欧洲央行-法案对谁收费：货币财政刺激的再分配后果（英）

EUROPEANCENTRALBANK

EUROSYSTEM

MichałBrzoza-Brzezina,JuliaJabłońska,MarcinKolasa,KrzysztofMakarski

WorkingPaperSeries

Forwhomthebilltolls:redistributiveconsequencesofamonetary-fiscalstimulus

No2998

Disclaimer:ThispapershouldnotbereportedasrepresentingtheviewsoftheEuropeanCentralBank(ECB).TheviewsexpressedarethoseoftheauthorsanddonotnecessarilyreflectthoseoftheECB.

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Abstract

DuringtheCOVID-19pandemic,governmentsintheeuroareasharplyincreasedspendingwhilethe

EuropeanCentralBankeasedfinancingconditions.Weusethisepisodetoassesshowsuchaconcertedmonetary-fiscalstimulusredistributeswelfarebetweenvariousagecohorts.Ourassessmentinvolvesnotonlytheincomesideofhouseholdbalancesheets(mainlydirecteffectsoftransfers)butalsothemoreobscurefinancingsidethat,toasubstantialdegree,occurredviaindirecteffects(withaprominentroleoftheinflationtax).Usingaquantitativelife-cyclemodel,andassumingthatthedeficitwaspartlyunfundedbyfuturetaxes,wedocumentthatyounghouseholdsbenefitedfromthestimulus,whilemiddle-agedandolderagentsmainlypaidthebill.Crucially,mostwelfareredistributionwasduetoindirecteffectsrelatedtomacroeconomicadjustmentthatresultedfromthestimulus.Asaconsequence,eventhoughallagecohortsreceivedsignificanttransfers,thewelfareofsomeactuallydecreased.

JEL:E31,E51,E52,H5,J11

Keywords:COVID-19;Fiscalexpansion,Monetarypolicy,Redistribution

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Non-technicalsummary

TheunexpectedonsetoftheCOVID-19pandemicinearly2020hasleftfiscalauthoritiesworldwidegrapplingwithsoaringexpensesandplummetingrevenues.Intheeuroareathesedevelopmentstranslatedintofiscaldeficitsequivalentto7%and5.2%ofGDPin2020and2021,respectively.Thefiscalexpansionwasconcomitantwithadeepmonetaryeasing.Withinterestratesclosetotheeffectivelowerbound(ELB),thiswasimplementedbyanewroundofquantitativeeasing.Thisexpansionarypolicymixfacilitatedthefinancingofessentialexpendituresandupheldeconomicstability.Nonetheless,italsocontributedtoanincreaseininflation.

Weusethisepisodetoanalyzetheimplicationsofsuchanextensivemonetaryandfiscalstimulusfortheredistributionofwelfareamongdifferentagegroups.Fiscalexpendituresallocatedincometovarioussegmentsofthepopulationinarelativelytransparentmanner,withtransfersandexpen-ditureswell-documentedinEurostatstatistics.Whatremainslesstransparent,yetarguablymoreintriguing,istheindirectredistributionresultingfrommacroeconomicadjustments.Byavertinganeconomicdownturn,themonetaryandfiscalstimulusbolsteredtheincomesofbothworkersandcapitalowners.However,theunforeseeninflationadverselyaffectedholdersofnominalassetssuchascashandbonds.Giventhatofficialtaxeshavenotbeenraised,thesegroupsarepresumedtohaveimplicitlyfinancedasignificantportionoffiscalexpendituresthroughaninflationtax.

Inordertoinvestigatetheseimpacts,wedevelopabusinesscyclemodelincorporatinglife-cyclefeatures.Wecalibratethismodeltocapturethekeydistributionalfeaturesofhouseholdbalancesheetsintheeuroareaandthenuseittoevaluatetheredistributiveoutcomesofthepandemicstimulus.Thisframeworkenablesusnotonlytoexaminethedirectredistributionresultingfromdisparateexpendituresamongdifferentagegroups,butalsotoassessthelessapparentaspectofredistributionstemmingfrommacroeconomic(socalledindirect)effects.Toevaluatetheredis-tributiveimpactofthestimulus,wecomputetheanticipatedlifetimewelfaregainofhouseholdsofvariousagesduetotheexpansion.

