Fiscal Policy, Elastic Labor Supply and Endogenous

FISCALPOLICY,ELASTICLABORSUPPLY,ANDENDOGENOUSGROWTH*StephenJ.TurnovskyUniversityofWashington,SeattleWA98195EndogenizinglaborsupplyleadstofundamentalchangesintheequilibriumstructureoftheAKgrowthmodel.Thebalancedgrowthequilibriumcanbedescribedintermsoftwotradeofflocirelatingtheequilibriumgrowthratetothefractionoftimedevotedtoleisure.Theimplicationsofendogenouslaborsupplyforfiscalpolicyareanalyzed.Threeissuesareaddressed.First,theeffectsofvariousdistortionarytaxchangesandgovernmentexpenditurechangesontheequilibriumgrowth-leisure(employment)tradeoffareanalyzed.Second,optimalfiscalpolicyischaracterized.Finally,theformalanalysisissupplementedbynumericalresults,focusingparticularlyonthequantitativewelfareimplications.RevisedVersionMay1998TheconstructivecommentsofTheoEicherandananonymousrefereeonearlierdraftsaregratefullyacknowledged.1.IntroductionRecentendogenousgrowthmodelshavestressedtheroleoffiscalpolicyasakeydeterminantoflong-rungrowth.1Onelimitationofthesenewmodelsisthatwithfewexceptionstheytreatlaborsupplyasinelastic,therebyabstractingfromthedecisiontoallocatetimebetweenworkandleisure.Thistreatmentseverelylimitscertainaspectsoffiscalpolicy,implyingforexample,thatbothaconsumptiontaxandataxonlaborincomeoperateasnon-distortionarylumpsumtaxes.Furthermore,itisfamiliarfromintertemporalRamsey-typemodelsthattheendogeneityoflaborsupplyisessentialforgovernmentconsumptionexpenditurepolicytohaverealeffectsonoutputandcapital;see,forexample,Turnovsky(1995).Inagrowthcontext,thewellknownEaton(1981)result,showinghowunderdebtfinancingtheequilibriumgrowthrateisindependentoftheshareofgovernment(consumption)expenditure,isamanifestationofthesamephenomenon.ThispaperintroducesanelasticlaborsupplyintoasimpleAKinvestment-basedgrowthmodel,usingthismodeltoanalyzefiscalpolicyintheformofdistortionarytaxesandgovernmentexpenditurechanges.Underplausibleconditions,theeconomywillalwayslieonitsbalancedgrowthpath,justasitdoesinthestandardone-sectorAKmodelwithfixedlaborsupply.However,endogenizinglaborsupplyleadstofundamentalchangesintheeconomy'sequilibriumstructure,aswellastoimportantimplicationsforfiscalpolicy.Thebalancedgrowthequilibriumforsuchaneconomycanbeconvenientlydepictedintermsoftwotradeofflocirelatingtheequilibriumbalancedgrowthratetothefractionoftimedevotedtoleisure.Thefirstlocusdescribesthecombinationsofthesetwoquantitiesthatmaintainconsistencyamongratesofreturn;theseconddescribesthecombinationsofthesetwoquantitiesconsistentwithproductmarketequilibrium.Theserelationshipsarehighlynonlinearandanequilibriummayormaynotexistinwhichbothconditionsaremetsimultaneously.Thisisincontrasttothebasicone-sectorAKmodel,inwhichtheexistenceofalong-runbalancedgrowthpathisalwaysassured.Themainfocusofouranalysisistoconsidertheconsequencesofendogenizinglaborsupplyforfiscalpolicy.Incontrasttothemorefamiliarcaseofaninelasticlaborsupply,allfiscal1Seee.g.Barro(1990),Rebelo(1991),Jones,Manuelli,andRossi(1993),Ireland(1994),andTurnovsky(1996).1variables,includingtaxesoncapitalincome,laborincome,andconsumption,aswellasbothgovernmentexpenditureonconsumptionandproduction,nowinfluencetheequilibriumgrowthrate.Inaddition,thebenefitsfromgovernmentexpenditure,bothinconsumptionandinproduction,areimportantinthetradeofflocithatdeterminetheexistence(orlackthereof)ofanequilibrium.2Ouranalysisoffiscalpolicyfocusesonthreegeneralissues.First,weconductanumberofcomparativestaticexercises,analyzingtheeffectsofdistortionarytaxchangesandexpenditurechangesontheequilibriumgrowth-leisure(employment)tradeoff.Thesecanbecarriedoutbysimplemanipulationofthetwoequilibriumtradeoffloci.Alltaxratesreducethelaborsupplyandthegrowthrate.Wealsoderivearankingfortheeffectsofgovernmentexpenditureonthegrowthrateunderdifferentmodesoftaxfinancing.Thisrankingisininverseordertotheadverseeffectoftheparticulartaxontheincentivestoaccumulatecapital.3Secondwecharacterizeoptimalfiscalpolicy.Ifgovernmentexpendituresaresetoptimally,thencapitalshouldnotbetaxed;consumptionandleisureshouldbetaxeduniformly.Ifgovernmentexpendituresarenotattheiroptimallevels,thenallthreetaxratesshouldbesetsoastocorrectthedistortionsinduced.Ingeneral,thisenablesthesupportofthefirst-bestoptimum.Finally,theformalanalysisissupplementedbysomequantitativeresults.Abenchmarkeconomyiscalibratedandthenumericaleffectsofvarioustypesofpolicyshocksassessed.Twoaspectstoreceiveparticularfocusare:(i)thewelfareoftherepresentativeagentasmeasuredbyhisintertemporalutility,and(ii)theintertemporalgovernmentbudgetbalance.Ournumericalcalculationssuggestthatreducingincometaxesandintroducingconsumptiontaxesmayyieldnumericallysignificantwelfaregains,whileatthesametimehavingafavorableeffectonthegovernment'sintertemporalbalance.Theoptimaltaxpoliciesarealsocomputednumerically.2TworecentpaperstointroduceleisureintoanendogenousgrowthmodelincludeBenhabibandPerli(1994)andLadrón-de-Guevara,Ortigueira,andSantos(1997).Thefocusofthesepapersisdifferentfromthatpresentedhere,inthattheyareconcernedwithissuesofexistenceofequilibrium,showinghowtheendogeneityoflabormayquiteplausib