gender Wage Gap and Controlling Components(Controlling for Age, Education, Formality and Occup.)-0.1YearsMult. of Female Wages Delta-F Delta-X Delta-M Delta-0 Gender Wage Gap and Controlling Components(Controlling for Age, Educ., Form., Occp. and Firm Size)-0.1YearsMult. of Female Wages Delta-F Delta-X Delta-M Delta-0 Figure12:CumulativeFunctionsofRelativeWagesbyGender Peru 1986-1999Cumulative Functions of Relative Wages By Gender10000.511.522.533.5Mult. of Average Females WagesCumulative Function (%) AllFemales All Males MatchedFemales MatchedMales anextractofFigure12.Thedierencesbetweenthe

26 matchedversionsofthecumulativefunctionso
matchedversionsofthecumulativefunctionsofwagesforfemalesandmalesaresmallerthanthedierencesoriginallyfoundinthecumulativefunctionsofwagesforfemalesandmales.Thegenderdierencesinwagesarereducedaftermatching.Thedistributionofhourlywagesformatchedfemalesdoesnotdiertoomuchfromthedistributionofhourlywagesforallfemales.Thisisbecause,byconstructionofthecounterfactual,there-samplinghasbeendoneinordertoensurethatthedistributionremainsunchangedonthecommonsupport.Theonlychangesareduetothenon-overlappingpartsofthesupportofcharacteristicsforfemales(and,asithasbeenshownpreviously,thecomponentofthegapisrelativelysmallcomparedtotheothercomponents).Formales,thesituationisdierent.Thecumulativedistrib

27 utionofhourlywagesforallmalesdiersfromth
utionofhourlywagesforallmalesdiersfromthedistributionthatconsidersonlymatchedmales(withtheappropriatere-weightingthatisrequiredtomimictheempiricaldistributionofindividualcharacteristicsoffemales),especiallyattheupperextremeofthedistributionThepreviousplotinspiresaquantileanalysisinthefollowingway:atanyheight(percentile),thehorizontaldistancebetweenthetwocumulativefunctionsobtainedaftermatchingisameasureoftheunexplainedgenderwagegapattherespectivepercentile.Graph14shows,bypercentiles,thesemeasuresofgenderwagegapthatremainaftermatching.Theplotshowsthatfortherst90percentilesofthedistributionofhourlywagesformalesandfemalestherearenomajordierencesinhourlywages.Thegapisroughlybelow.2tim

28 estheaveragewageforfemales.Itisinthetop1
estheaveragewageforfemales.Itisinthetop10%ofthedistributionsofhourlywagesformalesandfemalesthatthehighesterencesarefound.Atthe99thpercentilethegapattainsamaximumof2.2timestheaveragewage Figure15:RelativeGenderWageGapbyPercentiles Peru 1986-1999Relative Gender Wage Gap (After Matching) by Percentiles100%0102030405060708090100Percentile of Wage DistributionPercentage offemales.TheplotshowsevidencethatthegenderdierencesinpayinthebottompercentilesofthedistributiondonotcontributeconsiderablytotheaggregatemeasureofgenderdierencesinpayinPerufortheperiodofanalysis.TheaveragegenderwagegapinPeruisdrivenbygenderdierencesinpayatthetoppercentilesofthewagedistributions.Theassertionsoftheprevio

29 usparagrapharehidinganimportantresult,na
usparagrapharehidinganimportantresult,namely,thedierencesinhourlywagesthatarefoundinthebottompercentilesofthedistributionsofwagesaresmallinabsolutetermsbutnotinrelativeterms.Thetypicalmalewhoisinthebottom10thpercentileofthedistributionofhourlywagesearnsapremiumof12%ofaveragefemalewagesoverthe10thpercentilefemale(approxi-mately1.40PeruvianSolesof1994).However,thisrepresentsadierenceof60%ofthatfemale’searnings.Whenthesamecomparisonismadeatthebottomrstpercentilethedierencesareevenbigger.Thehourlywagegapinabsolutetermsisapproximately0.70PeruvianSolesof1994,butthatgurerepresentsadierenceof94%ofthecorrespondingfemaleearnings.Thepoorestmaleearnsalmosttwiceasmuchasthepoorestfemale.Thesepe