Assumingthat40%ofthedeficitremainedunfunded,ourresultsindicatethatyoungEuropeanhouseholdsreapedtherewardsofthemonetaryandfiscalstimulus,whereastheburdenwaspre-dominantlybornebymiddle-agedandolderhouseholds.Importantly,themajorityofredistributiveeffectsstemmingfromthestimuluscannotbeattributedtodirectincomeeffectsresultingfrom

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augmentedspendingbutrathertoitsindirectmacroeconomicconsequencesrelatedtoshiftsinas-setreturnsandlabormarketdynamics,withinflationbeingtheprimarydriver.Surpriseinflationbenefitedyoungerhouseholdsastheseholdnegativenominalassets(inparticularmortgageloans).Atthesametimeitadverselyaffectedolderhouseholdswithsubstantialnominalassetholdings(cash,deposits,bonds).Infact,fornumerouscohorts,theseindirecteffectsdominatedtheoverallpicture.

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1Introduction

1.1Motivationandmainresults

TheCOVID-19pandemicstruckunexpectedlyinearly2020.Itbroughthavoc,death,andsuffering.Fiscalauthoritiesaroundtheworldfacedsharplyincreasingbillsanddramaticallyfallingincome.Theformerresultedmainlyfromballooninghealthcareexpendituresandsubsidiestostrugglingfirms.Thelatterfollowedself-imposedrestrictionsofeconomicactivitybycitizenswhofearedtheinfection,aswellaslockdownsimposedbygovernmentsthattriedtoflattentheinfectioncurveandpreventthehealthcaresystemfromcollapsing.Intheeuroarea(onwhichthispaperconcentrates),thesedevelopmentsbroughtaboutfiscaldeficitsof7%and5.2%ofGDPin2020and2021,respectively.

Thefiscalexpansionwasaccompaniedbyadeepmonetaryeasing.Withinterestratesclosetotheeffectivelowerbound(ELB),thiswasimplementedbytheintroductionofanewroundofquantitativeeasing.TheEuropeanCentralBank(ECB)initiatedthePandemicEmergencyPurchaseProgram(PEPP)withatotalenvelopeforassetpurchasesofEUR1,850billion.Thisultra-expansionarypolicymixallowedthefinancingofnecessaryexpendituresandkepttheeconomyafloat.However,italsoresultedininflationarypressures.Inflationincreasedfrom1.2%justbeforethepandemicoutbreakinFebruary2020to5.9%inFebruary2022beforetheunprovokedaggressionoftheRussianFederationagainstUkrainemadefoodandenergypricessoarandblurredthepicturebyfurtherfuelinginflation.

Inthispaperweusethesedevelopmentstoassesshowsuchamassivemonetary-fiscalstimulusredistributeswelfareacrossdifferentagecohorts.Thedirecteffectsoffiscalpolicydistributedincometovariousgroupsofcitizensinarelativelytransparentway.VariouscategoriesoftransfersandexpendituresarewelldocumentedintheEurostatstatistics.Whatismuchlesstransparent,andatthesametimearguablymuchmoreinteresting,istheredistributionthathappenedindirectlyduetomacroeconomicadjustment.Bypreventingacollapseineconomicactivity,themonetary-fiscalstimulusincreasedtheincomesofworkersandownersofcapital.However,theunexpectedinflationitgeneratedhurtownersofnominalassets(cash,bonds).Asofficialtaxeshavenotbeenincreased,thesegroupsarethemostlikelytohaveimplicitlyfinancedmuchofthefiscalexpendituresbypaying

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aninflationtax.

Tostudytheseeffectsindetail,weconstructabusinesscyclemodelwithlife-cyclefeatures,carefullycalibrateittoreflectthemaindistributionalfeaturesofthebalancesheetsoftheeuroareahouseholds,andthenuseittoassesstheredistributiveconsequencesofthepandemicprograms.Suchaframeworkallowsusnotonlytolookatthedirectredistributionduetonon-uniformlyallocatedspendingbetweendifferentagecohortsbutalso,crucially,toassesstheobscurepartoftheredistributionthatoccurredindirectlyviageneralequilibriumeffects.Tothebestofourknowledge,thispaperisthefirstsuchattempt(notonlyforthepandemicstimulusbutalsomorebroadlyinthecontextofmonetary-fiscalstimuli),andhereweseeourmaincontributiontotheexistingliterature.

