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AnEstimatedDSGEModelforIntegratedPolicyAnalysishenMarcinKolasaJesperLindeHouWangpingZhouWP/23/135IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.2023*TheauthorswouldliketothankseminarparticipantsattheIMFforveryvaluablediscussionsandcomments.AspecialthankyoutoAtetWijosenoattheBankofIndonesiawhocontributedstronglytoanearlierversionofthemodelTheviewsexpressedhereinarethoseoftheauthorsandshouldnotbeattributedtotheIMF,itsExecutiveBoard,oritsmanagement.©2023InternationalMonetaryFundWP/23/135IMFWorkingPaperMonetaryandCapitalMarketsDepartmentAnEstimatedDSGEModelforIntegratedPolicyAnalysisPreparedbyKailiChen,MarcinKolasa,JesperLindé,HouWang,PawelZabczyk,JianpingZhouAuthorizedfordistributionbyJesperLindéJune2023IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.ABSTRACT:WeestimateaNewKeynesiansmallopeneconomymodelwhichallowsforforeignexchange(FX)marketfrictionsandapotentialroleforFXinterventionsforalargesetofemergingmarketeconomies(EMEs)andsomeinflationtargeting(IT)advancedeconomy(AE)countriesservingasacontrolgroup.Next,weusetheestimatedmodeltoexaminetheempiricalsupportfortheviewthatinterestratepolicymaynotbesufficienttostabilizeoutputandinflationfollowingcapitaloutflowshocks,andtheextenttowhichFXinterventions(FXI)canimprovepolicytradeoffs.OurresultsrevealsignificantstructuraldifferencesbetweenAEsandEMEs—inparticularFXmarketdepth—leadingtodifferenttransmissionofcapitaloutflowshockswhichjustifiesoccasionaluseofFXIinsomeEMEsincertainsituations.OuranalysisalsohighlightsthecriticalimportanceofaccountingfortheendogeneityofFXIbehaviorwhenassessingFXmarketdepthandpolicytradeoffsassociatedwithvolatilecapitalflowsinpastepisodes.JELClassificationNumbers:C6,F4,E5,O5Keywords:IntegratedPolicyFramework;EmergingMarkets;MonetaryPolicy;ForeignExchangeIntervention;EndogenousRisks;IncompleteFinancialMarkets;BayesianEstimationAuthor’sE-MailAddress:kchen4@,mkolasa@,Author’sE-MailAddress:hwang2@,pzabczyk@,jzhou1@IMFWORKINGPAPERSAnEstimatedDSGEModelforIntegratedAnalysis*TheauthorswouldliketothankseminarparticipantsattheIMFforveryvaluablediscussionsandcomments.AspecialthankyoutoAtetWijosenoattheBankofIndonesiawhocontributedstronglytoanearlierversionofthemodel.I.Introduction 5II.TheDSGEModel 8II.1.AggregateDemand 8II.2.AggregateSupply 11II.3.InternationalFinancialMarkets 14II.4.MonetaryandFiscalPolicy 17II.5.TheForeignEconomy 20III.ModelEstimation 21III.1.CountriesandData 22III.2.Priors 26III.3.EstimationResults 29IV.PosteriorPredictiveAnalysis 33IV.1.TransmissionofForeignInvestorsPortfolioOutflowShocks 33IV.2.TransmissionofInterestRatePolicyShocks 36IV.3.TransmissionofFXInterventions 38V.Regime-SwitchingEstimationResults 41VI.Conclusion 44References 46AppendixA.DerivationsofLinearizedRelationships 49A.1ResourceConstraint 49A.2UIPandNetForeignAssetDynamics 53A.3WageandPricingSchedules 57AppendixB.CalibratedParametersandFullEstimationResults 61FIGURES1.FXInterventionsduringRisk-offEpisodes 52.KeyMacroeconomicVariablesIncludedinEstimation 243.U.S.VariablesIncludedintheEstimation 254.PriorDistributions 285.DifferenceinLogMarginalLikelihoodversusCorrelationbetweenFXIandNER 326.Country-SpecificImpulsestoForeigninvestorsPortfolioOutflowShocks 347.AverageImpulsestoForeigninvestorsPortfolioOutflowShocks 358.ImpulsestoanUnexpectedInterestRateTightening 