On sunspot fluctuations in variable capacity utilization models Frédéric Dufourt.pdf

该【On sunspot fluctuations in variable capacity utilization models Frédéric Dufourt 】是由【小舍儿】上传分享，文档一共【15】页，该文档可以免费在线阅读，需要了解更多关于【On sunspot fluctuations in variable capacity utilization models Frédéric Dufourt 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..JournalofMathematicalEconomics76(2018)80–94ContentslistsavailableatScienceDirectJournalofMathematicalEconomicsjournalhomepage:ate/jmateco?OnsunspotfluctuationsinvariablecapacityutilizationmodelsFrédéricDufourta,AlainVendittia,b,*,RémiVivèsaaAix-RS,EHESS,CentraleMarseille,AMSE,Marseille,FrancebEDHECBusinessSchool,FrancearticleinfoabstractArticlehistory:WeinvestigatetheextenttowhichstandardonesectorRBCmodelswithpositiveexternalitiesandountforthelargehump-(2004):,whenlaborisinfinitelyelastic,ursthroughFlipandIndeterminacyHopfbifurcationsforalargesetofvaluesfortheelasticityofintertemporalsubstitutioninconsumption,Realbusinesscyclesthedegreeofincreasingreturnstoscaleandtheelasticityofcapital–,-,thehumpistoopersistentforthemodeltobeconsideredfullysatisfactoryfromanempiricalpointofview.?,weemphasizethelinkbetweendemandshocksHowever,sinceCassandShell(1983),afieldofeconomicresearchandexpectation-drivenfluctuationsbasedontheexistenceofhasbeendevelopedtoanalyzetheroleofagents’,,whichstandardone-sectorsunspotmodelswithpositiveexternal-researchershavehighlightedthefactthatagentscancollectivelyountfor‘‘boom-bustchangetheirexpectationsduetoexogenousreasons,notnecessar-cycles’’characterizedbyprocyclicalcovariationsofmostmacroe-,thesechangesinex-conomicvariablesandahump-shapedoutputresponsewhenthepectationsgeneratefluctuationswhichvalidateex-,-fulfillingprophecies.?ThefirstsunspotmodelusingtheframeworkoftheRBC/DSGEThisworkhasbenefitedfromthefinancialsupportoftheFrenchNationalliterature(BenhabibandFarmer,1994)wasshowntoperformasResearchAgency(ANR-15-CE33-0001-01).Wethanktheco-,,,,,orevenbetterthan,thecanonicalRBCmodel(FarmerandMagris,,,1994).However,amajorhurdlethisliteraturefacedwasthatThispaperalsobenefitedfrompresentationsatthe‘‘DoctoralWorkshoponQuan-theexistenceofsunspotequilibriarequiredverylargelevelsoftitativeDynamicEconomics’’,GREQAM,Marseille,September2016,theInterna-increasingreturnstoscale,-tionalWorkshopon‘‘Financialandrealinterdependencies:volatility,internationalnesswasconsideredoneofthemainchallengeforthemacroe-opennessandeconomicpolicies’’,GREQAM,Marseille,November2016,the21stConference‘‘TheoriesandMethodsinMacroeconomics’’,CatólicaLisbonSchoolconomicsunspotliteratureuntilWen(1998)proposedasimpleofBusiness&Economics,Lisbon,March2017,theSeminarinMacroeconomics,extensionconsistinginintroducingavariablecapitalutilizationUniversityofKonstanz,April2017,theASSETMetting,Algiers,October2017,rateintheBenhabib–Farmersetup,inthespiritofGreenwoodetthe6thAnnualLithuanianConferenceonEconomicResearch,Vilnius,June2017,al.(1988).1Itwasshownthatthissimpleextensiontothecanon-andtheInternationalConferenceon‘‘RealandFinancialInterdependencies:NewApproacheswithDynamicGeneralEquilibriumModels’’,ParisSchoolofEconomic,icalone-sectormodelwassufficienttoallowfortheexistenceofParis,*Correspondingauthorat:Aix-RS,EHESS,CentraleMar-seille,AMSE,Marseille,FranceandEDHECBusinessSchool,-mailaddresses:frederic.******@univ-(),1Analternativeexplanationistointroduceatwo-sectorsetupwithincreasingalain.******@univ-(),remi.******@univ-(ès)..(2015).https:///.