NBERWORKINGPAPERSERIES

SUPPLY,DEMAND,INSTITUTIONS,ANDFIRMS:

ATHEORYOFLABORMARKETSORTINGANDTHEWAGEDISTRIBUTION

DanielHaanwinckel

WorkingPaper31318

/papers/w31318

NATIONALBUREAUOFECONOMICRESEARCH

1050MassachusettsAvenue

Cambridge,MA02138

June2023

IwouldliketothankDavidCard,FredFinan,PatKline,MaurizioMazzocco,andAndrésRodríguez-Clarefortheirguidanceandsupport.ThepaperbenefitedfromcommentsfromBenFaber,ThibaultFally,CecileGaubert,JinyongHahn,BrianKovak,ThibautLamadon,ThomasLemieux,NicholasLi,JulianaLondo?o-Vélez,MagneMogstad,PiyushPanigrahi,RaffaeleSaggio,AndresSantos,YotamShem-Tov,AvnerStrulov-Shlain,JoséP.Vásquez-Carvajal,JonathanVogel,ChristopherWalters,fouranonymousreferees,andparticipantsatseveralseminarsandconferencepresentations.IalsothankLorenzoLagosandDavidCardforprovidingcodetocleantheRAISdatasetandGustavodeSouzaforprovidingtaskcontentdataforBrazilianoccupations.IgratefullyacknowledgefinancialsupportfromUCBerkeley'sDepartmentofEconomics,Berkeley'sInstituteforResearchonLaborandEmployment,andtheBeckerFriedmanInstituteforEconomicsattheUniversityofChicago.TheviewsexpressedhereinarethoseoftheauthoranddonotnecessarilyreflecttheviewsoftheNationalBureauof

EconomicResearch.

NBERworkingpapersarecirculatedfordiscussionandcommentpurposes.Theyhavenotbeenpeer-reviewedorbeensubjecttothereviewbytheNBERBoardofDirectorsthataccompaniesofficialNBERpublications.

?2023byDanielHaanwinckel.Allrightsreserved.Shortsectionsoftext,nottoexceedtwoparagraphs,maybequotedwithoutexplicitpermissionprovidedthatfullcredit,including?notice,isgiventothesource.

Supply,Demand,Institutions,andFirms:ATheoryofLaborMarketSortingandtheWage

Distribution

DanielHaanwinckel

NBERWorkingPaperNo.31318

June2023

JELNo.J24,J31,J38

ABSTRACT

Thispaperbuildsageneralequilibriumframeworkwithfirmandworkerheterogeneity,monopsonypower,andtask-basedproductiontoquantifythelong-runeffectsofeducation,biaseddemandshocks,andminimumwage.ItakeittoBraziliandatafor1998and2012andfindthat(i)supplyanddemandshocksincreasesortingofhigh-wageworkerstohigh-wagefirms,(ii)increasedentryofhigh-wagefirmsbooststheeffectofrisingschoolingattainmentonmeanlogwagesby25%,and(iii)theminimumwagereducesformalwageinequalitybutalsocauseswagelossformid-productivityworkersanddisemploymentforthoseattheverybottom.

DanielHaanwinckel

DepartmentofEconomics

UniversityofCalifornia,LosAngeles

8242BuncheHall

LosAngeles,CA90095

andNBER

haanwinckel@

Adataappendixisavailableat/data-appendix/w31318

1

1Introduction

Brazilexperiencedadramaticreductioninwageinequalitybetweenthemid-1990sandtheearly2010s.Inaliteraturereview,FirpoandPortella(2019)pointtothreeshocksasplausiblecausesofthatphenomenon:anincreasedsupplyofskilledlaborduetorisingeducationalattainment,labordemandshocksthatfavoredunskilledworkers(mostlyduetothe2000scommoditiesboom),andlargerealincreasesinthefederalminimumwage.UnderstandingthelabormarketeffectsoftheseshocksisimportantfornotonlythoseinterestedintheBraziliancasebutalsothoseseekingtoremedyrisingwageinequalityinothercontexts.

