Globalization, inequality and welfare

26 Pages·2017·1.64 MB·English

by  Pol Antràs

JournalofInternationalEconomics108(2017)387–412
ContentslistsavailableatScienceDirect
Journal of International Economics
journal homepage: www.elsevier.com/locate/jie
(cid:2)
Globalization, inequality and welfare
PolAntràsa,*,AlonsodeGortaria,OlegItskhokib
aHarvardUniversity,UnitedStates
bPrincetonUniversity,UnitedStates
A R T I C L E I N F O A B S T R A C T
Articlehistory: Thispaperstudiesthewelfareimplicationsoftradeopeninginaworldinwhichtraderaisesaggregate
Received6April2017 incomebutalsoincreasesincomeinequality,andinwhichredistributionneedstooccurviaadistortionary
Receivedinrevisedform20July2017 incometax-transfersystem.Weprovidetoolstocharacterizeandquantifytheeffectsoftradeopeningon
Accepted21July2017 thedistributionofdisposableincome(afterredistribution).Weproposetwoadjustmentstostandardmea-
Availableonline26July2017
suresofthewelfaregainsfromtrade: a‘welfarist’ correctioninspiredby theAtkinson(1970)indexof
inequality,anda‘costly-redistribution’correctioncapturingtheefficiencycostsassociatedwiththebehav-
JELclassification: ioralresponsesofagentstotrade-inducedshiftsacrossmarginaltaxrates.Wecalibrateourmodeltothe
F10 UnitedStatesovertheperiod1979–2007usingdataonthedistributionofadjustedgrossincomeinpublic
F60
samplesofIRStaxreturns,aswellasCBOinformationonthetaxliabilitiesandtransfersreceivedbyagents
D30
atdifferentpercentilesoftheU.S.incomedistribution.Ourquantitativeresultssuggestthatbothcorrec-
D60
H20 tionsarenonnegligible:trade-inducedincreasesininequalityofdisposableincomeerodeabout20%ofthe
gainsfromtrade,whilethegainsfromtradewouldbeabout15%largerifredistributionwascarriedoutvia
Keywords: non-distortionarymeans.
Globalization ©2017ElsevierB.V.Allrightsreserved.
Tradeintegration
Socialwelfare
Inequality
Costlyredistribution
1. Introduction of 4.9% to 7.7%, while the Gini coefficient associated with the dis-
tribution of U.S. market income grew dramatically from a level of
Two of the most salient phenomena in the world economy in 0.48allthewayto0.59.Furthermore,asisclearfromFig.1,trade
recent years have been a rapid increase in the extent to which integrationandinequalitygrewverymuchinparallel,especiallyin
economies have become interconnected and a significant rise in the1990sand2000s.Theextenttowhichthesetwophenomenaare
incomeinequalityinmanycountries.Forinstance,duringtheperiod causally related has beenthe subject of intenseacademic debates,
1979–2007,theU.S.tradeshare(definedastheaverageofexports butitisbynowawidelyacceptedviewthattradeintegrationhas
and imports divided by U.S. gross output) increased from a value beenasignificantcontributortoincreasedwageandincomeinequal-
ityintheU.S.andmanyotherindustrializedcountries.1Thepicture
emergingfromdevelopingcountriesalsopointstotheimportanceof
(cid:2) WethankElhananHelpman,NathanHendren,DaniRodrik,andEstebanRossi- trade-inducedinequality.GoldbergandPavcnik(2007)summarizea
Hansbergforfruitfulconversationsonthetopicofthispaper.Thispaperwaspre- bodyofliteraturestudyingtheconsequencesoftradeliberalization
viouslycirculatedunderthetitle‘Inequality,CostlyRedistributionandWelfarein
acrossanumberofdevelopingcountriesafter1970s,withthebulk
anOpenEconomy’.WeareindebtedtoXiangDingandTeresaFortfortheirhelp
ofepisodestriggeringsignificantincreasesininequality.
obtainingakeymomentinourcalibrationfromU.S.Censusdata,andtoDanielFeen-
bergforhisassistancewiththeNBER-IRSdata.TheCo-Editor(SteveYeaple)andtwo
anonymousrefereesprovidedveryusefulfeedback.Wearealsogratefultoseminar
audiencesatLSE,BarcelonaSummerForum,DegitXXinGeneva,SEDinWarsaw,AEEFI
inSanSebastián,PennState,ITSGinRome,IMF,Princeton,Stanford,UBC,National
UniversityofSingapore,Lausanne,NOITSinOslo,Bocconi,SeoulNationalUniversity,
Bayreuth,Harvard,FederalReserveBoard,ChineseUniversityofHongKong,Columbia 1 FeenstraandHanson(1999),forinstance,estimatethatoutsourcingalonecould
University,ParisTradeSeminarandUSCDornsife-iNETfortheirsuggestions. accountforasmuchas40%oftheincreaseintheU.S.skillpremiuminthe1980s.
*Correspondingauthor. Other studies, summarized in Krugman (2008), arrive at more conservative esti-
E-mail addresses:[email protected](P.Antràs),adegortaribriseno@fas. matessuggestingthattradeaccountedforabout15–20%oftheincreaseinincome
harvard.edu(A.deGortari),[email protected](O.Itskhoki). inequality.
http://dx.doi.org/10.1016/j.jinteco.2017.07.009
0022-1996/©2017ElsevierB.V.Allrightsreserved.
388 P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412
indexofinequality,whichhasbeenrarelyappliedintradecontexts.2
On the other hand, we derive a ‘costly-redistribution’ correction
whichcapturesthebehavioralresponsesofagentstotrade-induced
shifts across marginal tax rates. This second adjustment builds on
the voluminous public finance literature on the efficiency costs of
income taxation, and is especially related to the structural work
of Benabou (2002), although our approach is generalized to apply
to income distributions other than the lognormal one, and also to
modelswithanextensivemarginresponsetotaxation.
WebeginouranalysisinSection2withinafairlygeneralenvi-
ronmentthatillustratestherationaleforthesetwocorrectionswhen
evaluating any policy (not just trade liberalization) that has the
potentialtoaffecttheshapeoftheincomedistributionbeyondits
mean. In this environment, we derive explicit formulas for these
adjustmentsintermsofspecificmomentsoftheincomedistribution,
the level of progressivity of the tax-transfer system, the degree of
inequalityaversionofthesocialplanner,andtheelasticityoftaxable
incometochangesinmarginaltaxrates.
Fig.1. Tradeintegrationandincomeinequality:UnitedStates(1979–2007). OurenvironmentinSection2issilentontheprimitivedetermi-
nantsoftheincome-generationprocessorontheprecisemechanism
thatleadstoapositiveelasticityofincometochangesinmarginal
taxes.InSection3,wedevelopamicrofoundedsimplegeneralequi-
Despite these recent trends, the standard approach to demon- librium framework that illustrates how the ability of individuals
stratingandquantifyingthewelfaregainsfromtradelargelyignores and their labor supply decisions translate in equilibrium earnings
the implications of trade-induced inequality. The paradigm used and welfare levels given the tax system in place. When solving
to evaluate the social welfare consequences of trade integration for the closed-economy equilibrium of the model, we are able to
is the Kaldor-Hicks compensation principle (Kaldor, 1939; Hicks, decomposechangesinwelfareintothreeterms:(i)changesinthe
1939). This approach begins by computing the compensating (or welfareofahypothetical‘Kaldor-Hicks’economywithaccesstocost-
equivalent)variationofapolicychangeattheindividuallevel,and less redistribution and no inequality aversion, (ii) changes in the
then aggregates this money metric across agents. The celebrated welfarist correction, and (iii) changes in the costly-redistribution
‘gainsfromtrade’resultdemonstratesthat,incompetitiveenviron- correction.
ments,whenmovingfromautarkytoanyformoftradeintegration, TheeconomicenvironmentwedevelopbuildsonItskhoki(2008),
theloserscanalwaysbecompensatedandthereissomesurplusto and is inspired by the canonical optimal taxation framework of
potentiallyturnthisliberalizationintoaParetoimprovement.Akey Mirrlees(1971)andtheworkhorsemodeloftradeofMelitz(2003).