369.MeanImpulsestoanUnexpectedInterestRateTightening 3710.ImpactofFXIsonTransmissionofForeigninvestorsPortfolioOutflowShocks 3911.HowFXIsImpactTransmissionofanUnexpectedInterestRateTightening 40TABLES1.CountriesandSamplePeriodsincludedinEstimation 222.AllObservablesandShocksUsedinEstimation 23TitleofWPTitleofWPINTERNATIONALMONETARYFUND43.PriorandPosterior 294.ComparisonofModelEstimateswithDifferentFXISpecifications 315.Regime-SwitchingEstimation–Time-VaryingFXMarketDepthOnly 426.Regime-SwitchingEstimation–Time-VaryingFXMarketDepthandFXIRule 43APPENDIXTABLESAppendixB.TableB.1:ParametersCalibratedtoMatchEMEandAECharacteristics 61AppendixB.TableB.2:ParametersCalibratedtoCountry-SpecificCharacteristics 61AppendixB.TableB.3:Country-SpecificPosteriorandLogMarginalLikelihoodswithEndogenousFXIRuleinEMEs 62AppendixB.TableB.4:Country-SpecificPosteriorandLogMarginalLikelihoodswithExogenousFXIRuleinEMEs 63AppendixB.TableB.5:Country-SpecificPosteriorandLogMarginalLikelihoodsforEndogenousandExogenousFXIRulesinAEs 64IMFWORKINGPAPERSAnEstimatedDSGEModelforIntegratedAnalysisINTERNATIONALMONETARYFUND5I.IntroductionOverthelasttwodecadesmanyemergingmarketeconomies(EMEs)anddevelopingcountrieshavemovedawayfromfixedexchangerateregimesandadoptedamonetarypolicyframeworkbasedoninflationtargeting(IT).TheITframework,firstintroducedinNewZealandin1990andtheninmanyotheradvancedeconomies(AEs),wasfoundtobeverysuccessfulinstabilizingbothinflationandrealaggregates(Svensson,2010).However,unliketheiradvancedeconomycounterpartsmanyEMEcentralbankswithITframeworkshavecontinuedtorelyonforeignexchangeinterventions(FXIs)intheirmonetarypolicyoperations.Thiswasparticularlyevidentduringepisodesofvolatilecapitalflows(Hofmannetal.,2019),liketheTaperTantrumandthelustratethispointinFigurewhichshowsthatFXsalesduringthesetwoepisodesweremuchmoreprevalentinEMEsthaninAEs.Averysimilarpictureemergesifwerestrictthesampletoinflationtargetingcountries.35%30%25%20%15%10% 5%0%XInterventionsduringRiskoffEpisodes29%225%11%6%TaperTantrumTaperTantrumAdvancedEconomiesEmergingMarketEconomiesSource:OwncalculationsbasedonmonthlydatafromAdleretal.(2021).ThefigurepresentstheshareofcountrieswithineachveningifitwassellingFXreservesbroadwasatleast0.5%ofitsannualGDP.Asexploredindepthbye.g.,Adrianetal(2020,2021)andBasuetal.(2020),onereasonformorefrequentuseofFXIsinEMEsisthatthesecountriesfacemoredifficultstabilizationtradeoffsbecauseofseveral(oftenrelated)economiccharacteristicsthatsetthemapartfromAEs.EMEstypicallyhaverelativelylargernetforeignliabilitiesandmorelimitedaccesstointernationalfinancialmarkets,whichmakesthemmorevulnerabletosuddenchangesinglobalfinancialconditions.TheirFXanddomesticfinancialmarketsareoftennotasdeepasinAEs,implyingthatswingsininternationalcapitalflowsmayleadtolargeundesirablemovementsinINTERNATIONALMONETARYFUND6theexchangerate.Moreover,exchangeratevolatilitytendstohavemoreadverseeffectsinMEsbecauseoftheirlimitedabilitytohedgecurrencymismatchesandlargerandmorepersistentexchangeratepass-throughtoinflation.Thisreasoninghasrecentlyfoundsupportfromthetheoreticalliterature,whichidentifiedfrictionswarrantingtheuseofFXinterventionsincertaincircumstancesasmorelikelytoemergeinEMEsthaninAEs.OneofthekeyfrictionsisFXmarketshallowness,whichleadstoinefficientmovementsinuncoveredinterestrateparity(UIP)premiathatcanbeatleastpartiallyoffsetbyappropriateuseofFXI(see,e.g.,GabaixandMaggiori,2015;Cavallino,2019;Amadoretal.,2019;FanelliandStraub,2021).Anotherconsiderationisthepresenceofcurrencymismatchesthatmayprecipitateasharpriseintheborrowingspreadswhentheexchangeratedepreciatespossiblyleadingtoseverefinancialcrisesoftenreferredtoas‘suddenstops’(see,e.g.,JeanneandKorinek,2010;Mendoza,2010;Basuetal.,2020).Inarecentandmorequantitativelyorientedstudy,Adrianetal.