30 rcentagedierencesinhourlywagesbypercenti
rcentagedierencesinhourlywagesbypercentilesofthewagedistributionsareshownnextingraph15.TherelativegenderwagegapbywagepercentilesshowsaslightU-shapeinwhichtheminimumgap,18%,isfoundamongthoseindividualswhosewagesarebetweenthe8thand9thdeciles.Themaximumisfoundamongthepoor,95%. canbeexpressedas µF(SM)ZSMSFgF(x)(x) using anddenotingbythenumberofobservationsforfemaleswiththesetofcharacteristicsinthesample,Iconstructthesampleanalog nM(x)yMinF(x) nFnFXjFj1 which,afterdenoting nM(x)yMi (thesampleaverageofearningsformalesthatexhibitthesetofcharacteristics)and (thesampleproportionoffemalesthatexhibitthesetofcharacteristics),canbeinturnexpressedas yM(x)bF(x)nFXjFj1 Fromthisexpression,theasymp

31 toticdistributionofthesecondcomponentoft
toticdistributionofthesecondcomponentoftheright-handsideisstraightforwardtoobtain, nF¡ Whatisnottrivialtoobtainistheasymptoticdistributionoftherstcomponentoftheright-handside,butitcanbecomputedapplyingtheThedetailsofthatcomputationareshownintheappendix.Applyingthesameonrestrictedsamples,accordingtodierentsetsofcharacteristicsIalsoobtainedestimatorsforthemeanandthestandarddeviationoftheunexplaineddierencesinpayforthosedierentsetsofcharacteristics.Next,inFigure16,Iwillshowtheresultsforthewholepopulationandthosethatresultafterconditioningonmaritalstatusandmigratorycondition.Startingwiththegenderwagegapforthewholepopulationonthecommonsupportofindividualcharacteristics,aftercontrolling

32 forage,schooling,maritalstatusandmigrato
forage,schooling,maritalstatusandmigratorycondition,theaveragewagegapof28.03%hasastandarderrorof1.89%.Thiscanbetranslatedintoa99%condenceintervalfortheaverageunexplaineddierencesinpaythatrangesfrom24.92%to31.13%ofaveragefemalewages,whilea90%condenceintervalforthesamemeasurewouldrangefrom23.17%to32.89%.Concerningmigratorycondition,thereisaslightevidencethattheunexplaineddierencesinpayaresmalleramongmigrantindividualsthanamongthosewhoborninLima.Withregardtomaritalstatus,althoughthereisnoclearevidencethattheaverageunexplainedgenderdierencesinpaybetweenmarriedandsingleindividualsaredierent,thereismoreevidenceofdispersionofsuchunexplaineddiamongthemarriedthanamongthesingles.Thathigherd

33 ispersionofunexplainedwagescouldbeexplai
ispersionofunexplainedwagescouldbeexplainedintermsofothervariablesthatareconsideredasendogenoustoamodelofwagedeterminationinthe Figure17:CondenceIntervalsfortheUnexplainedGenderWageGap(1) Unexplained Gender Wage Gap By Age(After Controlling for Age, Education, Marital Status and Migratory Condition)Single Individuals-0.40.40.81.20ɂ.;က=20 &3ɐ.;耀=23 &7ɐ.;耀=27 &0͂.;က=30 &3͂.;က=33 &7͐.;耀=37 &2ѐ.;耀=42 &7т.;က=47 &4Ղ.;က=54AgeMultiple of Female Wages Figure18:CondenceIntervalsfortheUnexplainedGenderWageGap(2) Unexplained Gender Wage Gap By Age(After Controlling for Age, Education, Marital Status and Migratory Condition)Married