advantageoftheKaldor-Hickscriterionasatoolforpolicyevalua- Agents in our economy are workers in which each produce a dis-
tionisthatitcircumventstheneedtobasepolicyrecommendations tincttaskassociatedwiththeproductionofafinalgood.Unobserv-
oninterpersonalcomparisonsofutility,thusextricatingeconomists’ able heterogeneity in productivity across agents generates income
prescriptionsfromtheirownmoralconvictions(cf.,Robbins,1932). inequality, which an inequality-averse social planner may try to
As influential as the Kaldor-Hicks compensation principle has moderateviaaprogressivesystemofincometaxation.Thetwokey
proventobe,ithastwobasicshortcomings.First,thefactthatthere departuresfromtheclassicMirleesframeworkisthatweallowfor
is the potential to compensate those that are hurt from a particu- imperfectsubstitutabilityinthetaskservicesprovidedbydifferent
larpolicydoesnotimplythattheseloserswillbecompensatedin workers and that we restrict attention to a specific form of non-
practice. If one knew that the redistribution or compensation nec- lineartaxationthat,consistentlywithU.S.data,impliesalog-linear
essary for a policy to generate Pareto gains would not happen or relationshipbetweenincomelevelsbeforeandaftertaxesandtrans-
wouldnotbecomplete,shouldn’ttheevaluationofsuchapolicytake fers(seeHeathcoteetal.,forthcoming).Imperfectsubstitutabilityis
thisfactintoaccount?Second,thesimpleaggregationofindividual notessentialforourclosed-economyresultsbutisthesourceofthe
compensating or equivalent variations in the Kaldor-Hicks crite- welfaregainsfromtradelaterinthepaper.3
rion implicitly assumes the existence of non-distortionary means Beforemovingtothisopen-economyenvironment,inSection4
to redistribute part of the gains from the policy to those that do we provide a brief calibration of the closed-economy model that
not directly benefit from it. In reality, compensation often takes decomposestheevolutionofsocialwelfareintheU.S.overtheperiod
placethroughataxandtransfersystemembodyingnontrivialdead- 1979–2007intermsofthewelfaristandcostly-redistributioncorrec-
weightlosses,soitseemsreasonabletobuildthischaracteristicof tionsandthewelfareofthehypothetical‘Kaldor-Hicks’economy.We
redistributionintomeasuresofthesocialwelfareeffectsofapolicy. calibrateourmodelusingdataonthedistributionofadjustedgross
Inthispaper,westudythewelfareimplicationsoftradeopening incomeinpublicsamplesofIRStaxreturns,aswellasCBOinforma-
inaworldinwhichinternationaltradeaffectstheshape(andnotjust tiononthetaxliabilitiesandtransfersreceivedbyagentsatdifferent
the mean) of the income distribution, and in which redistribution pointsoftheU.S.incomedistribution.Ourcalibrationrevealsavery
policiesneedtooccurviaadistortionaryincometax-transfersystem. significantdeclineinthedegreeoftaxprogressivityoverthisperiod
Inthisenvironment,weprovidetoolstocharacterizeandquantify despite the concomitant increase in ‘primitive’ income inequality.
the actual amount of compensation that will take place following Thisnaturallyresultedinanexacerbatedincreaseininequalityinthe
trade opening, as well as the efficiency costs of undertaking such
redistribution. More specifically, we propose two types of adjust-
mentstostandardmeasuresofthewelfaregainsfromtrade.Onthe
one hand, we develop a ‘welfarist’ correction which captures the 2 ThreeveryrecentexceptionsaretheongoingprojectsbyRodriguez-Clareetal.
(2015),Artucetal.(2017)andCarrèreetal.(2015).
negativeimpactthatanincreaseininequalityinthedistributionof
3 ImperfectsubstitutabilitybetweendifferenttypesoflaborintheMirrleesmodel
disposableincomehasonthewelfareofaninequality-aversesocial
wasstudiedbyFeldstein(1973)andStiglitz(1982)inatwo-classeconomy,andmore
planner.ThisfirstadjustmentistightlyrelatedtotheAtkinson(1970) recentlybySachsetal.(2016)inamoregeneralenvironment.
P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412 389
distributionofdisposableincome.Asaconsequence,evenformodest Our model of the effects of trade on the income distribution is
degreesofinequalityaversion,theimpliedsocialwelfaregainsare highly stylized and abstracts from many features that have been
significantlylowerthantheaveragerealincomegainsrecordedover emphasized in past and more recent research on trade and labor
thisperiod.4 markets. For many years, the Heckscher-Ohlin (HO) model, and in
Wealsouseoursimplecalibrationtoshedlightonthegrowth particularitsStolper-Samuelsontheorem,providedthekeyconcep-
inaveragerealincomethattheU.S.wouldhaveattainedifthepro- tualframeworkusedtoanalyzethelinksbetweentradeandwage
gressivityoftheU.S.taxsystemhadbeenkeptconstantatits1979 inequality. Nevertheless, the empirical limitations of this frame-
level,oriftaxprogressivityhadincreasedtoavoidtheobservedrise work have become apparent in recent years. As mentioned above,
inincomeinequality.Wefindthatrealincomegrowthinthosecoun- sharpincreasesininequalityhappenednotonlyinrichbutalsoin
terfactualscenarioswouldhavebeenmarkedlylowerthanthe1.31% unskilled-labor abundant developing countries, a phenomenon at
annualincreaseobservedinthedata.Forinstance,forthecaseofa oddswiththepredictionsoftheHOmodel.5Inaddition,thecontri-
degreeofinequalityaversionequalto1andanelasticityoftaxable butionoftheresidualcomponentofwageinequalitywithingroups
incomeequalto0.5,wefindthatrealincomewouldhavegrownatan ofworkerswithsimilarobservablecharacteristicsappearstobeat
averageannualrateof0.85%iftaxprogressivityhadremainedcon- leastasimportantasthegrowingskillpremiumacrossgroups,which
stant,andatanevenlowerannualrateof0.40%ifprogressivityhad istheonlychannelcapturedbytheHOmodel.6 Finally,contraryto
increasedtokeepincomeinequalityunchangedovertheperiod. themainmechanismofadjustmentintheHOmodel,therealloca-
Armedwiththissuggestiveevidenceofthequantitativeimpor- tionwithinsectorsappearstobemoreimportantthanacrosssectors
tanceofourtwokeyinequalitycorrections,in Section5wemove forbothadjustmenttotradeandinequalitydynamics.7
toanopen-economyenvironment,whichisadirectextensionofthe Forthesereasons,recentworkhasexploredalternativemodels
closed-economyframeworkinSection3.Inparticular,ourassumed featuring richer interactions between labor markets and trade lib-
imperfectsubstitutabilityofthetasksperformedbydifferentwork- eralization. One branch of this literature has explored the role of
ersworldwideresultsinwelfaregainsfromtradeintegrationasso- searchfrictionsandothertypesoflabor-marketimperfections(see,
ciated with final output being produced with a wider range of forinstance,Helpmanetal.,2010,EggerandKreickemeier,2009aor
differentiatedtasks.Theselove-for-varietygainsfromtradearethus AmitiandDavis,2012,amongmanyothers),whileasecondbranch
analogoustothoseinKrugman(1980)orEthier(1982).Inorderto has focused on the role of sorting of heterogeneous workers into
generatenontrivialeffectsoftradeontheincomedistribution,we firmsortechnologies(see,forinstance,Yeaple,2005,Costinotand
followMelitz(2003)andintroducefixedcostsofexporting,which Vogel,2010orSampson,2014),orthematchingofheterogeneous
allowonlythemostproductiveagentstoparticipateininternational workersintoproductionteams(seeAntràsetal.,2006).Ourinter-
trade.Consequently,tradedisproportionatelybenefitsthemostpro- national trade model is more parsimonious than those developed
ductive agents in society, leading to greater income inequality in inthisrecentresearch,yetthemechanismthroughwhichitgener-
a trading equilibrium than under autarky. The progressivity of the atestrade-inducedinequalityisthesame.Thekeydistinctionofour
taxsystemattenuatestheriseininequalityfollowingtradeliberal- stylizedmodel,criticalforouranalysis,isthatitallowsustoincor-
ization,butunlesstaxprogressivityincreaseswithtrade,thedistri- porate behavioral responses to taxation, not featured in previous
butionofdisposableincomewillnecessarilybecomemoreunequal work.Anotherimportantadvantageforourpurposesisthat,despite
withtrade,thusleadingtoahigher‘welfarist’correctionthanunder beingstylized,ourmodelisreadilyamenabletothecalibrationofthe
autarky.Our‘costly-redistribution’correctionisalsogenerallyexac- fullincomedistributionandthequantificationofthecounterfactual
erbated by a process of trade integration. This is for two reasons. inequalityeffectsfromatradeliberalization.Anopenquestionfor
First,thewideningspreadintheincomedistributionimpliesthatrel- futureresearchistheextenttowhichtheinequalitycorrectionsaris-
ativelyrichindividualsmovetohighermarginaltax‘brackets’,which ingfromourframeworkaresimilarinmagnitudetothoseonewould
haslargedisincentiveeffectsontheirlaborsupply,therebyreduc- obtaininricherframeworks.8
ing the aggregate income response to trade opening. And second, Withintheinternationaltradefield,ourpaperisalsorelatedto
selectionintoexportingintroducesanextensivemarginthatisalso previous work studying the redistribution of the gains from trade.
sensitive to national redistribution policies and that magnifies the FollowingDixitandNorman(1980,1986),thisstrandofthelitera-
overallefficiencycostsoftaxation. turehasmainlyfocusedonthepossibilityofcompensatingthelosers
InSection6,wecalibrateouropen-economymodelwiththesame fromtradethroughavarietyoftaxinstruments.DixitandNorman
IRStaxreturnsdataemployedinSection4,togetherwithmeasures themselvesfocusedonthesufficiencyofcommodityandfactortax-
oftradeexposuretocalibratethekeytradefrictionsparametersof ation for ensuring Pareto gains from trade, while Spector (2001)
themodel.Wethenperformcounterfactualstogaugetheeffectsof and Naito (2006) showed how Mirrlees-type incentive constraints
tradeonaggregateincomeandinequality.Ourquantitativeresults could undermine differential factor taxation, thereby opening the
suggestthatourtwosuggestedwelfarecorrectionsarenonnegligi- door for the possibility that trade could lead to welfare losses by
ble.Underourpreferredparametrization,trade-inducedincreasesin
disposableincomeinequalityerodeabout20%oftheU.S.gainsfrom
trade,whilegainsfromtradewouldhavebeenabout15%largerif
redistributionhadbeencarriedoutvianon-distortionarymeans.The
size of the two corrections also appears to be fairly insensitive to
5 A related observation is that the movements in relative prices of skilled to
alternativeparametrizationsofthemodel.
unskilledgoods,whichareatthecoreoftheStolper-Samuelsonmechanism,tended
tobesmall(e.g.,seeLawrenceandSlaughter,1993).