Theaggregateimplicationsofouranalysisarenotsurprising:withoutthestimuluspackage,thepandemicrecessionwouldhavebeenworse,anddeflationwouldloom.However,whiletheexpansioncontributedtofasterpost-pandemicrecovery,italsoresultedinrisinginflation,andthesetwobroaddevelopmentsaffectdifferentagecohortsdifferently.Toassessthetotalredistributiveeffectsofthemonetary-fiscalexpansion,wecalculatetheexpectedremaininglifetimewelfaregainseparatelyforeachcohort.Whatdowefind?Accordingtoourpreferredparameterization,whichassumesthat40%ofthedeficitwasleftunfunded,youngEuropeanhouseholdsbenefitedmostfromthestimulusasfiscalexpendituresandimprovedlabormarketconditionssupportedtheirincomes.Moreover,thenominalassetholdingsoftheyoungarerelativelysmall(orevennegative),sotheydidnotpaymuchoftheinflationtax(mortgageholdersgainedinfact).Oldergenerations,ontheotherhand,footedmostofthebill.Theybenefitedfromtransferstofirmsandtherelatedstockmarketappreciation.However,thesegainsdidnotoutweighlossesfromtheinflationtaxonnominalassets,asmiddle-agedandoldhouseholdstendtoowntheminsubstantialamounts.

Ourmostimportantfindingis,however,thatmostofthetotalredistributionassociatedwiththemonetary-fiscalexpansionoccurredviaindirect(generalequilibrium)channelsrelatedtolabormarketperformance,surpriseinflation,andstockmarketappreciation.Formanycohorts,theseeffectsactuallydeterminedthesignofthetotalwelfareeffect.

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1.2Monetaryandfiscalpolicyduringthepandemic

Inthissection,wediscussthemonetary-fiscalstimulusof2020-21.Letusstartwithfiscalexpendi-tures.Asiswellknown,governmentsinalleuroareacountriessharplyincreasedspendingwithoutraisingtaxes.Howexpenditurewasdividedbetweengovernmentconsumptionandvarioustypesoftransfersmatterssomewhatforthemacroeconomicpicture,andalotfortheincomesideoftheredistribution.Weusegovernmentexpenditurestatisticstocalculatetheincreaseinspendinginfivecategories(governmentconsumptionaswellastransferstoemployees,households,firmsandretirees).Leavingtechnicalitiesandthepresentationofdetailedresultstosection3,letusnowonlyreportthetotalsizeofthestimuluspackages,whichweestimateat4%ofGDPin2020and5.4%ofGDPin2021.

Now,letusmovetomonetarypolicy.WiththemacroeconomicpicturegrimingintheWinterof2020,theECBlaunchedanewasset-purchaseprogram,thePEPP.InMarch2020,theGoverningCouncildecidedtostartassetpurchaseswithamaximumvolumeofEUR750billion.ThisenvelopewasfurtherincreasedinJuneandDecember2020toatotalofEUR1850billionoralmost14%ofGDP,ofwhichEUR1718billionwereultimatelyusedbyMarch2022,whennetpurchasesweresuspended.ThePEPPwassupposedtobringmonetaryaccommodationbyeasingfinancingconditionsfortheprivateandpublicsectors(Lane,2022).1

Consequently,virtuallyallnewlyissuedpublicdebtwasacquiredbytheEurosystem(ES),creatingcentralbankreserves.Atthesametime,almostnotraditionalmonetarypolicyreactionoccurred.Interestrateswerenotloweredduringthepandemicastheywerealreadyclosetotheireffectivelowerbound.Amonetarypolicytighteningstartedonlyinthesecondhalfof2022.TheECBdecidedtokeepPEPPrelatedassetholdingsandtoreinvestallmaturingprincipalpaymentsatleastuntiltheendof2024(ECB,2023).Figure1showshowallthemaincategoriesdiscussedabovewereevolvingovertheanalyzedperiod.

Asisknownfromtheliterature(discussedinthenextsection),themacroeconomiceffects

ofgovernmentspendingcruciallydependonthecurrentandexpectedfuturereactionofmonetary

1Beyondattemptingtoeasepolicyontheaggregate,theECBwasalsoactivelycounteractingthefinancialfrag-mentationoftheeuroarea(i.e.risingyieldsofcertaincountriesgovernmentsecurities).Thispartofthestoryis,however,beyondthescopeofourstudy,andwepayattentionneithertothisnortotheimpactofthePEPPonavoidingapossiblewidespreadpanicinfinancialmarkets.