34 Individuals-0.40.40.81.20ɂ.;က=20
Individuals-0.40.40.81.20ɂ.;က=20 &3ɐ.;耀=23 &7ɐ.;耀=27 &0͂.;က=30 &3͂.;က=33 &7͐.;耀=37 &2ѐ.;耀=42 &7т.;က=47 &4Ղ.;က=54AgeMultiple of Female Wages Figure20:CondenceIntervalsfortheUnexplainedGenderWageGap(4) Unexplained Gender Wage Gap By Years of Schooling(After Controlling for Age, Education, Marital Status and Migratory Condition)Married Individuals-0.60.61.21.82.401234567891011121314151617Years of SchoolingMultiple of Female Wages 5.4MatchingversusLinearRegressions.AnEmpiricalComparisonAftertheintroductionofthematchingapproachthatdecomposesthegenderwagegapandavoidslinearregressions,thereisacomparativequestionthatrequiresa

35 nanswer:Towhatextentdotheresultsobtained
nanswer:Towhatextentdotheresultsobtainedbymatchingbedierfromthoseobtainedbylinearregressions?Insomesense,matchingisequivalenttoBlinder-Oaxacawhentheestimationsoftheearningsequationsformalesandfemalesarerestrictedtothecommonsupportandperformedwiththesamematchingvariablesandalltheirpossiblepowersandinteractions.Weshouldthereforeexpectsimilarresultsfromboth.Inthispaperthatquestionwillbeansweredempirically,comparingtheresultsobtainedthroughmatchingandlinearregressionsfortwoparticularyearsofthesample:1999and2000.Iwillempiricallyshowthatwhileweobtainsimilarresults(overthecommonsupport),thefailuretorecognizethegenderdierencesinthesupportsaccountsforanover-estimationoftheunexplainedgender

36 dierencesinpay.Aswaspointedoutpreviously
dierencesinpay.Aswaspointedoutpreviously,theBOdecompositionbasedonlinearregressionsdependsonthelinearspecicationoftheearningsequations.Forthispurposeitisinformativetocomparethematchingresultswiththoseobtainedfromfourdierentlinearspecications.Therstspecicationincludesthefollowingvariables:age(asacontinuousvariable),agesquared,3dummiesmeasuringeducationalattainment(“ele-mentaryschool”,“highschool”and“collegedegree”,with“noeducation”asthebasecategory),11dummiesmeasuringyearsofoccupationalexperienceandalltheinteractionsbetweeneducationalattainmentand Figure21:ComparisonAmongDierentDecompositionsoftheGenderWageGap Urban Peru 1999Gender Wage GapDecompositionsDelta-FDelta-0Delta-XDelta-M

37 Unexplained Component of the GapExplaine
Unexplained Component of the GapExplained by Individual CharacteristicsMatching(No specification required)0.0140.2280.0640.0500.2280.129Linear SpecificationsIdentifying Differences in SupportsSpecification 10.0430.2090.0360.0680.2090.148Specification 20.0430.2290.0160.0680.2290.127Specification 3-0.0100.2160.0640.0870.2160.141Specification 4-0.0100.2260.0530.0870.2260.130Without Identifying Differences in SupportsSpecification 10.2240.1320.2240.132Specification 20.2370.1200.2370.120Specification 30.2770.0800.2770.080Specification 40.2720.0850.2720.085 thisexample,itisfoundthatthe“regression”(or“logarithms”)measureissubstantiallylowerthanthe“matching”measure.Whiletheformerreportsth

38 atmalesearnonaverage35.7%morethanfemales
atmalesearnonaverage35.7%morethanfemales(perhour),thelatterreportsagureof62.1%.Letmenowturntothecomparisonofdierentdecompositions.First,Iwillcomparetwosetsoflinearspecications:thosethattakethegenderdierencesinthesupportsintoaccountwiththosethatdonot.Ifoundthatdierencesinsupportsaccountforasignicantshareofthegap,particularlybecausethereisasignicantpercentageofmaleswithindividualcharacteristicsthathavenofemalecounterparts.Accountingforgenderdierencesinthesupportschangestheunexplaineddierencesinearningsfromanestimatedaverageof22.4%-27.7%toanestimateof20.9%-22.9%for1999.Thepreviouscomparisons–madeforthesamelinearspecicationsbutwithdierentassumptionsonthesupportsofthedistributionsofind