6 Forexample,seeAutoretal.(2008)fortheevidenceforUSandAttanasioetal.
4 Throughout the paper we equate consumption with disposable income. An (2004)fortheevidenceforadevelopingcountry(Colombia).
activeliteratureinmacroeconomicshasdiscussedtheextenttowhichconsumption 7 Forexample,Faggioetal.(2007)showthatmostoftheincreaseinwageinequality
inequalityhastrackedincomeinequalityinrecentdecades.UsingdatafromtheU.S. intheU.K.happenedwithinindustries,whileLevinsohn(1999)showstherelative
ConsumerExpenditureSurvey,KruegerandPerri(2006)initiallyfoundthatconsump- importanceofwithin-industryreallocationinresponsetotradeliberalizationinChile.
tioninequalityhadgrownmuchlessthanincomeinequalitybetween1980and2004. SeealsoBursteinandVogel(forthcoming).
Nevertheless,Attanasioetal.(2012)andAguiarandBils(2015)haveshownthatwhen 8 Forinstance,itwouldbeinterestingtoexploretherobustnessofourresults
properlyaddressingmeasurementerrorbiases,consumptioninequalitywithinthe toanenvironmentwithnonhomotheticpreferences.Whethertradeintegrationhas
U.S.appearstohaveincreasedbetween1980and2010bynearlythesameamount increasedordecreasedincomeinequalitythroughitseffectonthepriceindexrele-
asincomeinequality.SeealsoJonesandKlenow(2016)forwelfaremeasuresthat vanttoindividualswithdifferentlevelsofincomeisanopenempiricalquestion(see
incorporatetheroleofconsumption,leisure,mortality,andinequality. BrodaandRomalis,2008,FajgelbaumandKhandelwal,2016,orJaravel,2016).
390 P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412
hampering redistribution.9 Relative to this body of work, our goal weformalizethesecorrectiontermsinacontextofasimpleyetfully
is to instead characterize and quantify the actual efficiency costs microfoundedgeneral-equilibriummodel,andweillustratehowto
ofredistributiongiventheobservedfeaturesofthesystemusedto usethisframeworktoprovideback-of-the-envelopecalculationsof
carryoutsuchcompensationintherealworld.10 Inthatsense,our welfarechangeswhenbothaggregateincomeandinequalitychange
focus on the income tax-transfer system as the vehicle for redis- overtime.
tribution is motivated by the small scale and limited relevance of
moredirectmeansofcompensation,suchastradeadjustmentassis- 2.1. Economicenvironment
tanceprograms.Forinstance,intheirinfluentialrecentstudyonthe
U.S.labor-marketimplicationsoftheriseofChineseimportcompeti- Consider a society composed of a measure one of individuals
tion,Autoretal.(2013)findthattheestimateddollarincreaseinper indexed by their ability level v with associated real earnings rv.
capitaSocialSecurityDisabilityInsurance(SSDI)paymentsfollowing Agents’preferencesarerepresentedbyautilityfunctionudefined
trade-inducedjobdisplacementsismorethanthirtytimesaslargeas overconsumptionc ofagoodthatalsoservesasnuméraire.Agents’
v
theestimateddollarincreaseinTradeAdjustmentAssistance(TAA) consumption is in turn equal to their real disposable income rd,
v
payments. definedas:
Finally,ourwelfaristandcostlyredistributioncorrectionsarenot
only related to the contributions of Kaldor (1939), Hicks (1939), (cid:2) (cid:3)
Atkinson(1970),andBenabou(2002),buttheyalsoconnecttoalarge rvd = 1−t(rv) rv+Tv, (1)
body of related work. The welfarist approach to policy evaluation
originatesinthepioneeringworkofBergson(1938)andSamuelson where t(rv) denotes a nonlinear income tax and Tv represents a
(1948),and hasconstitutedan importantparadigmintheoptimal lump-sumtransfer.Thedistributionofvinthepopulationisgivenby
policy literature since the seminal work of Diamond and Mirrlees thecumulativedistributionfunctionH ,whiletheassociatedincome
v
(1971),andthemorerecentliteraturethatspunfromtheworkof distributionforrealbefore-taxearningsisdenotedbyFr.Forsimplic-
Saez(2001).Similarly,wearecertainlynotthefirsttoincorporate ity,weassume–forthetimebeing–thatthegovernmentbudgetis
the costs of redistribution into the analysis of the welfare effects balancedsothat
ofpolicies.TheneedtodosowasactuallyanticipatedbyHicksin
(cid:4) (cid:4)
the concluding passages of his 1939 paper, and was subsequently
exploredbyKaplow(2004)and,morerecently,byHendren(2014). rvddHv= rdFr=R.
Hendren(2014),inparticular,estimatestheinequalitydeflatorasso-
ciatedwiththetransferofonedollarofincomefromindividualsat
The society is evaluating the consequences of a policy (such as
differentpositionsintheU.S.incomedistributiontotherestofthe
atradeliberalization)thatwouldgenerateheterogeneouschanges
U.S.population.Hefindsthatthisdeflatorishigherforrichindivid-
inthemappingbetweenagents’abilitiesandrealincomes,thereby
ualsthanforpoorindividualsandusesittoquantifytheeffectsof
leadingtoashiftfromtheinitialdistributionofearningsFrtoanew
increasedincomeinequalityonU.S.economicgrowth.Hisapproach distributionofrealmarketincomeF(cid:2).Dependingalsoonhowthetax
r
tocostlyredistributioniscertainlymoresophisticatedthantheone
system(i.e.,t(rv)andTv)adjuststothechangeintheenvironment,
adoptedinthispaper,asitinvolvesanestimationofthejointdistri-
thepolicywouldthenbeassociatedwithashiftfromaninitialdis-
butionofmarginaltaxratesandtheincomedistributionusingthe tributionofrealdisposableincomeFdtoanewoneFd(cid:2).Thequestion
r r
universeofU.S.incometaxreturnsin2012.Thethoughtexperiment
weposeis:whatarethewelfareconsequencesofthischangeinthe
thatmotivateshisworkishoweverdistinctfromours.Whileweseek environment?11Wediscussbelowthreedifferentapproachestothe
to understand the efficiency costs associated with the behavioral
evaluationofthesocialwelfareimplicationsofsuchapolicyshock.
responsesofagentstriggeredbytrade-inducedshiftsacrossmarginal
taxrates,hisfocusisonunderstandingtheefficiencyconsequences
2.2. TheKaldor-Hicksprinciple
oflocalchangestothenonlinearincometaxscheduleaimedatcom-
pensatingthelosersfromaparticularpolicy.Itmightbefruitfulto
The Kaldor-Hicks compensation principle constitutes the stan-
adopthisapproachtothestudyoftheeffectsoftradeliberalization,
dard approach to evaluating the welfare effects of a policy. To
butweleavethisforfutureresearch.
identifyaKaldor-Hicksimprovement,onestartsbycomputingthe
compensatingorequivalentvariationforeachindividualassociated
2. Inequalityandwelfare:aprimer withtheparticularpolicyunderstudy,andthesemoneymetricsare
thenaggregatedacrossallindividuals,withtheimplicitassumption
We begin our analysis in this section by considering various beingthatsocietyhasaccesstolump-sumtransfersT tocompen-
v
approachestomeasuringtheevolutionofsocialwelfareintheface sate any individual who is made worse off by the policy. In our
ofchanginginequalityandwhencompleteandcostlessredistribu- exampleabove,thisprincipleimpliesthatmeanrealincomegrowth
tionisinfeasible.WefirstreviewtheKaldor-Hicksprincipleandthe isasufficientstatisticforcomparingsocialwelfareunderFr andFr(cid:2),
Atkinsonwelfaristapproach,andthenpresentourcostlyredistribu- regardlessoftheeffectofthepolicyonthehighermomentsofthe
tionapproach.Whiledoingso,weintroduceourtwomaininequality incomedistribution.
correction terms for measuring welfare gains – the welfarist cor- Letusillustratethisforthecaseofthecompensatingvariation,
rectionandthecostly-redistributioncorrection–anddiscusstheir whichwedenotewithvvforanindividualoftypevandisdefined
properties.Inordertosimplifytheexposition,theframeworkdevel- by:
opedinthissectionwillleavesomeoftheprimitivedeterminantsof
income,welfareandcostlyredistributionunspecified.InSection3, (cid:5) (cid:6) (cid:5) (cid:6)
u rd(cid:2)+v =u rd . (2)
v v v
9 DavidsonandMatusz(2006)designthelowestcostcompensationpoliciesforthe
losersfromtradeinatwo-sectoreconomywithheterogenousagentsandparticipation
decisions,butfixedlaborsupply(seealsoEggerandKreickemeier,2009b). 11 Weassociatethechangeinthemappingbetweenabilityandincometoapol-
10 Rodrik(1992)isanoteworthyantecedenttoourworkindiscussingthecostsof icyshock,buttheanalysisofcourseappliestoanytypeofchangeintheeconomic
redistributionfollowingchangesintradepolicy. environmentthataffectstheincomedistribution.