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policyaswellasonwhethertheresultingdeficitsareexpectedtoberepaidbyfuturefiscaltightening.Inthiscontext,itisimportanttonotethat,atthetimethePEPPwasintroduced,expectationsofmonetarypolicypointedtowardsaprolongedperiodofaccommodation,accompaniedbyadeclineininflationexpectations,whileexpectationsoffiscalpolicysuggestedthatspendingshockswerelargelyperceivedasunfunded.InMarch2020,EONIAforwardratesdeclinedbelowzeroforahorizonofupto20years.Theforecastsofprimaryfiscalbalancesdeclinedsharplyintonegativeterritoryin2020,andsurpluseswerenotforecastedevenwhenthispaperwaswritten(seebottomrowofFigure1).

Basedonthefactsdescribedabove,ourbaselinemodelingstrategyassumesafiscalexpansionwhichisonlypartlyfundedbyfuturetaxincreases2andisotherwiseaccommodatedbyapassivemonetarypolicyreactioninthesenseofLeeper(1991).Itshouldbemadeclearthatwethinkoftheanalyzedepisodeasaspecialfeatureofthepandemictimesandnotnecessarilyasanadequateapproachtomodelingmonetary-fiscalpolicyinteractionsinothercircumstances.

1.3Therelatedliterature

First,ourworkisrelatedtoagrowingliteratureemphasizingthepotentialredistributiveeffectsofmonetaryandfiscalpolicies.Usingdetailedmicro-leveldataonincomeandconsumptionforU.S.households,Coibionetal.(2017)findthatcontractionarymonetarypolicyincreasesinequal-ityinlaborearningsandtotalincome.Dosscheetal.(2021)documentthatamonetarypolicyeasinghasaninequality-reducingimpactmainlybyreducingunemploymentamongthepooresthouseholds.LenzaandSlaˇc´alek(2021)cometothesameconclusionintheirstudyofquantitativeeasing.DoepkeandSchneider(2006)showthatunexpectedinflationtransfersresourcesfromtheold(typicallythebondholders)totheyoung(withfixed-ratemortgagedebt)inthepostwarU.S.economy.Similarconclusionscanalsobedrawnforothercountries.FortheOECDeconomies,theevidenceisprovidedbyAlbanesi(2007),whodemonstratesthepositiverelationshipbetweeninflationandincomeinequality.Fortheeuroarea,AdamandZhu(2016)usetheHouseholdFinanceandConsumptionSurvey(HFCS)datatoshowthatunexpectedpricelevelmovementsgenerateaquantitativelysignificantwealthredistribution.Pallottietal.(2023)usethesamedatatomeasure

2AsexplainedindetailinSection(3),wecalibrateourbaselinestimulusscenariosothatapproximately40%ofthedeficitremainsunfunded.

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thewelfareeffectsofrisinginflationbetween2021and2022,identifyingthoseaged25-44asnetwinnersastheyarelesslikelytoownlargebalancesofnominalassetsandmoreoftenholdnominaldebt.HeterogeneousagentNewKeynesian(HANK)modelsarealsoincreasinglygaininggroundinthecontextofdistributionaleffects,showingi.a.thatpoorhouseholdsaremorestronglyaffectedbymonetarypolicyshocks(seee.g.,Kaplanetal.,2018;Guoetal.,2023).

Regardingdistributionalaspectsofthepandemicfiscalstimulus,Faria-eCastro(2021)analyzestheeffecsofvariouspolicytoolsontheincomesofhouseholdgroups(borrowersvs.savers),whileBayeretal.(2023)useaHANKmodeltocalculatetheeffectivenessofvarioustransfersinstabilizingtheeconomy.ClosesttoourworkisBhattaraietal.(2023),whoanalyzethedistributionalconse-quencesofvariousfiscaltoolsanddiscusstheroleoftheirinflationaryconsequencesinatwo-agent(Ricardianandhand-to-mouth)model.Tothebestofourknowledge,discussingthedistributionalconsequencesoffiscalpolicyalongtheagedimension,theirdirectvs.indirectcomponent,andtheirdependenceontheshapeofmonetarypolicyhavenotbeenstudiedsofar.

