Hansen(1985)--INDIVISIBLE-LABOR-AND-THE-BUSINESS-C

JournalofMonetaryEconomics16(1985)309-327.North-HollandINDIVISIBLELABORANDTHEBUSINESSCYCLEGaryD.HANSEN*UnioersifyofCalifornia,SantaBarbara,CA93104,USAAgrowthmodelwithshockstotechnologyisstudied.Laborisindivisible,soallvariabilityinhoursworkedisduetofluctuationsinthenumberemployed.Wefindthat,unlikepreviousequilibriummodelsofthebusinesscycle,thiseconomydisplayslargefluctuationsinhoursworkedandrelativelysmallfluctuationsinproductivity.Thisfindingisindependentofindividuals’willingnesstosubstituteleisureacrosstime.Thisandotherfindingsaretheresultofstudyingandcomparingsummarystatisticsdescribingthiseconomy,aneconomywithdivisiblelabor,andpost-warU.S.timeseries.1.IntroductionEquilibriumtheoriesofthebusinesscycle,suchasKydlandandPrescott(1982)orLucas(1977),havebeencriticizedforfailingtoaccountforsomeimportantlabormarketphenomena.Theseincludetheexistenceofunem-ployedworkers,fluctuationsintherateofunemployment,andtheobservationthatfluctuationsinhoursworkedarelargerelativetoproductivityfluctuations.Equilibriummodelshavealsobeencriticizedfordependingtooheavilyonthewillingnessofindividualstosubstituteleisureacrosstimeinresponsetowageorinterestratechangeswhenaccountingforthelastobservation.Thiscriticismisbasedatleastpartiallyonthefactthatmicrostudiesusingpaneldataonhoursworkedbyindividualshavenotdetectedtheintertemporalsubstitutionnecessarytoexplainthelargeaggregatefluctuationsinhoursworked[seeAshenfelter(1984)].Inthispaper,asimpleone-sectorstochasticgrowthmodelwithshockstotechnologyisconstructedinwhichthereishighvariabilityinthenumberemployedandtotalhoursworkedeventhoughindividualsarerelativelyunwillingtosubstituteleisureacrosstime.Themodeldiffersfromsimilarmodels,suchasKydlandandPrescott(1982),inthatanon-convexity(indivisi-blelabor)isintroduced.Indivisiblelaborismodeledbyassumingthatindivid-*ThispaperispartofmydoctoraldissertationwrittenwhileastudentattheUniversityofMinnesota.IhavebenefitedfromconversationswithmanypeopleincludingRobertKing,ThomasSargent,ChristopherSims,NeilWallace,SumruAltug,PatrickKehoe,RamonMatimon,IanBain,andRodyManuelli.Iowemygreatestdebt,however,tomyadvisor,EdwardPrescott.IwishtoalsoacknowledgetheFederalReserveBankofMinneapoliswhichhasprovidedsupportforthisresearch.Allerrors,ofcourse,aremine.0304-3923/85/.%3.3OSl985,ElsevierSciencePublishersB.V.(North-Holland)310G.D.Hunsen.Indivisibleluborundthebminessqdeualscaneitherworksomegivenpositivenumberofhoursornotatall-theyareunabletoworkanintermediatenumberofhours.Thisassumptionismotivatedbytheobservationthatmostpeopleeitherworkfulltimeornotatall.Therefore,inmymodel,fluctuationsinaggregatehoursaretheresultofindividualsenteringandleavingemploymentratherthancontinuouslyem-ployedindividualsadjustingthenumberofhoursworked,asinpreviousequilibriummodels.ThisisconsistentwithanimportantfeatureofU.S.post-wardata:mostfluctuationinaggregatehoursworkedisduetofluctuationinthenumberemployedasopposedtofluctuationinhoursperemployedworker.Thisisafactthatpreviousequilibriumtheorieshavenottriedtoaccountfor.’Existingequilibriummodelshavealsofailedtoaccountforlargefluctuationsinhoursworkedalongwithrelativelysmallfluctuationsinproductivity(ortherealwage).Prescott(1983),forexample,findsthatforquarterlyU.S.timeseries,hoursworkedfluctuatesabouttwiceasmuch(inpercentageterms)asproductivity.Inthispaperitisshownthataneconomywithindivisiblelaborexhibitsverylargefluctuationsinhoursworkedrelativetoproductivity.Thisstandsinmarkedcontrasttoanotherwiseidenticaleconomythatlacksthisnon-convexity.Inthiseconomyhoursworkedfluctuatesaboutthesameamountasproductivity.2Equilibriumtheoriesofthebusinesscyclehavetypicallydependedheavilyonintertemporalsubstitutionofleisuretoaccountforaggregatefluctuationsinhoursworked.’Thewillingnessofindividualstosubstituteintertemporallyismeasuredbytheelasticityofsubstitutionbetweenleisureindifferenttimeperiodsimpliedbyanindividual’sutilityfunction.However,thetheorydevel-opedhereisabletoaccountforlargeaggregatefluctuationsinhoursworkedrelativetoproductivitywithoutrequiringthatthiselasticitybelarge.Thisfollowsbecausetheutilityfunctionofthe‘representativeagent’inourmodelimpliesanelasticityofsubstitutionbetweenleisureindifferentperiodsthatisinflnite.4Thisresultdoesnotdependontheelasticityofsubstitutionimpliedbythepreferencesoftheindividualswhopopulatetheeconomy.Thus,thetheorypresentedhereisinprincipleconsistentwiththelowestimatesofthiselasticityfoundfromstudyingpaneldata[seeAltonji(1984)orMaCurdy(1981)].‘ThefactthatexistingequilibriummodelsareinconsistentwiththisobservationhasbeenstressedbyHeckman(1983)andColeman(1984).‘KydlandandPrescott(1982)attempttoexplaintheabovefactbyincludingpastleisureasanargumentintheindividual’sutilityfunctionsoastoenhancetheintertemporalsubstitutionresponsetoaproductivityshock.However,evenafterintroducingthisfeature,KydlandandPrescottwerestillunabletoaccountforthisobservation.3Thisistrueforthetechnologyshocktheories,suchasKydlandandPrescott’s(1982).aswellasthemonetaryshocktheoriesofLucasandBarre[seeLucas(1977)].41nthismodelthereisacrucialdist