P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412 391
Itfollowsthattherequiredaggregatecompensationsatisfies: two distributions of disposable income with the same mean, one
(cid:4) (cid:4) (cid:4) (cid:4) (cid:4) wouldexpectsocietytoprefertheonewiththelowestdispersionor
− vvdHv= rvd(cid:2)dHv− rvddHv= rdFr(cid:2)− rdFr. (3) iinneeqquuaalliittyy(acvfe.rAstikoinnsoonn,t1h9e7p0a),rtwoitfhththeescoocniaclavpiltaynonferu.(I•t)irseflimecptionrg-
tanttoemphasizethat,undertheplausibleassumptionthatagents’
Clearly,theright-hand-sideofEq.(3)correspondstothechangein preferencesfeaturediminishingmarginalutilityofincome,inequal-
aggregaterealincome,whichwewriteasR(cid:2)−R.Ifthisquantityis ityaversioniscompletelyconsistentwithautilitariansocialplanner
positive,itmeansthattheamountofmoneynecessarytorestorethe that simply seeks to maximize the sum of agent’s utilities. A sec-
losers’welfaretoitspre-policylevelislowerthantheamountthat ond justification for the concavity of u(•) is that it might capture
winnersarejointlywillingtogiveupforthepolicytobeadopted.In risk aversion on the part of ex-ante identical individuals in some
ordertoquantifythewelfareimplicationsofthepolicy,itisstandard sortof“originalposition”attemptingtocomputetheindividualwel-
toexpressthechangeinEq.(3)asapercentagechangerelativetothe fare implications of changes in the environment behind a “veil of
initiallevelofaggregaterealincomeR,whichwecandenoteby ignorance”(cf.,Vickrey,1945;Harsanyi,1953).14
(cid:7) To fix ideas, we shall follow Atkinson (1970) and consider a
W(cid:2)(cid:7)(cid:7)(cid:7) =1+lR≡ R(cid:2). (4) constant-elasticityfunction:
W R
Kaldor-Hicks
(cid:5) (cid:6)
Thewelfaregainsfromthepolicythuscorrespondtothemeanreal u(cid:5)rd(cid:6)= rvd 1−q−1, (6)
incomegrowthlR itgenerates.Moregenerally,theoverallwelfare v 1−q
impactofotherexogenousshockscanbeevaluatedanalogouslyby
onlyconsideringtheireffectonaverageincome(orGDP). whereq ≥ 0canbeinterpretedasreflectingaconstantdegreeof
Althoughwehaveassumedthatallagentshaveacommonindi- inequality aversion on the part of the social planner or a constant
rectutilityfunctionu,itisclearfromEq.(2)thattheresultinEq.(3) degreeofriskaversiononthepartofagentsintheoriginalposition
willapplyevenwhenagentsareheterogeneousnotonlyinincome (oracombinationofboth).Inordertoexpresssocialwelfarechanges
butalsoinpreferences.ThisisakeyappealingfeatureoftheKaldor- intermsofaggregateconsumptionequivalentchanges,itwillfurther
Hicks criterion: it does not rely on interpersonal comparisons of proveconvenienttoconsiderthesimplemonotonictransformation
utility.12
AsnotedintheIntroduction,therearehowevertwokeylimita- W=[1+(1− q)V]1/(1−q) (7)
tions of the Kaldor-Hicks criterion. First, the fact that there is the
potential for the winners to compensate the losers does not mean
that this compensation will actually takes place in practice. If lit- of the social welfare function in Eq. (5). With this transformation,
tleredistributiontakesplaceandtheex-postdistributionofincome socialwelfarecanbeexpressedasamultiplicativelyseparablefunc-
is much more unequal than the ex-ante one, it is less clear that tion of aggregate real income R and a term D, which is inversely
meanincomeshouldbeasufficientstatisticformeasuringwelfare related to the level of inequality underlying the distribution of
changes. Second, the focus on compensating or equivalent varia- disposableincome:
tions is justified only in the presence of lump-sum taxes, which
ensure a frictionless redistribution of gains across the individuals. W=D×R, (8)
Whileausefultheoreticaltool,lump-sumtransfersareinformation-
allyintensiveandrarelyfeasibleinpractice.Naturally,compensation
where
mayalsobeachievableviaotherformsofredistribution,butthese
athltuesrnthateivmeaignnstitruudmeeonfttshaerewleiklfealryetgoaiimnspfarcotmecaopnoolmiciyc.efficiencyand (cid:5) (cid:6) (cid:8)E(cid:5)rd(cid:6)1−q(cid:9)1−1q
v
In light of these limitations, we next discuss two alternative D=D Fd,q = . (9)
(andcomplementary)approachestopolicyevaluationthatexplicitly r Erd
v
correctfortheinducedeffectofapolicyonincomeinequality.
The term D, which we will refer to as a welfarist inequality
2.3. Thewelfaristapproach correction, corresponds exactly to one minus the Atkinson (1970)
index,awidelyusedmeasureofinequality.ByJensen’sinequalitywe
The welfarist (or social welfare) approach to policy evaluation havethatD≤1,withD=1onlyifeitherthereisnoinequalityaver-
begins by positing the existence of a social welfare function that sion(q = 0)orifthedistributionofdisposableincomeFd isfully
r
mapsthevectorofagents’welfarelevelsintoasinglerealnumber.It
egalitarian(haszerodispersion).Furthermore,Dtendstobelower,
iscustomarytoexpressthisfunctionasanintegralofconcavetrans- thehigheristhelevelofinequalityinthedistributionofincomeFd
r
formationsofagents’actual(andnotpotential)disposableincomes
orthehigherisinequalityaversionq.Tobemoreprecise,whileD
(andthusconsumptionlevels):13
isinvarianttoproportionalchangesoftheincomedistribution(i.e.,
(cid:4) (cid:5) (cid:6) whenallincomelevelsarescaledbythesameconstant),Disreduced
V= u rd dH , (5) bymean-preservingspreadsofthedistributionofdisposableincome
v v
(cf., Atkinson, 1970). And holding constant the distribution of dis-
posableincome,Fd,thehigheristhedegreeofinequality(orrisk)
where u(cid:2)(•)>0 and u(cid:2)(cid:2)(•) ≤ 0. There are at least two possible r
aversion q, the greater is the correction and the smaller is D (see
justifications for specifying u(•) as a concave function. First, given
AppendixA.1foraformalproof).AsweshowinAppendixA.2,for
12 In other words, the welfare gains in Eq. (4) are independent of the particu-
larcardinalutilityfunctionsthatarechosentorepresenttheordinalpreferencesof 14 This assumes that agents are not able to ex-ante insure against this ex-post
individuals. dispersioninincome.Weviewtradeshocksasparticularlyhardtoinsureagainst.
13 Moregenerally,thesocialwelfarefunctioncanberepresentedasanincreasing Furthermore, as mentioned in the Introduction, at least in the U.S., consumption
andconcavefunctionoftheindividualwelfarelevels. inequalityappearstohavetrackedincomeinequalityinrecentdecades.
392 P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412
certainoften-useddistributionsofincome,itisalsopossibletorelate willnowfocusontheparticularcase,usedamongothersbyBenabou
DtotheGinicoefficientassociatedwithFd. (2002)andHeathcoteetal.(forthcoming),inwhich
r
TheexpressionforwelfareEq.(8)immediatelyimpliesthatthe
(cid:2) (cid:3)
percentagewelfaregainsfromapolicyaregivenby: rvd = 1−t(rv) rv=krv1−0, (11)
W(cid:2)(cid:7)(cid:7)(cid:7)(cid:7) =(cid:5)1+lR(cid:6)×D(cid:2), (10) bfourdsgoemt eiscobnasltaannctekd.thAavtecraangebenseett-otfo-teanxsurraetetshatthtuhsegdoevcreeransmeenint
W Welfarist D reportedincomeataconstantrate0,withthisparametergoverning
thedegreeofprogressivityofthetaxsystem.When0=0,allagents
facethesametaxratekandthereisnoredistributionfromtherich
wherelR(cid:5)isth(cid:6)egrowthrateofrealincomeasdefinedinEq.(4)and tothepoor;infact,withbudgetbalancethereisnoredistribution
D(cid:2) = D Fd(cid:2),q correspondstothecorrectiontermunderthenew whatsoever. When 0 = 1, Eq. (11) implies that all agents end up
r
with the same after-tax income and thus redistribution is full and
incomedistribution.Thusintheabsenceofanyeffectofthepolicy
eliminatesinequality.15
oninequalityascapturedbyD,thechangeinwelfarecorresponds
exactlytothepercentagechangeinrealincomelR,asintheKaldor- ThespecificationinEq.(11)mayseemquiteadhocandunlikely
toprovideavalidapproximationtothecomplicatedtaxandtransfer
HickscompensationprincipleapproachinEq.(4).Nevertheless,ifthe
policyincreasesinequality,thenwelfareincreasesbylessthan1+lR, systemsemployedinmoderneconomies.Nevertheless,itsimplied
log-linear relationship between market income and income after
withalargerdownwardcorrectionthelargerisqand,ofcourse,the
taxesandtransfersfitsU.S.dataremarkablywell,aswewillillustrate
largertheincreaseininequality.Theparticularsizeofthecorrection
inmoredetailinSection4(seealsoHeathcoteetal.,forthcomingand
canbeeasilycomputedwithdata(realorcounterfactual)onthedis-
Guneretal.,2014).