Second,ourpaperisrelatedtothetheoreticalandempiricalliteratureonthemacroeconomiceffectsoffiscalpolicy,focusingoneithertheroleplayedbymonetarypolicybehaviororonhowthefiscalstimulusisfunded.Theformerconcursthattheeffectsoffiscalpolicyarehighlydependentonhowmonetarypolicyisshaped.Inparticular,changesingovernmentspendingortaxesandtransfersmayhavemoresignificantmultipliereffectsunderzerolower-boundconditionscomparedtoperiodswhenthereismoreroomtomaneuvertheinterestrates.Christianoetal.(2011)documentthatfiscalmeasuresaimedatincreasingaggregatedemandareparticularlypowerfulattheeffectivelowerboundwhileErcegandLinde(2014)considertheconditionsunderwhichtheymayevenbecomeself-financing.SimilarresultsareobtainedbyWoodford(2011),showinganincreaseinwelfarewhengovernmentpurchaseshelpclosetheoutputgapcreatedduetotheinabilitytoreduceinterestrates.Moregenerally,empiricalevidencepresentedbyCloyneetal.(2020)emphasizesthecrucialroleofmonetarypolicyinshapingthesizeoffiscalmultipliers.

TheotherlineofpapersfollowsLeeper(1991)andLeeperandLeith(2016),whointroducetheconceptofanactivefiscal-passivemonetarypolicyarrangementunderwhichfiscaldeficitsareaccommodatedbyexpansionarymonetarypolicy.Inthisvein,Bianchietal.(2023)introduce

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thedistinctionbetweenfundedandunfundedfiscalshocks,thelatternotbackedbyfuturefiscaladjustmentsandconsequentlyleadingtoasharpincreaseinoutputandinflation.FocusingontheAmericanRescuePlanActfrom2021,thatpaperconcludesthattheprogramexacerbatedtheriseininflationbecauseitwaspartiallyunfunded.Arelatedstreamofliteratureshowssimilareffectsofamoney-financedfiscalexpansion,which,asarguedbyHallandSargent(2022),wasthekeywayoffinancingtheUSfiscalresponsetoCOVID-19.Englishetal.(2017)findthatmoney-financedfiscalprogramsseenascrediblebythepubliccanstronglyboosttheeconomy.Gal´ı(2020)showsthatundernotbindingELB,money-financedgovernmentinitiativesgiveamoreconsiderableboosttotheeconomythanadebt-financedfiscalstimulus.ReisandTenreyro(2022)discusstheimpactofhelicopterdropsasaresponsetoseveraleconomicshocks,includingtheredistributionofwealthacrossagentsovertime.

Lastbutnotleast,ourworkisalsorelatedtopapersusinganOLGsetupwithNewKeynesianfeatures,typicallyrelyingonthestylizedBlanchard-Yaariframework.Thisliteratureincludes,amongothers,Gal´ı(2021)onrationalbubbles,DelNegroetal.(2012)onresolvingtheforwardguidancepuzzle,Nistic´o(2012)aboutstockpricesindrivingmonetarypolicy,Eggertssonetal.(2019)onquantifyingthesecularstagnationhypothesisandAngeletosetal.(2023)onthepossibilityoffiscaldeficitsbecominglargelyself-financingduetotheirexpansionaryeffectonthetaxbaseandinflation.Byincorporatingadetailedlife-cyclesetupinwhichagentsarecharacterizedbyage-dependentassetportfoliosthatcloselymatchthedistributionsamongeuroareahouseholds,ourmodelingenvironmentisclosesttotheframeworkofBieleckietal.(2022).

2Model

Wedevelopageneralequilibriumoverlappinggenerations(OLG)modelthatfeaturesaNewKey-nesianproductionsectorwithstickypricesandwages,aswellasgovernmentandbankingsectors.3Below,wepresentitsmainbuildingblocks.TheAppendixprovidesfurtherdetails,includingthe

3ThemodelbuildsonBieleckietal.(2022).Wemodifytheirframeworkmostlybyenrichingtheassetstructurethathouseholdshold.Moreover,weexpandthemonetary,fiscalandbankingsectorstoaccommodatethesalientfeaturesofthepolicyinterventionthattookplaceduringtheCOVID-19pandemic,includingthepossibilityofmonetarypolicybeingpassive.

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completesetofaggregateequilibriumconditions.Aperiodinthemodelcorrespondstooneyear.Variableswithouttimesubscriptsindicatetheirrespectivesteadystatevalues.