Tothatend,thispaperdevelopsatractableframeworkthatdescribeshowsupply,demand,andminimumwagejointlydeterminethelong-runwagedistributioninimperfectlycom-petitivelabormarkets.Iemploymatchedemployer-employeedatatotestitstheoreticalpredictionsandtostructurallyestimatealocallabormarketsmodeloftheBrazilianecon-omy.Finally,Isimulatecounterfactualscenariosbasedontheestimatedmodeltoquantifytheindividualimpactsofeachshock,aswellastheirinteractions.

Currentacademicliteratureemploystwoseparateframeworkstostudythelabormarketef-fectsofthoseshocks.Supplyanddemandfactorsaretypicallyexaminedundertheas-sumptionofperfectcompetition,usingmodelswithrepresentative?rms(e.g.,BoundandJohnson,1992;CardandLemieux,2001)orassignmentmodelsbasedoncomparativead-vantage(e.g.,Teulings,1995;AcemogluandAutor,2011).Insuchmodels,inequalitytrendsre?ectchangesinproductivitygapsbetweenworkers.Bycontrast,leadingquantitativemod-elsoftheminimumwage,suchasthosedevelopedbyFlinn(2006)andEngbomandMoser(2022),areimperfectlycompetitive.Thosemodelsemphasizethecontributionofcross-?rmwagedifferentialsbetweenequallyproductiveworkers(henceforth,?rmwagepremiums)tooverallwageinequality.

Althoughtheuseofdifferentframeworksfordifferentshocksfacilitatestractability,italsoimposesrestrictionsoncausalpathways.Incompetitivemodels,supplyanddemandfactorscannotaffectwagesthrough?rmwagepremiumsorsorting,de?nedinthispaperastheassortativenessbetweenworkerskillandthe?rmwagepremiumtheyearnattheircurrentemployer.Butthosechannelsmaybequantitativelyimportant.Forexample,Card,HeiningandKline(2013)andSongetal.(2018)showthatlong-runchangesinsortingaccountforsigni?cantsharesoftheoverallincreaseinwageinequalityinWestGermanyandtheUS,re-spectively.Ifthosechangesinsortingaredrivenbysupplyanddemandfactors,competitive

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modelsmayprovideanincompleteaccountoftheirlabormarketeffects.Ontheminimumwageside,theleadingmodelsimposestrongrestrictionsonhowproductivitygapsbetweenworkersmaychangebyassumingperfectsubstitutabilitybetweenworkertypes,rulingoutchangesintechnologies?rmsmayuse,ordisallowingcostpass-throughs.

AdescriptiveanalysisoftheBraziliancaseshowsthattheserestrictionsmaybeconsequen-tial.Iusematchedemployer-employeedatatocalculatelabormarketstatisticsfor151mi-croregionscomparabletoUScommutingzones.Thosestatisticsincludeseveralmeasuresofwageinequality,minimumwagebindingness,andformalemploymentratesfor1998and2012.IalsousethemethodologydetailedbyKline,SaggioandS?lvsten(2018)toobtainreduced-formestimatesoftheimportanceof?rmwagepremiumsandsorting,basedontwo-way?xedeffectsregressionsinthetraditionofAbowd,KramarzandMargolis(1999).

Manyofmydescriptive?ndingsalignwithpreviousworkonBrazil:thefallininequalityislarge,widespread,andassociatedwiththereduceddispersionof?rmwagepremiums(Alvarezetal.,2018).However,Ialsodocumentanewfactnotreadilyexplainedbyexistingtheoreticalapproaches:assortativematchingrisesinmostregions.AlthoughpaperssuchasEngbomandMoser(2022)allowfortheminimumwagetoimpactsorting,itactsintheoppositedirection.

Motivatedbythese?ndings,Idevelopanewframeworktoinvestigatewhetherthetrans-formationsobservedinBrazilianlabormarketscanbeparsimoniouslyexplainedbysupply,demand,andminimumwageshocksand,ifso,todeterminewhatroleeachofthemplays.

Itfeaturesrichworkerand?rmheterogeneity,atask-basedmodelofproduction,monop-sonypowerbasedonidiosyncraticworkerpreferences,generalequilibriuminthemarketforgoods,andfreeentryof?rms.Thedistinguishingfeatureofmyframeworkisthatitcombinesthetwotheoreticalperspectivesmentionedabovebyallowingallshockstoaffectwagesviachangesinlaborproductivity,thedispersionof?rmwagepremiums,andsorting.