tributionofdisposableincomebeforeandafterthepolicy,asweshall
Alargerdegreeofprogressivitytendstocompresstheafter-tax
illustrateinSections4and6.
incomedistribution,butitimpliesthatrichpeoplefacedispropor-
As mentioned above, an advantage of using the function W in
tionately larger marginal tax rates. More specifically, the marginal
EEqq.. ((57))iisnsthteaatdthoef cahnayngoethienrwmeolfnaoretoinnicEqtr.a(n1s0fo)ramlsaotioconrsreosfpoVndins taxrateimpliedbyEq.(11)isgivenbytm(rv) = 1−k(1−0)rv−0
and thus rises with both the degree of tax progressivity 0 as well
totheconsumption-equivalentchangeinsocialwelfareofmoving
from Fd to Fd(cid:2). More specifically, it is easy to verify (see Appendix as the level of income rv. To the extent that higher marginal tax
r r rates generate behavioral responses of agents that lead them to
A.1)thatifoneweretocomputethepercentagechangeinallagents’
generatelessincomethantheywouldunderalowermarginaltax
consumptionordisposableincomethatwouldmakesocietyindif-
f(cid:10)e1r+enltRb(cid:11)et×wDe(cid:2)en−F1rdraengdarFdrd(cid:2)l,etshseoafnwswheetrhoenresowcoiaulldwgeelftawreoiusldmbeeasluCre=d roaftep,rothgereisnscivreitaysewdirlledgiesntreirbautteiocnosbtrso.uTgohtcaapbtouurtebtyhiashciogshtelyrdaesgpreecet
D of redistribution in a simple though fairly standard way, we posit
intermsofthefunctionVorofanymonotonictransformationofV
the existence of a positive, constant elasticity of taxable (realized)
(includingW).
incometothenet-of-marginal-taxrate1−tm:
Throughoutthissection,wehavefocusedonstudyingthewelfare
consequencesofapolicybasedonitseffectonthedistributionofdis-
∂logr
posableincome.Naturally,howthepolicyshapesdisposableincome e≡ (cid:10) v (cid:11) ≥0, (12)
is in turn shaped by how the policy alters the mapping between ∂log 1−tm(rv)
individuals’abilitiesandmarketincome,aswellasbyhowthetax
systeminplaceisitselfaffectedbythepolicy.Ifnon-distortionary wheretm(rv)isthemarginaltaxratefacedbyagentswithincomerv.
lump-sum transfers T were available, an inequality-averse social ThecombinationofaprogressivetaxsystemofthetypeinEq.(11)
v
planner would simply set these transfers to eradicate inequality. and a positive elasticity of taxable income e makes redistribution
Wenextturntothemorerealisticcaseinwhichonlydistortionary fromrichpeopletopoorpeoplecostly,therebymotivatinganalter-
meansofredistributionareavailable. nativecorrectiontothestandardmeasuresofthewelfareeffectsofa
policy.Morespecifically,onecanmanipulateEqs.(11)and(12)and
imposebudgetbalance,toobtain:
2.4. Thecostly-redistributionapproach R=H×R˜, (13)
Despite its widespread use in the optimal policy literature, the
˜
whereRisthepotentialincomeintheabsenceofprogressiveredistri-
welfarist approach remains controversial. This is in large part due
bution(i.e.,thecounterfactualincomeobtainedwhensetting0=0
tothesensitivityofitsprescriptionstothevalueofcertainparame-
inthetaxschedule),and
ters,suchasthedegreeofinequalityaversion(or,moregenerally,the
socialmarginalweightsassignedtoagentswithdifferentincome), (cid:10) (cid:11)
tdhifaftearerentdeiffithciucaltltvoiemwesa.sureandoverwhichpeoplemighthavevastly H=H(Fr,0,e)=(1−0)e(cid:5)Erv1−0E(cid:6)rev•(cid:5)1E+rev1+e0(cid:6) (14)
Wenextconsideracomplementaryapproachthatismoreakinto
theKaldor-Hickscompensationprinciple,butthatexplicitlymodels
isatermwerefertoasourcostly-redistributioninequalitycorrection.
thefactthatredistributioniscostly,withthecostsofredistribution
Although perhaps not immediate from inspection of Eq. (14),
increasingintheextentofeconomicinequality.Thewelfarecorrec-
Hölder’sinequalityimpliesthatthesecondtermisnolargerthan1,
tioninthiscasequantifiestheforgonegainsinrealincomedueto
thecostlyredistributionmechanismputinplacebysocietytoreduce
incomeinequality.
For this purpose, we return to our previous example but now 15 Moregenerally,theresultsinJakobsson(1976)andKakwani(1977)implythat,
assumethatlump-sumtransfersarenotfeasible(i.e.,T ≡ 0)and starting from a fixed arbitrary distribution of pre-tax income, an increase in 0
v necessarilyleadstoamoreegalitariandistributionofafter-taxincome,inthesense
redistribution has to work through the income tax system. Above,
thatitmakesdisposableincomemoreevenlydistributedaccordingtotheLorenz
we have introduced a general nonlinear income tax t(rv), but we criterion.
P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412 393
whichinturnimpliesH≤1.Furthermore, H=1ifandonlyifthetax- 3. Inequalityandwelfareinaconstant-elasticitymodel
transfersystemfeatureszeroprogressivity(0=0)oriftheelasticity
oftaxableincomeiszero(e =0).Itthusfollowsthat,when0>0 In this section, we develop a simple general equilibrium
ande>0,realincomeislowerthanitwouldbeintheabsenceofdis- framework,whichspecifieshowtheabilityofindividualsandtheir
tortionaryredistribution.Infact,inAppendixA.1weshowthatHis laborsupplydecisionstranslateintoequilibriumearningsandwel-
strictlydecreasinginthetaxprogressivityrate0foranyprimitivedis- farelevelsgiventhetaxsysteminplace.Inlightofourchoicesof
tributionofpotentialoutputr˜ ,thusformalizingtheefficiencycosts functional forms, we refer to our model as the constant-elasticity
v
ofenhancingredistribution.Holdingtheotherparametersconstant, model.
thetermHalsodependsontheprimitivedegreeofincomeinequality: The model features four constant elasticity parameters, which
Hishighestwhenevertheincomedistributionisperfectlyegalitar- we introduce below: (i) a constant Frisch elasticity of labor sup-
ian and it tends to be lower the more unequal is the distribution ply (1/(c − 1)); (ii) a constant elasticity of substitution between
ofincome.Morespecifically,whenconsideringtwodistributionsof thelaborservices(ortasks)performedbydifferentagentsinsoci-
incomeFrandFr(cid:2),itiseasytoshowthatH(Fr(cid:2),0,e)<H(Fr,0,e)when ety(1/(1−b));(iii)aconstantdegreeoftaxprogressivity(0);and
Fr(cid:2) isameanpreservingmultiplicativespreadofFr.16 Conversely,H (iv)aconstantsocialinequalityaversion(q).Thisconstant-elasticity
isinvarianttoproportionalchangesoftheincomedistribution(i.e., structure results in a tractable general equilibrium characteriza-
whenallincomelevelsincreaseproportionately).Inanalogytothe tion,whichisparticularlyusefultoillustrateourwelfarecorrections
Atkinson index, one can interpret H as a complementary welfare- terms. We should emphasize, however, that our model will place
relevantmeasureofinequality,andforcertainstandarddistributions, little structure on the underlying primitive distribution of ability,
H can be related directly to the Gini coefficient associated with Fr and can thus flexibly accommodate any equilibrium distribution
(seeAppendixA.2fordetails). of income one may choose to calibrate the model to. Let us next
Wearenowreadytorevisitourinitialquestionofhowshould introducethekeyingredientsofthemodelmoreformally.