39 ividualcharacteristics–showempiricalevid
ividualcharacteristics–showempiricalevidenceaboutoneoftheclaimsofthispaper,namely,thefailuretorecognizegenderdierencesinthesupportsimpliesaslightoverestimationoftheunexplainedcomponentofthegap().Thispointisilluminatedbythematchingapproach.Nowletusturntothecomparisonbetweenthedecompositionbasedonlinearregressionsandthedecompositionbasedonmatching.Asmentionedpreviously,thedierencebetweenbothapproachesisontheweightingofthelocaleects.Themeasureoftheunexplainedwagegapreportedbymatching(22.8%)fallsinsidetherangeofestimatorsobtainedwiththedierentlinearspecicationsconsideredin ByJensen’sinequalityitisknownthat ln( and ln( butitisnotpossibletodetermineanorderrelationshipbetween ) ln(ln( ln

40 ( ). obtainedfromthematchedsamplecanbeco
( ). obtainedfromthematchedsamplecanbeconsideredas“unexplaineddierences”which,asusual,canberegardedasasignoftheexistenceofbothdiscriminationandunobservablecharacteristicsdeterminingparticipation(unemployment).Thenexttwographsreporttheevolutionofgenderdierencesinunemploymentandparticipationratestogetherwiththecontrolled–bymatching–versionsofsuchratesformales,consideringage,education,maritalstatusandmigratoryconditionasmatchingvariablesappliedoverthewholepopulation. Urban Peru 1986-2000Evolution of Participation Rates by Gender40%45%50%55%60%65%70%75%80%85%YearPercentage Fermales Males Males after controlling forage, education, maritalstatus and migratorycondition Urban Peru 1986-20

41 00Evolution of Unemployment Rates by Gen
00Evolution of Unemployment Rates by Gender10%12%14%YearPercentage Fermales Males Males after controlling forage, education, marital statusand migratory condition Theresultssuggestthatgenderdierencesinage,education,maritalstatusandmigratoryconditiondonotexplaingenderdierencesinparticipationorunemploymentrates.Ifany,thecontrolledunemploymentratesformalesareslightlysmallerthanthe“raw”unemploymentrates.Thereareotherdeterminantsofsuchdierences,anddiscriminationmaybeoneofthose,butitalsomaybechoice,inthesensethatthisissolelytheresultofdierencesinpreferencesbetweenfemalesandmales. Urban Peru 1986-2000Fraction of Total Labor Income Generated by Males for Different Age GroupsYearPercentage

42 Older People (33years old andmore) You
Older People (33years old andmore) Younger People(less than 33years old) Thismeasurecanbeconsideredasrawinthesensethatitdoesnottakeintoaccountgenderdiencesintheindividualcharacteristicsthatdetermineparticipation,employmentandwages.Again,thegenerationofacounterfactualisrequiredinordertoanswerthequestion:Whatfractionoftotallaborin-comewouldbegeneratedbymalesincasetheirindividualcharacteristicsaredistributedinthepopulationaccordingtotheempiricaldistributionofindividualcharacteristicsoffemales?Thematchingalgorithmisappliednow,notonlytotheworkingpopulationreportingpositivewagesaswasdoneforthehourlywagegapanalysis,butalsotothenon-working,economicallyactivepopulation.Themeasurethatmat