Thisuni?edapproachprovidesnovelinsightsintohowtheseshocksaffectwageinequal-ity.The?rstinsightisanewexplanationforwhyincreasesinthesupplyofskilledlabormayhavelimitedeffectsontheaggregateskillwagepremium,ormayevenwidenit(Blun-dell,GreenandJin,2021;Carneiro,LiuandSalvanes,2022).Thisphenomenonistypicallyexplainedusingmodelsofendogenousinnovation,whichcreatesnon-convexitiesintheag-gregateproductionfunction(Acemoglu,1998,2007).Myframeworkfeaturesnosuchnon-convexities.Instead,theaggregateskillpremiumcanrisewhenthesupplyshockleadstothecreationofskill-intensive,high-wage?rms,andthegainsin?rmpremiumsforskilled

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workersreallocatedtothosenew?rmsoutweighdecreasesinproductivitydifferentialsbyskill.1

Ialsoshowthatthecombinationofmonopsonypower,?rmheterogeneity,andtask-basedproductioncanleadtoqualitativechangesinminimumwageeffects.Workersofdifferentskilllevelsmaybecomplementsathigh-wage?rmsthatuseabroadsetoftasksinproduc-tion,butsubstitutesinlow-wage?rmsspecializedinsimpletasks.Whentheminimumwagereallocatesunskilledlaborfromlow-tohigh-wage?rms,productivitygapsbetweenskilledandunskilledworkersmaywidenwithinthedestination?rms.Buttheremaybenochangeinproductivitydifferentialsattheorigin?rms.Asaresult,theimpactofminimumwagesmaybenegativeinthemiddleofthewagedistributionandpositiveatthetop,contrast-ingwiththesmoothinequality-reducingeffectspredictedbycompetitivetask-basedmodels(Teulings,2000).

Thetheoreticalresultshavebroaderrelevancetominimumwageliterature,astheycallatten-tiontoidenti?cationthreatsinreduced-formdesigns.Somestudiesmeasureminimumwageeffectsusingpaneldataatthe?rmlevel,de?ningtreatmentandcontrol?rmsbasedontheinitialfractionoftheiremployeeswithwagesbelowthenewminimum.Asdiscussed,high-wage?rmsmaybeaffectedbytheminimumwageduetoreallocationin?ows,evenintheabsenceofgeneralequilibriumresponses.However,becausesuch?rmsarelikelytohavealow“fractionaffected”duetotheirwagepremium,theregressionusesthemascontrolunits.Similarconcernsmayapplytodesignscomparingworkerswithinitialwagesbelowthenewminimumandothersinthesameregionwithhigherwages.

Withtheobjectiveofperformingpolicycounterfactuals,Iestimateaparsimoniousparame-terizationoftheframeworkusingasimultaneousequationnonlinearleastsquaresprocedure.Conceptually,theexerciseresemblesKatzandMurphy(1992)orKruselletal.(1999),whousesupply/demandmodelstoexplainrisingwageinequalityintheUS.Itargetanarrayofendogenousoutcomesattheregion-timelevel:wageinequalitybetweenandwithinthreeeducationalgroups,thevarianceof?rmeffects,thecovarianceof?rmandworkereffects,minimumwagebindingnessmetrics(includingthesizeoftheminimumwagespike),andformalemploymentratesbyeducationtype.Althoughover-identi?ed,themodel?tsthedatawell.Iinterpretthequalityof?tasdemonstratingthat,atleastintheBraziliancontext,

1ThismechanismiscomparabletothatofAcemoglu(1999)butdiffersinthatitisnotbasedonsearchfrictions.Inaddition,?rmsinmymodelarelargeandsimultaneouslyemploymanyworkertypes,withwithin-?rmimperfectsubstitutionbetweenskilllevels.ThisgeneratessmoothlabormarketresponsestosupplyshocksinsteadofthediscreteregimechangespredictedbyAcemoglu(1999).

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seculartrendsinwageinequality,thedispersionof?rmwagepremiums,andsortingcanbelargelyexplainedbysupply,demand,andminimumwage.