society evaluate the welfare implications of a policy affecting the
mappingbetweenabilityandincome.Evenwhenoneadherestoa 3.1. Preferences,technologyandindividualbehavior
welfarecriterion,suchastheKaldor-Hicksprinciple,thatjudgespoli-
ciesbasedontheirimplicationsforrealincomegrowth,withcostly Considerfornowaclosedeconomyinhabitedbyacontinuumof
redistribution,societywilltakeintoaccounttheeffectsofthepolicy agentswithGHHpreferences(cf.,Greenwoodetal.,1988)overthe
onhighermomentsoftheincomedistribution.Thereasonforthis consumptionofanaggregategoodcandlabor(cid:3):
isthat,intheabsenceoflump-sumtransfers,thosehighermoments
shapethedeterminationofmeandisposableincome.Moreprecisely, u(c,(cid:3))=c − 1(cid:3)c. (16)
buildingonEq.(13)wecanexpresstheaggregaterealincomegains c
ofthepolicyas
Theparameterc ≥ 1controlstheFrischelasticityoflaborsupply,
1+lR= R(cid:2)(cid:7)(cid:7)(cid:7)(cid:7) =(cid:5)1+l˜R(cid:6)×H(cid:2), (15) wenhciechofiselgaisvtiecnalblyys1u/p(pclie−d1la)baonrd,thiseodreectriecaaslliyn-ggrionuncd.eIndmtheeaspureress-
R CostlyRed. H ofwelfareneedtocorrectincomeforthedisutilitycostsofproducing
it,anissueweignoredinSection2.Thisutilityspecificationresultsin
where1+l˜R≡R˜(cid:2)/R˜ measurestherealincomegainsintheabsence noincomeeffectsonlaborsupplyandisoftenadoptedintheoptimal
taxationliterature.
of costly redistribution. Whenever the policy has no measurable Each individual produces output y = v(cid:3) of his own variety of
impact on H, the change in welfare corresponds exactly to real
a task (or intermediate good) where v is individual ability and is
income growth of a hypothetical Kaldor-Hicks economy that could
distributedaccordingtoH asinSection2.Thetasksperformedby
v
uselump-sumtransfersforredistributionpurposes.Suchanequiv-
differentagentsareimperfectsubstitutesandarecombinedinthe
alence would hold when the policy increases the incomes of all
productionoftheaggregateconsumption(final)goodaccordingto
agents proportionately (and 0 and e do not change). If however
the policy increases inequality and thereby lowers H, the implied (cid:12)(cid:4) (cid:13)1/b
changeinaggregateincomewillbestrictlylowerthaninthecase Q= ybdH ,
v v
in which inequality had remained unaffected. To summarize, the
costly redistribution correction measures the forgone gains in real
whereb∈(0,1]isaparameterthatcontrolstheelasticityofsubstitu-
incomeduetotheinteractionbetweentheincreasedinequalityand
tion1/(1−b)acrosstasks.Inthelimitingcaseofb=1,theindividual
theprogressivityofthetaxschedule.
tasksbecomeperfectsubstitutes,andthemodelturnsintoaspecial
Althoughwehopethatthediscussioninthissectionhasserved
case of a neoclassical Mirrlees (1971) economy. Imperfect substi-
ausefulpedagogicalrole,aproperanalysisofhowthewelfaristand
tutabilitybecomesessentialwhenweintroduceanexplicitmodelof
costly redistribution corrections shape social welfare requires the
internationaltradeinSection5,butforthequalitativeimplications
developmentofafullyspecifiedmodelinwhichtheincomedistribu-
ofthissectionwhetherb=1orb<1isnotimportant.
tionisendogenizedandinwhichtheresponseofagentstotaxation
Under the above assumptions, the market (real) earnings of an
ismicrofoundedandtakenintoaccountincomputingsocialwelfare.
individualsupplyingyunitsofhistasktothemarketaregivenby:17
Weturntothistaskinthenextsection.
r=Q1−byb. (17)
rt1h(cid:2)6e=rTeh(1eex+disitshst)rraibwuratitinohdnoEmF(rh(cid:2))visa=raia0mb.leeNaonhteipnrtdehesaeptrevnHidneigsnmtleuosslftittphhleiacnaotroiivngeiensaeplvreeinnacdowmohfeeFnrrawslulhceahngeethvneatsrt t1h7epTrhiecedoemftahnedvfaorrieatnyiannddivPid=ua(cid:14)lt(cid:15)apsk−vv1−babrideHtyv(cid:16)is−g(1i−vbe)n/bbiysqth=epQri(cpe/Po)f−th1−1ebfi,nwaelrgeopodis.
sharethesameincomeandthusthereisnoredistributioninequilibrium.Thereason
forthisisthatwhenconsideringanoff-the-equilibriumpathdeviationthatwould WenormalizeP=1sothatallnominalquantitiesintheeconomyareintermsofthe
increaseanagent’sincome,thisagentunderstandsthatitwillbetaxedasaresult finalgood,andthusareinrealtermsaswell.Underthesecircumstances,taskrevenues
ofthatdeviation.Thisiscapturedbytheterm(1−0)einEq.(14). arer=pq=Q1−byb,wherewehavesubstitutedthemarketclearingconditionq=y.
394 P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412
Notice that when b < 1, the demand for each individual task is toafter-taxincomebecausetheutilitycostoflaboreffortispropor-
increasinginaggregateincome tional to disposable income under the optimal allocation. Equilib-
(cid:4) riumrevenuesareapowertransformationofunderlyingindividual
abilities,withthepowerincreasingintheelasticityparameterseand
Q=R= r dH ,
v v b,anddecreasingintheprogressivityoftaxation0.Taxprogressiv-
itynotonlyreducesthedispersionofafter-taxincomesandutilities,
yettheagentsfacedecreasingdemandschedulesandasaresulttheir butalsocompressesthedistributionofpre-taxmarketrevenuesasit
revenuesareconcaveintheirownoutput.Whenb=1,theindivid- hasadisincentiveeffectonlaborsupply,whichisparticularlyacute
ualrevenuesaresimplyr=y,andthusareonlyafunctionoftheir forhigh-abilityindividualsfacinghighermarginaltaxrates.
abilityandlaborsupplydecisions.
Individualconsumptionequalsafter-taxincome,c = rd = [1− 3.2. Aggregateincomeandsocialwelfare
t(r)]r.AsinSection2,weassumethatthetax-transfersystemiswell
approximatedbyEq.(11),wheretheparameter0governstaxpro- Thecharacterizationofequilibriumrevenuesandutilitiesrelies
gressivityandtheparameterkcontrolstheaveragetaxrateacross on two endogenous aggregate variables, k and Q. The closed-form
agents.Thegovernmentusescollectedtaxesforredistributionand solutionsforthesevariablesareprovidedinAppendixA.3,wherewe
tofinanceexogenousgovernmentspendingG,andrunsabalanced showthataggregateincome(GDP)oftheeconomycanbeexpressed
budget.Inotherwords,thetotalincomeoftheeconomyequalsthe as
sumoftotalprivateconsumptio(cid:15)n(aggregatedisposableincome)and
governmentspending,soQ = rvddHv+G.Wefurtherassumethat Q=HjQ˜, (21)
governmentspendingisafractiongofGDP,i.e.G=gQ,anditdoes
not directly affect the individual utilities in Eq. (16). Under these
circumstances,wecanrewritethegovernmentbudgetbalanceas: where H < 1 is the same costly-redistribution correction term
introducedaboveinEq.(14),andwhere
(cid:4)
k r1−0dH =(1−g)Q, (18) (cid:12)(cid:4) (cid:13)
v v j
Q˜ =[b(1−g)]je vb(1+e)dHv
whichdefinesarelationshipbetweenkandggiventhetaxschedule
progressivity 0. In other words, given the exogenous share of isthecounterfactual(potential)aggregaterealGDPwithaflattax
governmentspendingg,thereexistsauniqueaveragetaxparameter schedulecharacterizedby0=0andk=1−gtofinancegovernment
k which balances the government budget for any given level of spending.Intheseexpressions,theauxiliaryparameter
tax progressivity 0. Because the level of k affects all incomes
proportionately,thevalueofg(orG)doesnotaffecttheshapeofthe 1
incomedistribution. j≡ 1−(1−b)(1+e) ≥1
Individuals maximize utility Eq. (16) by choosing their labor
supplyandconsumingtheresultingdisposableincome,aprogram
captures an amplification effect associated with the aggregate
thatcombiningEqs.(11)and(17)wecanwriteas:
demandexternality(or love-for-varietyeffect)stemmingfrom the
(cid:17) (cid:18) (cid:19) (cid:20) imperfectsubstitutabilityoftasks.19
uv=m(cid:3)ax k Q1−b(v(cid:3))b 1−0−c1(cid:3)c . incoSmeveerianlEcqo.m(2m1e)ndtespaernedisnoonrdtheer.cFoisrtslty, nreodteisttrhibatutaiogngrceograrteectrieoanl
term H and on potential real income, which is a simple function
Thesolutionforequilibriumrevenuesandutilitiesisgivenby:
of the primitive fundamentals of the model, namely the ratio g of
government spending to GDP, the distribution of ability H , the
(cid:18) (cid:19) v
rv=[b(1−0)k]1+ee0 Q1−bvb 11++ee0, (19) task-substitutabilityparameterb,andtheFrischelasticityoflabor
supplyc(whichtogetherwithbdeterminetheelasticityoftaxable
incomee).Second,intheabsenceofprogressivetaxation,realized
u = 1+e0kr1−0, (20) and potential GDP coincide because remember that when 0 = 0,
v 1+e v
H = 1. Third, note that Eq. (21) is the counterpart to Eq. (13) in
Section2,withtheonlydifferencebeingthatnowtheoutputloss
wherewehavemadeuseofthefollowingauxiliaryconstant: Q/Q˜ isamplifiedbytheaggregatedemandexternality,whichman-
ifestsitselfintheexponentj>1onH,andoperatesinthemodel
b
e≡ , wheneverb<1.