43 tersforthepurposeofthisnewexerciseisthet
tersforthepurposeofthisnewexerciseisthetotallaborincomegeneratedbyfemalesandmalesinthematchedsample.Thevariablesconsideredforthismatchingexercisebelongtoasetofvariablesthatcanbeconsideredas“exogenous”tothelabormarket:age,education,maritalstatusandmigratorycondition.Theresultsareshownnext. Peru 1986-2000Fraction of Total Labor Income Generated by Males19861987198919901991199219931994199519961997199819992000YearPercentage Fraction of Total Labor Income Fraction After Controlling forAge and Education Fraction After Controlling forAge, Education, Marital Statusand Migratory Condition 40 takedirectly.Bymeansofmatching,insteadofobtainingonlyaveragemeasuresofunexplaineddiinpay,itispossib

44 letoalsoobtainadistributionforsuchunexpl
letoalsoobtainadistributionforsuchunexplaineddierencesinpay.Toexplorethedistributionofunexplaineddierencesinpayprovidedinterestinginsights.Theaveragegenderwagegapismainlydrivenbygenderdierencesinpayatthetoppercentilesofthewagesdistribu-tions.WagesatthehighestquintileofthedistributionsofwagesforfemalesandmalesexplainmorethanonehalfoftheaveragewagegapinPerufortheperiodofanalysis.Atthepoorestpercentilesofearnings,thewagegapinabsolutetermsissmallanddoesnotcontributesubstantiallytotheaveragewagegapofthepopulation;butthesamewagegapinthepoorestpercentiles,measuredinrelativetermsisthehighestamongallpercentiles(around94%).Also,Ifoundthatthereismoredispersionoftheunexplainedgendererencesinp

45 ayamongthemarriedthanamongsingles.Therei
ayamongthemarriedthanamongsingles.Thereisalsoslightevidenceofanincreaseinthegenderwagegapwithageformarriedindividualsandasubstantiallyhigher(andmoredisperse)unexplainedgenderwagegapamongthehighlyeducated(morethancollegedegree).Thesetwoadvantagesofmatchingoverlinearregressionsarenotafreelunch.Thereisacosttopay:thecurseofdimensionality.Theinclusionofmanyexplanatoryvariables–thatis,theuseofmanymatchingcharacteristics–mayreducethechancesofobtaininganadequatenumberofmatchedobservations,limitingasaconsequencethepossibilityofexploringthedistributionofunexplaineddierencesinpay.Theattempttoexplaingenderdierencesinparticipationandunemploymentratesintermsofob-servableout-of-the-labor-marketv

46 ariables(age,education,maritalstatusandm
ariables(age,education,maritalstatusandmigratorycondition)failsconsiderably.Thisisalsotrueforgenderdierencesinthegenerationoftotallaborincome.Thatlackofexplanatorypowerhastwointerpretations.Ontheonehand,itmaybethecasethatthediscriminatorypracticesaccordingtogenderaremoresevereinhiringandworkloadthaninthedeterminationofhourlypayments.Ontheotherhand,itmaybealsothecasethatthesegenderdierencesinparticipationareexplainedbydierencesinothernon-observableindividualcharacteristics(amongwhichwecaninclude“preferences”or“socialroles”).Ingeneral,thismatchingapproachcanalsobeusedtocontrolforobservedcharacteristicsinanyothermeasureforwhichitisexpectedtondsomesortofexplainedandunexplainedcomponen

47 ts.Itonlyrequiresthegenerationoftheadequ
ts.Itonlyrequiresthegenerationoftheadequatecounterfactuals.References[1]Abadie,AlbertoandGuidoImbens(2002).“SimpleandBias-CorrectedMatchingEstimatorsforAverageTreatmentEects.”Unpublished. [14]Gardeazabal,J.andA.Ugidos(2000).“MeasuringtheWageDistributionGenderGapatQuantiles.”paperpresentedattheconference,Bonn.[15]Hansen,JorgenandRogerWahlberg(1999).“EndogenousSchoolingandtheDistributionoftheGenderWageGap.”DiscussionPaperNo.78.InstitutefortheStudyofLabor(IZA),Bonn.[16]Heckman,JamesJ.andJereySmith(1995).“AssessingtheCaseforSocialExperiments.”ofEconomicPerspectives,9,No.2,85-110.[17]Heckman,JamesJ.andJereyA.Smith(1996).“ExperimentalandNonexperimentalEvaluation.”Schmid,GuntherO’Reilly,