Armedwiththeestimatedmodel,Imeasurethelabormarketimpactsofeachshockandtheirinteractions.Consistentwithpreviouswork,I?ndthatdemandshocksandtheminimumwagearethemaincausesofthedeclineinwageinequalityinBrazil’sformalsector.Ialso?ndsigni?cantinteractionsthatwouldnotbedetectablewithoutauni?edframework.Theinequalityeffectsoftheminimumwagearetwiceaslargewhenthatshockactsinisolation,comparedtoascenariowhereitisaccompaniedbysupplyanddemandtransformations.Supplyanddemandshocksincreasemeasuredsorting,withtheireffectmagni?edwhentheyacttogether.Theminimumwagereducessorting,butitseffectisweakerwhensupplyanddemandarealsochanging.

Ialsoconducttwodecompositionexercisesthatdemonstratethequantitativerelevanceofthenewtheoreticalpathways.Inthe?rstexercise,Ishowthatincreasedentryofhigh-wage?rmsampli?estheeffectsofrisingschoolingachievementonmeanlogwagesby25%.

Thesecondexercise?ndsthattheminimumwagehasnegativewageeffectsonworkersinthemiddleoftheproductivitydistributionduetoendogenouschangesinwagespostedbyhigh-wage?rms.Theseeffectsdiffermarkedlyfromsimulated“minimumwagespillovers”becausetheminimumwagecausesdisemploymentforverylow-skilledworkers(suchthatspilloversarisefromtruncationofthelatentproductivitydistribution).IincludeadiscussionofthereasonsthatmyresultsdifferfromtherecentworkofEngbomandMoser(2022),whoobservesmallemploymenteffectsinBrazilusingbothreduced-formmethodsandastructuralmodel.

Thepaperproceedsasfollows.Thenextsectiondetailshowthisworkbuildsuponandcontributestodifferentstrandsofliterature.ThethirdsectioncontainsadescriptiveanalysisoftheBraziliandata.Thefourthsectionpresentsthetask-basedmodelofproductionandsomeofitsimplicationsinpartialequilibrium.The?fthsectiondescribesthecompletegeneralequilibriumframeworkanddiscussesitspredictionsconcerningtheeffectsofsupply,demand,andminimumwage.Thesixthsectioncontainsthequantitativeexercises.The?nalsectionconcludeswithdirectionsforfurtherresearch.

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2Literatureandcontribution

Thispaper’sframeworkcanrationalizealargesetofempiricalfactsdocumentedinrecentyears.Itcanexplainwhythecontributionof?rmwagepremiumsandsortingtowagein-equalitymaychangeinthelongrun(Card,HeiningandKline,2013;Songetal.,2018;Al-varezetal.,2018).Sortingoriginatesfromdifferencesindemandforskillsbetween?rms,asdocumentedbyDemingandKahn(2018).Because?rmsuseproductionfunctionsfeaturingcomplementaritybetweenworkertypes,theframeworkrationalizeschangesinwithin-?rmwagesinresponsetoshiftsinitsinternalworkforcecomposition,suchasthosedocumentedbyJ?gerandHeining(2022).Minimumwagecancausepositiveemploymenteffects,reallo-cationofworkersfromlow-tohigh-wage?rms(Dustmannetal.,2021),spillovers(Fortin,LemieuxandLloyd,2021),andchangesinhowselective?rmsarewhenhiring(Butschek,2022).Minimumwagesmayalsoprecipitatechangesinthetypesof?rmsoperatingintheeconomy(Rohlin,2011;Aaronsonetal.,2018)andrelativeconsumerprices(HarasztosiandLindner,2019).Includingallthosepotentialchannelslendscredibilitytothemodel’squantitativepredictions.

Onthetheoreticalside,mytask-basedmodelofproductionbuildsupontheworkofSattinger(1975)andTeulings(1995),amongmanyothers.Iderivenewformulasforelasticitiesofcomplementaritybetweenworkertypesandprovidecomputationallyef?cientparameteriza-tion.Butthecorecontributiontothisliteratureischaracterizingtask-basedproductioninanenvironmentwithmonopsonypowerandheterogeneous?rms.Ishowthattheoptimalassignmentofworkerstotasksmaydifferbetween?rmsand?ndsupportforthatpredictioninthedata.Ialsodiscusshowsubstitutionpatternsdifferbetween?rmsandwhythatmattersforcomparativestatics.