c−b
Sofar,wehavefocusedonadiscussionofthedeterminationof
aggregaterealincomeinthemodel.Eq.(20)providestheutilitylevel
whichalsoequalstheoverallelasticityoftaxableincometochanges
associatedwiththedisposableincomeandlaborsupplydecisionsof
inmarginaltaxrates,aspreviouslydefinedinEq.(12).18Whentasks
anindividualwithabilityv.Inordertoaggregatetheseutilitylevels
areperfectlysubstitutable(b=1),thiselasticityecoincideswiththe
intoameasureofsocialwelfare,weadoptthewelfaristapproachand
Frischelasticityoflaborsupply1/(c−1).Yetwithimperfectsubsti-
expresssocialwelfareas
tutabilityintasks(b<1),thiselasticityisreducedbythedownward
pressureofincreasedoutputonprices. (cid:12)(cid:4) (cid:13)
1
Eqs.(19)–(20)showhowindividualabilitytranslatesintoequilib- W= u1−qdH 1−q, (22)
v v
riummarketrevenueandindividualutility.Thelatterisproportional
18 Toseethis,rememberthatthemarginaltaxrateassociatedwithEq.(11)isgiven 19 Notethatwhenb=1,j=1,butjisotherwiseincreasingineanddecreasing
bytm(rv) = 1−k(1−0)rv−0.PluggingthismarginaltaxrateintoEq.(19)and inb.Asisclearfromthedefinitionofj,weneedtoimposethestabilitycondition
simplifyingdeliversrv=(b(1−tm(rv)))e(Q1−bvb)1+e. (1−b)(1+e)<1,whichissatisfiedifeisnottoolargeorbisnottoosmall.
P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412 395
˜
whichistheexactcounterparttoourearlierEq.(7).Notethatthe welfareWdiscountedinturnbythetwocorrectionterms,whichare
riskaversionparameterq ≥ 0isinconsequentialforthechoicesof bothlessthan1(seeourdiscussioninSection2).
individualsinthisstaticmodel,andonlymattersforcross-individual Theeffectofinequalityaversiononsocialwelfareiscapturedby
welfare comparisons. Therefore, q can be viewed as either the the exact same term D derived in Section 2, and is closely related
propertyofindividualutilitiesoftheagentsorthesocialinequality totheAtkinsoninequalitymeasure.Theeffectofcostlyredistribu-
aversionparameter.Whenq=0,socialwelfarecorrespondstothe tionisinsteadslightlymodifiedrelativetoourpreviousderivations
simpleintegralofutilitylevelsacrossindividuals,whichremember inSection2.First,andasalreadydiscussedabove,thepresenceof
arelinearinrealdisposableincome. aggregate demand externalities magnify the loss of output associ-
Thiscompletesthedescriptionofthemodelenvironment,andwe ated with distortionary taxation, and H < 1 is now raised to a
cannowcharacterizeequilibriumwelfareWgiventhesolutionfor power j>1. Second, note that Eq. (24) incorporates a new term
equilibrium utilities in Eq. (20). We do this in two steps. First, we (1+e0)whichcapturesthefactthatloweroutputcomesalongwith
characterize(seeAppendixA.4foraproof): a lower disutility of labor effort, which other things equal, raises
welfare.Despitethepresenceofthisterm,theoveralleffectofdis-
tortionary taxation captured by the term (1+e0)Hj inherits the
Proposition1. Thewelfareintheeconomywithzerotaxprogressivity
same properties of the term H described in Section 2. In particu-
(0=0)andnoinequalityaversion(q=0)isgivenby: lar, t(cid:10)his t(cid:11)erm c(cid:21)an(cid:8)b(cid:5)e spli(cid:6)t in(cid:5)to the p(cid:6)r(cid:9)oduct of (1 + e0)(1 − 0)je
and Erv j(1+e) Erv1−0 e• Erv1+e0 , with both of these terms
W˜ = 1−g ×Q˜. (23) beingstrictlylessthan1when0>0andthedispersionofincome
1+e ispositive.Thefirsttermcapturestheutilitylossfromtaxationin
theabsenceofinequality(andcontinuestobedecreasingineand
NotethatwelfareinthiscaseiscloselyrelatedtorealGDP,with 0), while the second term captures the additional loss due to the
the(welfare)costofproducingGDPcapturedbythediscountterm interactionofinequalitywithaprogressiveincometaxschedule.
infrontofQ˜ inEq.(23).Thenumerator1−gofthistermreflectsthe Althoughthisisnotthefocusofthispaper,thewelfaredecom-
shareoftheoutputoftheeconomythatgoestowardstheprovision position in Eq. (24) captures the tradeoff faced by a benevolent
ofthepublicgood,whichisfinancedviaaproportionaltaxsched- government (maximizing social welfare W) when deciding on the
ulek = 1−gwhen0 = 0.20 Thedenominator1+ereflectsthe degree of progressivity 0 of the tax system. Because the welfarist
˜
disutilitycostsofproducingtheoutputQ.Theimmediatecorollary correctionDisnegativelyaffectedbyanincreaseininequalityindis-
ofProposition1isthatintheabsenceofinequalityaversionandtax posableincome,thiscorrectiontermisincreasingin0.Conversely
progressivity,changesinwelfarecanbemeasuredusingthegrowth thecostly-redistributioncorrection(andalsothefullcorrectionterm
rateofGDP (1+e0)Hj)isdecreasingin0,duetothehighermarginaltaxrates
associatedwithamoreprogressivetaxsystem.Therefore,whenset-
W˜(cid:2)−W˜ Q˜(cid:2)−Q˜ tingtheoptimal0,thegovernmentnecessarilybalancesthesetwo
˜ =l˜R= ˜ , conflictingforces(seeAppendixA.1fordetails).
W Q
To summarize, we have shown that social welfare can be
expressed as a multiplicatively separable function of three terms:
providedthattheelasticityeandtheshareofpublicspendinggstay
(i)potentialwelfareinahypothetical(Kaldor-Hicks)worldwithnon-
constantovertime.
distortionary taxation, discounted by (ii) our welfarist correction,
This result illustrates that a criterion analogous to the Kaldor-
and (iii) our (modified) costly-redistribution correction. The pres-
HicksprescriptioninEq.(4)maystillapplyinmoregeneralsettings,
ence of these two correction terms introduces a tradeoff for the
even when lump-sum taxes are unavailable and average taxes are
policymakerwhendecidingontheoptimaldegreeoftaxprogres-
positive, provided that society does not care about inequality and
sivity. Independently of the amount of redistribution that society
doesnotuseaprogressivetaxsystemtoaddressit.
choosestoimplement,thesetwocorrectionsreducewelfaredispro-
Nevertheless, outside this limiting case with 0 = q = 0, real
portionatelymoreinenvironmentswithhighereconomicinequality.
incomegrowthisnolongeranappropriatemeasureofwelfaregains,
Inthemodeldevelopedsofarsuchincreasesininequalitycanonly
andinsteadwehave(seeAppendixA.4foraproof):
originate from increases in the dispersion of ability across agents
(perhapsduetoskill-biasedtechnologicalchange)orfromincreases
Proposition 2. Outside the case 0 = q = 0, social welfare can be intheprimitiveparametersbandc.InSection5,wewillshow,how-
writtenas: ever,thattradeintegrationcangeneratequalitativelysimilareffects.
Beforedoingso,andtobuildsomeintuitionforourquantitativeanal-
ysis,inthenextsubsectionweprovideapreliminarylookatU.S.data
W=D×(1+e0)Hj×W˜, (24) throughtheprismofourclosed-economymodel.
whereD andH arethewelfaristandthecostly-redistributioncorrec-
4. Apreliminarylookatthedata
tionsdefinedinEqs.(9)and(14),respectively.
Althoughthemaingoalofthispaperistoapplythetoolsdevel-
opedsofartothestudyofthewelfaregainsfromtradeintegration,
Note that the two inequality correction terms that were
inthissectionwetakeabriefdetourtoillustratetheusefulnessof
introduced earlier in Section 2 appear explicitly in the welfare
ourclosed-economymodelininterpretingtheconsequencesofthe
expressioninEq.(24).Indeed,realizedwelfareWequalspotential
observedriseininequalityintheU.S.inrecenttimes.