48 JacquelineSchomann,Klaus,eds.Internation
JacquelineSchomann,Klaus,eds.InternationalHandbookofLabourMarketPolicyandEvaluation.Cheltenham,U.K.andLyme,N.H.:Elgar,37-88.[18]Heckman,JamesJ.,HidehikoIchimuraandPetraE.Todd(1997).“MatchingasanEconometricEvaluationEstimator:EvidencefromEvaluatingaJobTrainingProgramme.”ReviewofEconomic64,No.4,605-54.[19]Heckman,JamesandCarmenPages(2000).“TheCostofJobSecurityRegulation:EvidencefromLatinAmericamLaborMarkets.”NBERWorkingPaperNo.7773,NationalBureauofEconomicResearch,Cambridge,MA.[20]Heckman,James,LanceLochnerandPetraTodd(2001).“FiftyYearsofMincerEarningsRegressions.”Unpublished.[21]Jenkins,S.P.(1994).“EarningsDiscriminationMeasurement–ADistributionalApproach.”ofEconometrics,61,81-102.

49 [22]Juhn,Chinhui;KevinMurphyandBrooksPie
[22]Juhn,Chinhui;KevinMurphyandBrooksPierce(1993).“WageInequalityAndTheRiseInReturnsToSkill.”TheJournalofPoliticalEconomy,Vol.101,Issue3,410-442.[23]LaLonde,Robert(1986).“EvaluatingtheEconometricEvaluationsofTrainingProgramsWithEx-perimentalData”AmericanEconomicReview,76,604-20.[24]Machado,JoseandJoseMata(2001).“EarningFunctionsinPortugal1982-1994:EvidencefromQuantileRegressions.”EmpiricalEconomics,26(1),115-134.[25]Meyer,Bruce(1995).“NaturalandQuasi-ExperimentsinEconomics.”JournalofBusiness&Eco-nomicStatistics,Vol.13,No.2.[26]Montenegro,Claudio(1999).“WageDistributioninChile:DoesGenderMatter?AQuantileRegres-sionsApproach.”Mimeo,TheWorldBank [40]Smith,JereyandPetraTodd(2000).“Does

50 MatchingOvercomeLalonde’sCritiqueofNonex
MatchingOvercomeLalonde’sCritiqueofNonexperi-mentalEstimators?”Unpublished. Applyingthedeltamethod W=YMP ,thelimitingdistributionoftheproductcanbeapproximatedas Insuchaway,theasymptoticvarianceoftherstcomponentoftheright-handsideof(9)canbecomputedas 2¡ yM(xi)¢2+b2i³bF(xi)´22KXi1XjF(xi)bF(xj) 2 yM(xi) yM(xj). 967 M. Lechner R. Vazquez-Alvarez The Effect of Disability on Labour Market Outcomes in Germany: Evidence from Matching 6 12/03 968 M. Blázquez M. Jansen Efficiency in a Matching Model with Heterogeneous Agents: Too Many Good or Bad Jobs? 1 971 J. De Loecker J. Konings Creative Destruction and Productivity Growth in an Emerging Economy: Evid

51 ence from Slovenian Manufacturing 4
ence from Slovenian Manufacturing 4 12/03 972 J. Köllõ Transition on the Shop Floor - The Restructuring of a Weaving Mill, Hungary 1988-97 4 12/03 973 Occupational Choice across Generations 1 12/03 976 J. D. Angrist K. Lang Does School Integration Generate Peer Effects? Evidence from Boston’s Metco Program 6 01/04 977 M. Corak G. Lipps Family Income and Participation in Post- 1 01/04 980 H. Ñopo J. Saavedra Ethnicity and Earnings in Urban Peru 1 01/04 981 H. Ñopo Matching as a Tool to Decompose Wage Gaps 1 01/04 An updated list of IZA Discussion Papers is availab