ThesecondstrandofliteratureIbuilduponconcernsmonopsonymodelsoflabormarketsbasedonidiosyncraticworkerpreferencesfor?rms.IembedthemodeldevelopedbyCardetal.(2018)intoageneralequilibriumframeworkwithtask-basedproduction,?rmentry,endogenousparticipationdecisions,andminimumwages.Ishowhow?rmheterogeneityinskillintensityandwagepremiumsemergefromdifferencesinproductiontechnologiesavailabletoentrepreneurswhentheycreate?rms.Ialsoshowthattheelasticityoflaborsupplytoindividual?rms—akeycomponentofmonopsonymodels—canbeidenti?edfromthesizeoftheminimumwage“spike”inlogwagedistributions.2,3

2Ithankananonymousrefereeforthissuggestion.

3Withinthemonopsonyliterature,mypaperresemblestheworkofLamadon,MogstadandSetzler(2022),

6

Morebroadly,thispaperrelatestomodelsthatquantifytheeffectsofchangingsupplyofanddemandforskills.Withinthatliterature,itisclosesttothosewheresupply/demandshocksalterthecompositionofjobsintheeconomy.Someworkinthattradition,suchasKremerandMaskin(1996)andLindenlaub(2017),abstractfromtheroleof?rmwagepremiums.Others,suchasHelpmanetal.(2017),ShephardandSidibe(2019),andLiseandPostel-Vinay(2020),featureimperfectcompetitionand?rmwagepremiumsbutassumeworkersareperfectsubstituteswithin?rms(orthateach?rmhiresonlyoneworker).Insuchmodels,labormarketimperfectionsaretheonlyreasonforobservingskillsdispersionwithina?rmtype.Bycontrast,?rmsinmymodelhiremultipletypesofworkerstobene?tfromthedivisionoflabor,evenwhenlabormarketsarecompetitive.Accurate?rm-workersortingpatternsareimportantforcapturingthepartoftheeffectsofsupply/demandshocksthatderivefromendogenous?rmentryandchangingprices.4

Finally,Idescribehowmyframeworkdiffersfromquantitativemodelsofminimumwagesdevelopedinrecentyears.EngbomandMoser(2022)buildamodelwithon-the-jobsearchinthestyleofBurdettandMortensen(1998).Similartomystudy,theyestimatetheirmodelusingBraziliandataandmatchmomentsfromtwo-way?xedeffectsdecompositions.Be-causetheirmodelfeaturessearchfrictions,itisbettersuitedtostudyingjobladdersandtransitionsintoandoutofunemployment.However,itabstractsfromnon-wageamenitiesandassumesperfectsubstitutabilitybetweenworkertypes.

Berger,HerkenhoffandMongey(2022b)andHurstetal.(2022)buildmonopsonisticmin-imumwagemodelswithimperfectsubstitutionacrosslabortypes.Berger,HerkenhoffandMongey(2022b)includecross-?rmdifferencesinproductivityandallowforvariationinmarkdownsdependingonthe?rmsizerelativetothemarket.Hurstetal.(2022)abstractfrom?rmheterogeneitybutincludesearchfrictionsandaputty-claytechnologythatallowsthemtodistinguishbetweenshort-andlong-runminimumwgaeeffects.Theyalsostudyhowminimumwagecanbepairedwithtransferstoachieveredistributiongoals.

whosemodelalsogeneratesrealistic?rmwagepremiumsandsortingpatterns.Theyallowforworkerreallo-cationacrossregionsandricherformsof?rmheterogeneitybutdonotmodelwithin-?rmcomplementaritiesbetweenworkertypes,endogenousparticipationdecisions,?rmentry,orminimumwages.