2.1Households

2.1.1Demographics

Weassumethathouseholdsenterthelabormarketattheageof20,whichcorrespondstoindexj=1inourmodel,andliveforamaximumofj=J=80periods.Ineachperiod,theyfaceage-dependentmortalityriskwithanage-specificprobabilitydenotedasωj,withωJ=1.ThesizeofagecohortjinperiodtisdenotedasNj,t.Itevolvesaccordingtothefollowingformula

Nj+1,t+1=(1−ωj)Nj,t(1)

andthetotalpopulationisgivenby

Nj,t(2)

WeassumethatthesizeoftheyoungestcohortN1,tchangesataconstantraten.Sincetheage-specificsurvivalprobabilitiesdonotchangeovertime,eachagecohort,andhencethetotalpopulation,alsogrowsatraten.

2.1.2Budgetconstraint

Ineachperiod,householdsdecideontheirconsumptioncj,tandaccumulationofthefollowingfourtypesofassets,allexpressedinrealterms:housingχj,t,depositsmj,tthatyieldnominalgross

returnR,financialassetsaj,tthataremanagedbyinvestmentfunds4andthatofferage-specific

nominalgrossreturnR,t,andanadjustable-ratemortgageloansj,tonwhichbankschargenominal

grossinterestR.Householdsalsosupplydifferentiatedlaborserviceshj,t(ι)tolaborunionsthat

payrealwagezjwt(ι)netoftaxatrateτ,withιindexingindividualhouseholdsandzjdenotingage-specificproductivity.HouseholdscanworkuntiltheyreachretirementageJR=45,whichis

4Inourmodel,householdsdecideontheamountoftotalfinancialassetsaj,ttheywanttohold.Thesecompriserealassets(claimsoncapitalandfirmprofits)andnominalbonds.Thesharesofeacharedeterminedexogenouslytomatchtheassetprofilesobservedinthedata.Theportfolioismanagedbyinvestmentfunds,asexplainedlater.

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operationalizedinthemodelbyassumingthatzj=0forj≥JR.Householdscanalsoreceivefour

typesoftransfers:t,t,t,t,andt,t,whichareextendedto,respectively,allhouseholds,working

households,firmowners,andretiredhouseholds.Finally,householdsreceiveunintendedbequestsbeqj,t,whichconsistofassetsleftbyotherhouseholdsthatdiebeforeageJandaredistributedevenlyacrosscohortsnoolderthanJR−10.Duetostaggeredwagecontracts,householdlaborincomecandifferwithinacohort.However,weassumethatthisidiosyncraticriskcanbeperfectlyinsuredsothatallotherallocationschosenbyagentsinthesamecohortareidentical.Thisallowsustoomitindexιonthesevariablesandwritethebudgetconstraintofcohortjasfollows

wherepχdenotestherealpriceofhousing,δχistheannualdepreciationrateofhousingstock,πt=Pt/Pt−1isthegrossinflationrate(withPtdenotingtheaggregatepricelevel),andΞj,t(ι)standsfornetrealpaymentsfromthelaborinsurancescheme.

Toensurerealisticdynamicsofmortgagedebt,weassumethathousingloansaretakenformultipleperiodssothatsj,tevolvesaccordingtothefollowingformula

whereℓj,tdenotesnewloansgrantedinperiodttohouseholdsofagejandmisaparametercontrollingtheeffectiveloanduration.Theseloansaresubjecttothefollowingloan-to-value(LTV)constraint

ℓj,t≤LTVjχj,tpχ,t(5)

whereLTVjistheage-specificloan-to-valueratio.

2.1.3Wagestickiness

Differentiatedlaborservicesofvarietyιaresoldtoperfectlycompetitiveaggregatorswhobundlelaborfromallhouseholdsofagejaccordingtothefollowingformula

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whereµwdeterminesthedegreeofsubstitutabilitybetweendifferentiatedlaborservices.Weassumethatthethusdefinedeffectivebundlesoflaborservicesofdifferentagecohortsareperfectsubsti-tutes,soaggregatorsarepaidthesamerealwagewtperunitofhj,tforallj.Laboraggregatorsmaximizethefollowingobjectivefunctionwthj,t−.

Wagesettingisperformedbymonopolisticallycompetitivelaborunions.Fortractability,weassumethattheyoperateonbehalfofallhouseholds,implicitlyaggregatingthemarginalrateofsubstitutionbetweenconsumptionandleisureoverthewholeworking-agepopulation.Laborunionssetwagessubj