-4068/?.:.../JournalofMathematicalEconomics76(2018)80–,BenhabibandWen(2004)showedbusinesscycle(boom-bustcycles).Thekeyingredientsforobtain-thatthismodelcouldalsoexplainmanydimensionsofobservedingthisresultaretoconsideravalueforEISinconsumptioninthebusinesscycleswhenthemodelissubmittedtocorrelatedfun-upperrangeofavailableempiricalestimates,,paredtotheaccountforPigoucycles:periodsofboomsandbuststriggeredCobb–Douglasproductionfunction,andaslightlylargerdegreeofbyexogenouschangesinagents’,–Wen(henceafterBW)showthattheobtainedhump-shapeddynamicsistoopersistentmodelthenputanendtoyearsofdiscussionsaboutthecredibilitytobeconsideredentirelyconsistentwithobserveddata,,acarefulexaminationoftheresultspresentedbyBWre-ageneralizedversionoftheone-sectormodelwithvariablecapitalvealsthatthereremainsonedimensionforwhichthemodelisnotutilizationrateinSection2,aswellasthecorrespondingintertem-,hoursworked,–consistentlywiththedata–ountforthestylizedfactsarenothump-,startingwiththeassociatedwithacanonicaldemandshockwhenthesourceofseminalanalysisofBlanchardandQuah(1989),(throughvariousassumptions)habitformationinconsumptionordynamiclearningbydoingin‘‘demandshock’’ishump-,-fulfillingpropheciestobefullyconvincing,,weobservethatin(1998)andBenhabibandWen(2004).posedtheinitialBWmodel,verytightrestrictionsonthespecificationofofalargenumberofidenticalinfinitely-livedagentsandalargepreferencesandontheproductionsideoftheeconomyareconsid-,,,buttherearecycleproperties:theelasticityofintertemporalsubstitution(EIS),thedegreeofincreasingreturnstoscale(IRS),thewage-elasticityoflaborsupply,andthecapital–,itisposedofalargenumberofiden-,,,,,-shapedoutputTheproductionfunctionisdynamicsinresponsetoapuresunspotshockisrobust–.,struc-turaltothemodel–orifitisduetothefactthatthismodelwasYt=Af(utKt,Lt)e(uˉtKˉt,Lˉt)()evaluatedundertoostrongrestrictionsregardingthespecifica->0isascalingtechnologyparameterande(utKt,Lt),,undertheclassofgeneraladditivelyseparablepreferencesnotrestricttheproductionfunctiontobeCobb–,andageneralproductionfunction,ursourproductionfunctionisgeneralandsatisfies:(uK,L)isC2overR2,increasingin(uK,L),con-thedegreeofIRS,theEISinconsumptionandthecapital–labor2++1caveoverR++(uˉKˉ,Lˉ)isCoverelasticityofsubstitution,,thedegreeofIRScanbemadearbitrarilysmallR++andincreasingin(uˉK,L).,Firmsrenteffectivecapitalunitsattherealrentalratertandurforarangeofvaluesforthecapital–-elasticityofsubstitutionthatextendswellbeyondone–including,gramofthefirm,whenthedegreeofIRSisnottoolarge,,weperformaquantitativeanalysisofmaxYt?wtLt?rtutKt,{Yt,Lt,utKt}themodeldirectedtowardtheabilitytoreplicateahump-,fromatheoreticalpointofview,astandardone-sectormodellaborLt:withvariablecapacityutilizationinthespiritofBWisabletor=Af(uK,L)e(uˉKˉ,Lˉ)()reproducesuchahump-shapeddynamics,whilemaintainingthet1ttttttprocyclicalityofallthemainmacroeconomicvariablesalongthewt=Af2(utKt,Lt)e(uˉtKˉt,Lˉt).():.../JournalofMathematicalEconomics76(2018)80–94es(uK,L),,suchelasticityofcapital–laborsubstitutionσ(uK,L)andtheelasticitiesthatoftheexternalityvariablewithrespecttolaborεeL(uˉKˉ,Lˉ)andγˉˉˉutcapitalεeK(uK,L):δt=∈(0,1),withγ>1.()γuKf1(uK,L)s(uK,L)=∈(0,1),umulationequationconstraintcannowbewrittenf(uK,L)()(1?s(uK,L))f1(uK,L)asfollows:σ(uK,L)=?>0uKf11(uK,L)kt+1=(1?δt)kt+wtlt+rtutkt?ct()e1(uˉKˉ,Lˉ)Kˉe2(uˉKˉ,Lˉ)(uˉKˉ,Lˉ)=,εeL(uˉKˉ,Lˉ)=.(()and(),theconsumerthussolvesthefollow-e(uˉKˉ,Lˉ)e(uˉKˉ,Lˉ)inglifetimeutilitymaximizationprogram(whereβ∈(0,1)istheItcanbenotedthatthechoiceofaCobb–Douglasproductiondiscountfactor)function,asinBW,impliesσ(uK,L)=1whereastheuseofagen-eralproductionfunctionentailsσ(uK,L)∈(0,+∞).Tosimplify∑+∞notation,wenowdenotebys,σ,εandεthecorrespondingmaxE0βt[u(ct)+Bv(??lt)]eKeL{c,k,l,u}elasticitiesevaluatedatthesteady-+1ttt=0...∞t=0()uγ()parisonwithBW,=1?tk+wl+ruk?cassumptiononexternalitiest+=sΘandεeL=(1?s)ΘwithΘ>-orderconditionsforaninteriorsolutioncanbewrittenasInthiscase,wegetindeedεeK+εeL=Θ,′(??lt)=wtu′(ct)()′′u(ct)=βEtRt+1u(ct+1)()Thereexistsacontinuumofmass1ofidenticalhouseholdsr=uγ?1()