4EeckhoutandPinheiro(2014)andTrottner(2019)alsomodellarge?rmswithmultiplejobs,butwithcommonelasticitiesofsubstitutionacrossallpairsofworkertypes.Herkenhoffetal.(2018)allowsforsearchfrictionsandwithin-?rmcomplementarities,but?rmsmayonlyemployuptotwoworkers.Modelsofhierar-chical?rmsinthetraditionofGaricano(2000),GaricanoandRossi-Hansberg(2006),andAntràs,GaricanoandRossi-Hansberg(2006)implywithin-?rmdivisionoflabor,butthemodelingofcostlyinformationtrans-missionwithin?rmsreducestheirtractability.Myproductionstructurecanbeviewedasahierarchical?rmsmodelwithoutthatcostandwithouttherestrictionthathierarchiesneedtobepyramidal.

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Asatoolforevaluatingminimumwages,myframeworkisuniqueinfourways.First,substitutionpatternsbetweenworkertypesdependonwhethertheyarecloseordistantintermsofskillandalsoonthetaskdemandsofthe?rmemployingthem.Second,itallowsforcostpass-throughsandendogenouschangesinthecompositionof?rmsoperatingintheeconomy.Third,itmeasureshowminimumwagesinteractwitheducationaltrendsandmanytypesoflabordemandshocks.Fourth,itincludesanestimationprocedurebasedonregionalandtimevariation.Thatprocedureshowcasesthemodel’stractability(becauseeachiterationoftheestimationprocedurerequiressolvingforequilibriamorethan15thousandtimes)anditsabilitytoexplaincross-sectionalvariationinfeaturessuchastheminimumwagespike.Italsoallowsformeasuringhowminimumwageeffectsdifferbetweenlocallabormarkets,whichmaybeimportantincontextswithsigni?cantregionalheterogeneity.

3WageinequalityandsortinginBrazil

Inthissection,Ipresentdescriptivestatisticsthatmotivatethetheoreticalframework.Iusetwodatasources.The?rstistheRAIS(Rela??oAnualdeInforma??esSociais),acon-?dentiallinkedemployer-employeedatasetmaintainedbytheBrazilianMinistryofLabor.FirmsaremandatedbylawtoreporttotheRAISattheestablishmentlevel.Thedatasetcon-tainsinformationaboutboththeestablishment(includinglegalstatus,economicsector,andthemunicipalityinwhichitisregistered)andeachworkeritformallyemploys(includingeducation,age,earningsinDecember,contracthours,andhiringandseparationdates).

TheotherdatacomefromtheBraziliancensusesof1991,2000,and2010.Fromthem,Iobtainstatisticsfortheoverallpopulation,suchasthenumberofadultsineacheducationalgroupandtheproportionofthosewhoholdformaljobs.IalsoextractfromtheCensustheshareofworkersinagriculture,manufacturing,orothersectors.5

Ifocusonindividualsbetween18and54yearsofage.IntheRAIS,IselectindividualsinthatagerangewhoareworkinginDecember,havingbeenhiredinNovemberorearlier.Ifaworkerhasmorethanonejobinthesameyear,Ionlykeepthehighest-payingone.

Allthestatisticsarecalculatedatthelocallevel.Iusetheconceptof“microregion”asde?nedbytheBrazilianStatisticalBureau(IBGE).Microregionsgroupnearby,economi-

5The1998outcomesareinterpolatedusingthe1991and2000Censuses.The2012outcomesareextrap-olatedusing2000and2010.Theinterpolationsandextrapolationsarelinearforformalemploymentratesandsectoralshares,andlinearinlogsforpopulationcounts.

8

callyconnectedmunicipalities("IBGE",2003).Theyarecommonlyusedtode?nelocallabormarketmodelsinBrazil(e.g.,Costa,GarredandPessoa,2016;PonczekandUlyssea,2021).6

Iusealocallabormarketsapproachfortworeasons.First,regionalvariationhelpsiden-tifykeyparametersofthestructuralmodel.Second,locallabormarketsmorecloselymaptheorytoempirics.If?rm-workersortingismeasurednationally,itwilllargelyre?ectge-ographicalbarriersinadditiontothesupply-demand-minimumwagedynamicsemphasizedbytheframework.IreturntothispointattheendofthepaperwhenIcomparemyresultstopreviousworkstudyingtheBraziliancase.