(2021)arguethatthesefrictionsmaycreateaparticularlydifficulttradeoffforcentralbanksineconomieswithstrongpriceandwageindexationmechanisms,fastpass-throughofexchangeratetoconsumerprices,andhighstickinessofexportpricesinforeigncurrency,thelasttwofeaturesstressedbythedominantcurrencyparadigmliterature(Gopinathetal.,2020).Thegoalofthispaperistotesttheempiricalrelevanceofthesemechanismsandquantitativelyverifytheirimplications,includingtheconditionsunderwhichFXIcanbeuseful,byembeddingtheminamicrofoundedmacroeconomicframeworkthatcanbetakendirectlytothedata.Tothisend,wedevelopadynamicstochasticgeneralequilibrium(DSGE)modelthatcanbeseenasanempiricalformulationofthetwo-countrymodeldescribedinAdrianetal.(2021).ThemodelisaNewKeynesiansmallopeneconomysetupwithpotentiallyshallowFXmarkets,FXmismatchesandarangeofnominalrigiditiesconsideredintheDSGEliterature,includingstickypricesandwageswithindexationtopastinflationandpossiblyalsoexchangeratemovements.Pricesaresetinlocalcurrency,whichletsthedataspeaktothedegreeofexchangeratepass-through.Additionally,toaddressthewell-knownforward-guidancepuzzleimpliedbymodelswithfullyrationalagents(Giannonietal.,2015),weallowforamodestdegreeofboundedrationalitybyusingtheframeworkdevelopedbyGabaix(2020)andextendedtoanopeneconomysettinginKolasaetal.(2022).MostimportantlyandincontrasttopreviouspapersmicrofoundingthedeploymentofFXIweestimatethemodelforasetofEMEsaswellasasetofsmallopenAEsthatweuseasacontrolgroup.WeuseBayesianmethods,drawingonthelargeliteraturedealingwithopeneconomyDSGEmodels(e.g.,Adolfsonetal.,2007;JustinianoandPreston,2010).AcriticalassumptionintheestimationisthatweadoptthesamepriorsforEMEsandthecontrolgroupofAEs.Thisimpliesthatanyposteriordifferencesintheparameters,andconsequentlyanydifferencesinshocktransmission,aredrivenbycross-countryvariationinthetimeseriesusedINTERNATIONALMONETARYFUND7inestimationTakingthemodeldirectlytothedataallowsustoassessandcomparethequantitativeimplicationsofinternationaldifferencesinthetransmissionmechanismandcouldeasilybecomplementedbyscenarioanalysesassessingcountry-specificpolicytradeoffs.rtantlyapartfromincludingthestandardsetofmacroeconomictimeseriesasobservableswhenestimatingthemodel,weusetheAdleretal.(2019)estimateofFXinterventionsasanadditionalobservable.Bydoingso,weovercomeasignificantobstacleinidentifyingFXmarketdepthinmacroeconomicmodels,whereincountrieswithshallowFXmarketsmayseemtohavedeepmarketssincetheircentralbankshavesystematicallyreliedonFXinterventionstomitigateexchangeratevolatilityduringthesampleperiod.TheadditionoftheFXIproxyasobservableinestimationthusfacilitatesjointidentificationofFXIpoliciesandFXmarketdepth,especiallyincountrieswherewefindstrongevidenceforactiveFXinterventions.Moreover,wealsoestimateavariantofourmodelinwhichwerelaxtheassumptionthatFXmarketdepthandthesystematicpartoftheFXIruleareconstantandinsteadallowforthepossibilitythattheyvaryovertimeusingregimeswitchingmethodsadvocatedinMaih(2015