More specifically, in this section we decompose social welfare
in the U.S. over the period 1979–2007 according to Eq. (24), thus
20 RememberthatpotentialoutputisgivenbyQ˜ =[b(1−g)]je(cid:5)(cid:15)vb(1+e)dHv(cid:6)j,and backing out the size and evolution of the welfarist and inequal-
henceisitselfdecreasingink=1−gduetothedisincentiveeffectoftheaveragetax ity correction terms. We then use this expression to compute the
rategevenintheabsenceofprogressivityoftaxation. incomeandwelfarelevelsthatwouldhaveattainedincounterfactual
396 P.Antràsetal. /JournalofInternationalEconomics108(2017)387–412
scenariosinwhichU.S.incomeinequalityhadnotincreasedasmuch besensitivetofinefeaturesoftheincomedistribution(suchasthe
asitdidoverthisperiod. shapeofitsrighttail),wedeemitnecessarytoseekricherinforma-
tionontheU.S.incomedistributionthanthatprovidedbytheCBO
4.1. Calibration dataweusedtocalibrate0.Followingrecentempiricalworkontop
income levels (e.g., Piketty and Saez, 2003), we employ the public
Inordertoputtheabovemodeltowork,itisnecessarytocali- usesamplesofU.S.FederalIndividualIncomeTaxreturnsavailable
brateitskeyparameters.Rememberthattheprimitiveparameters fromtheNBERwebsite.Theseamounttoapproximately3.5million
of the model are the Frish elasticity parameter c, the task substi- anonymized tax returns (about 150,000 per year) over the period
tutabilityparameterb,thedegreeoftaxprogressivity0,theshareof 1979–2007.Contrarytosurvey-basedsourcesofincomedistribution
governmentspendinginGDPg,thedistributionofabilityinsociety data,theNBERIRSdataismorelikelytoprovideanaccuratepicture
Hv,andtheinequalityaversionparameterq.Someoftheseobjects, of the income of particularly rich taxpayers. To ensure the repre-
suchasthedistributionofagents’ability,arenotoriouslydifficultto sentativenessofthesample,wefurtherapplythesamplingweights
calibrate.Fortunately,weshallseethat,forourpurposes,itwillsuf- providedbytheNBER.Wemapbefore-taxincomervinthemodelto
ficetocalibrate(i)thedegreeoftaxprogressivityofincome0,(ii)the adjustedgrossincome(AGI)inline37ofIRSForm1040andrestrict
distributionofmarketincomer ,(iii)theelasticityoftaxableincome the sample to returns with a strictly positive AGI. Together with
v
e = b/(c−b),and(iv)thedegreeofsubstitutabilitybetweenthe ouryearlyestimatesof0,itisthenpossibletoestimatedisposable
tasksprovidedbydifferentworkers,ascapturedbyb.Letusdiscuss incomervduptoaconstant(k)whichisirrelevantforthecomputation
eachoftheseinturn. ofourtwoinequalitycorrections.23
Considerfirstourmodelingofthetax-transfersysteminEq.(11). In the left panel of Fig. 4, we plot the cumulative distribution
Thisspecificationmayseemquiteadhoc,butthelog-linearrelation- of income for the year 2007, and for comparison we also plot the
shipbetweenmarketincomeandincomeaftertaxesandtransfers bestlognormalfitofthedistribution.Ascanbeseen,theempirical
impliedbyEq.(11)fitsU.S.dataremarkablywell.Thisisillustrated distributionofincomeisprettywellapproximatedbyalognormal
inFig.2usingCBOdataforeightpercentilesoftheincomedistribu- distribution.Nevertheless,therightpanelofFig.4demonstratesthat
tionforvariousyearsintheperiod1979–2007.21Thebestlog-linear thelognormalfitisreallypoorforrelativelyhighincomes,andinthat
fitofthedataachievesaremarkableR-squaredof0.983orhigherin range,aParetodistributionappearstofitthedatamuchbetter.More
allyears.InspectionofthedifferentpanelsofFig.2suggeststhatthe specifically, following Diamond and Saez(cid:10)(2011), th(cid:11)is right panel
degreeoftaxprogressivityappearstobelowerinrecentyearsthan plots the ratio rm/(rm −r), with rm = E rv|rv>r , for different
atthebeginningoftheperiod.ThisismoreclearlyillustratedinFig.3, valuesofincomer.ConsistentlywiththepropertiesofaParetodistri-
whichreportstheestimateof0yearbyyear.Giventheremarkable bution,forlargeenoughincomelevelsthisratioisrelativelyflat(at
fitofEq.(11),wewillusetheseyearlyestimatesof0tocalibratethe avaluecloseto1.5),whereasalognormaldistributionwouldpredict
timepathofprogressivityovertheperiod1979–2007. thistermtorisewithincome.
It is clear that the tax formula in Eq. (11) is stylized and does Havingdiscussedthecalibrationoftheprogressivityparameter
notcapturemanysubtletiesoftheU.S.taxandtransfersystem.For 0andtheincomedistributionforeachyearin1979–2007,weare
instance,inreality,marginaltaxratesmaybepositiveandquitehigh leftwiththeparameterse,bandq.Thesizeoftheelasticityoftax-
forcertainlow-incomehouseholdsthatseeaphase-outoftransfers ableincomeehasbeenthesubjectofheateddebatesintheacademic
if they increase their reported income. Similarly, Eq. (11) predicts literature.TheinfluentialworkofChetty(2012)hasdemonstrated,
thatmarginaltaxratesgrowmonotonicallywithincome,whilein however,thatwheninterpretingthewiderangeofestimatedelas-
realitytheyremainconstantattheverytop.Analternativeapproach ticitiesthroughthelensofamodelinwhichagentsfaceoptimization
wouldhavebeentousetheNBERTAXSIMprogramtocomputereal- frictions,anelasticityoftaxableincometochangesinmarginaltax
istictaxliabilities,andthenincorporateinformationontransfersto ratesofaround0.5canrationalizetheconflictingfindingsofprevious
computedisposableincome.Thisispreciselytheapproachfollowed studies.Withthatinmind,weshallsete = 0.5inourbenchmark
byHeathcoteetal.(forthcoming),whousedataonreportedincome calibration.24
andtransfersfromthePanelStudyofIncomeDynamics(PSID)for Movingontothesubstitutabilityparameterb,inourbenchmark
surveyyears2000,2002,2004,and2006.Interestingly,theyfindan calibration we will set b = 0.8. The resulting elasticity of substi-
equally good fit of the log-linear relationship in Eq. (11), with an tution 1/(1−b) = 5 is slightly larger than that the one typically
impliedvalueof0=0.181,whichisverymuchconsistentwiththe estimatedwithproduct-leveltrade(seeBrodaandWeinstein,2006)
estimatesweobtainfromCBOduringtheperiod2000–06.Adown- orwithfirm-levelmark-updata(seeBernardetal.,2003orAntràs
sideofthisalternativeapproachisthatthePSIDundersamplesthe etal.,forthcoming),butitseemsreasonabletoustopostulatethat
veryrich.22 workers’tasksaremoresubstitutablethantheproductsthatembody
We next turn to our calibration of the distribution of market
income. Because we are wary that our quantitative results might
23 WecouldhaveinprincipleobtaineddisposableincomebyusingtheNBERTAXSIM
programwhichcalculatesfederalandstateincometaxliabilitiesfrommarketincome
21 Inparticular,eachpanelofFig.2depictsmarketincomeandincomeaftertaxes data.Nevertheless,thiswouldhavemissedgovernmenttransferswhichareessen-
andtransfersforthefirstfourquintilesoftheincomedistribution,aswellasthe81st tial for understanding why disposable income is higher than market income for
to90thpercentiles,the91stto95thpercentiles,the96thto99thpercentiles,and low-incomeindividuals.
thetop1percent,fortheperiod1970–2007.Marketincomeconsistsoflaborincome, 24 ItshouldbenotedthatfiveofthefifteenstudiesChetty(2012)buildsontopro-
businessincome,capitalgains(profitsrealizedfromthesaleofassets),capitalincome videboundsontheintensivemarginlaborsupplyelasticityarebasedontheresponse
(excludingcapitalgains),incomereceivedinretirementforpastservices,andother ofhoursworked(ratherthantaxableincome)tochangesinmarginaltaxrates.Inour
sourcesofincome.Governmenttransfersincludecashpaymentsandin-kindbenefits model,thesetwoelasticitiesarenotidenticalduetotheimperfectsubstitutabilityin
fromsocialinsuranceandothergovernmentassistanceprograms.Federaltaxliabil- tasks.WehavehoweverreplicatedChetty’s(2012)calculationsrestrictingtheanalysis
itiesincludeindividualincometaxes,socialinsuranceorpayrolltaxes,excisetaxes, tothetenpapersestimatingtaxableincomeelasticities.Theresultingintensivemargin
andcorporateincometaxes. elasticityisequalto0.33,whichisidenticaltotheoneobtainedbyChetty(2012)when
22 AnotherconcernwithfocusingonthetaxruleinEq.(11)isthatitisnotmoti- usingallfifteenpapers.Chetty(2012)alsofindsthatthecompensatedanduncom-
vatedinnormativeterms.Nevertheless,HeathcoteandTsujiyama(2015)estimate pensatedelasticitiestaxableincomeareverysimilar,whichhelpstomotivateour
verysmallwelfaregainsassociatedwithmovingfromanoptimaltaxsystemwithin assumptionofGHHpreferencesinEq.(16).Itisimportanttomentionhoweverthat
theclassdescribedbyEq.(11)toanoptimaltaxschedulebelongingtothegeneral theevidencesuggeststhattheseelasticitiesappeartobehigherforrichindividuals
classofnonlinear(Mirrlees)taxschedules. thanforpoorones,afeaturethatisabsentinourmodel.