The?nalsampleisrestrictedtomicroregionswithatleast15,000workersintheRAISdatain1998and2012andatleast1,000formalworkersineachofthethreeeducationalgroupsde?nedbelow.7Thatleavesasetof151microregionsencompassing73%oftheadultpopulation.AppendixTableD1presentstheconsequentsamplesizes.

Differingfromthepatterninmanyhigh-incomecountries,wageinequalityhasbeendown-wardtrendinginBrazilsincethe1990s.The?rsttwopanelsinTable1reporttheevolutionofseveralinequalitymetricscalculatedatthemicroregionlevelandaveragednationallyus-ingtotalformalemploymentinbothbaseyearsasweights(thismeansthatregionweightsareconstantovertime).Almostallmetricsaredeclining,someofthemdramatically.Theoneexceptionisthecollegepremium,whichwidenedin47outof151regions.Becausethoseregionstendtobelarger,theaveragecollegepremiumincreased.

Igaugethecontributionof?rmwagepremiumsandsortingusingregion-speci?cvariancedecompositionsbasedontwo-way?xedeffectsregressionsoflogwages(henceforthAKMregressionsafterAbowd,KramarzandMargolis,1999).Thelogwageofworkeriinregionrattimeriswrittenas:

logyi,r,r=vi,r＋wJ(i,r,r)＋6r,r＋ui,r,r

wherevi,ristheworker?xedeffect,wjisestablishmentj’s?xedeffect,J(i,r,r)denotesthe

6Usingdatafor2000and2010,Dix-CarneiroandKovak(2017)calculatethatlessthan5%ofworkerslivedinoneregionandworkedinanother.Thatnumber,combinedwiththeiraveragesize,makesBrazilianmicroregionsanalogoustocommutingzonesintheUS.Aftercombiningsomemicroregionstoensurethattheirboundariesremainconstantthroughoutthestudyperiod,mybasesamplefeatures486microregions.

7Mystructuralestimationprocedurerequiresalowlevelofmeasurementerrorinformalemploymentratesbyeducationalgroupandminimumwagebindingness.Thoserestrictionsalsoyieldbetterestimatesofthecontributionof?rmwagepremiumsandsortingtolocalwageinequality.

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Table1:Evolutionofwageinequalitymeasuresandsorting

19982012

PanelA:Variancesoflogwages

Allworkers

Lessthansecondary

Secondary

Tertiary

PanelB:Meanlogwagegapsin

Secondary/lessthansecondaryTertiary/secondary

inbase

years

0.7150.4100.684

0.5440.2410.3550.624

0.1681.038

0.702

baseyears

0.4980.965

PanelC:Variancedecompositionusingthree-yearpanels

Totalvariance

Varianceofworkereffects

Varianceofestablishmenteffects2xCovarianceworker,estab.effectsCorrelationworker,establishmenteffects

0.6880.4190.1160.0980.224

0.5770.3840.0560.0970.315

Notes:PanelsAandBdisplayaveragewageinequalitymeasuresforthebaseyearsof1998and2012.PanelCshowstheaverageoutcomesofregion-speci?clogwagedecompositionsbasedonEquation(1),usingtheestimatorprovidedbyKline,SaggioandS?lvsten(2018).Allnumbersareaveragedoverregionsusingthetotalnumberofformalworkersinbothbaseyearsasweights.

establishmentemployingworkeriinregionrattimer,6r,risaregion-timeeffect,andui,r,risaresidual.Then,thewithin-regionvarianceoflogwagescanbewrittenasfollows:

Var(logyi,r,rlr)=Var(vi,rlr)＋Var╱wJ(i,r,r)lr、＋2Cov╱vi,r,wJ(i,r,r)lr、

＋Var(6r,rlr)＋2Cov╱vi,r＋wJ(i,r,r),6r,rlr、＋Var(ui,r,rlr)(1)

Ifwagesdiffersubstantiallyacrossestablishmentsforsimilarworkers,thevarianceofestab-lishmenteffectsmaybelarge,addingtooverallwagedispersion.Ifhigh-wageworkersaremorelikelytoworkathigh-wageestablishments,thenthe?rstcovariancetermwillbeposi-tive,furtherboostinginequality.Basedonthislogic,the