).OuranalysisconfirmstheempiricalrelevanceoffrictionsinEMEs,whichmaywarranttheuseofFXIincertaincircumstances.ThemodelestimatesshowthatFXmarketsareshalloweronaverageinEMEsthanAEs,implyingthatUIPpremiumshockscanleadtolargermovementsintheexchangerate.Inflationexpectationsarealsolesswell-anchoredinEMEs,whichcanposedifficultoutput-inflationtradeoffsfollowingexchangeratedepreciations.ThemodelestimatesalsosuggestthatafewEMEshaveusedFXItorespondtoexchangeratemovementsinasystematicandrulebasedmanner.BylimitingexchangeratedepreciationduetocapitaloutflowsFXI–intheformofFXsales–reducetheneedtoraiseinterestratestocontaininflation,andthereforeimprovepolicytradeoffs.Afinalmodelextensionfeaturingregimeswitchingprovidesevidencefortime-varyingmarketdepthand,consequently,greaterimpactofFXIinperiodswhenmarketsareshallow.Therestofthepaperisorganizedasfollows.SectionIIpresentstheDSGEmodel.SectionIIIdescribesthemodelestimationprocedureandreportsourestimationresults.SectionIVpresentsimpulseresponsestokeyshockstoquantifyshocktransmissionandpolicytradeoffs.InSectionVweassessempiricalsupportfortheviewthatFXmarketdepthandthesystematicpartoftheendogenousFXIrulearetime-varyingbyestimatingthemodelusingregime-switchingmethods.Thelastsectionconcludes.IMFWORKINGPAPERSAnEstimatedDSGEModelforIntegratedAnalysisINTERNATIONALMONETARYFUND8II.TheDSGEModelWestartbydescribinganempiricalsmallopeneconomyformulationofthefullyfledgedtwo-countrymodelinAdrianetal.(2021),whichinturndrawsonthemodelinAdrianetal.(2020).Theframeworkisestimatedusingasetofstandardmacroeconomictimeseriesfor12emergingmarketcountriesand5smallopenadvancedeconomiesthatallpursueindependentmonetarypolicy(somevariantofinflationtargeting).Itdrawsheavilyonthetwo-countrymodel,butmakesanumberofsimplifyingassumptionsandintroducesanumberofdata-drivenadd-onsmeanttoenhanceitsempiricalproperties.Thefirstoftheseisthesmallopeneconomyassumption—wepositthatthesizeofthedomestic(home)economy(3)isarbitrarilysmallrelativetotheforeignthattheforeigneconomyisessentiallyexogenousSecondweattempttocapturetradeinintermediategoodsbyassumingthatexportingfirmscombinedomesticallyproducedgoodswithimportedgoodsbeforesellingthemabroad.Thiswaythemodelcanreconcileveryvolatileexportsandimportswitharelativelystabletradebalance(asashareofGDP).Third,andinanotherimportanttwistonthetwo-countrymodelabove,weallowforhouseholddiscountinginthespiritofGabaix(2020)andKolasaetal.(2022),whichhelpsmitigatetheforwardguidancepuzzle(seeDelNegroetal.,2008).Fourth,sinceweconsideralog-)linearizedformulationofthemodel,wedonotallowfortheoccassionallybindingexternaltipliertonthebanksborrowingconstraintishencesettoniltobeginwith.BeforeturningtoBayesianestimation,wenextprovidemoredetailsontheempiricalmodelandhighlightitsrelationshiptothemicrofoundedDSGEmodelofAdrianetal.(2021).II.1.AggregateDemandThehomeeconomyresourceconstraintcan(underconditionsdiscussedinAppendixA.1)beexpressedasashare-weightedaverageofhomeconsumptionct,governmentspendinggt,and“netexports”(thedifferencebetweenexportsmandimportsmt)weightedbythe(steady-state)tradesharemyyt=cyct+gygt+my(m−mt).(1)ofconsumption入c,ttofuturemarginalutilityofconsumptionandshort-termrealinterestratesfacedbyconsumersrb,t,入c,t=6cEt入c,t+1+rb,t.IMFWORKINGPAPERSAnEstimatedDSGEModelforIntegratedAnalysisINTERNATIONALMONETARYFUND9TtTt=Et∑0{6(it+j−几c,t+j+1)+6(ib,t+j−it+j)}=T+Ψt.wherea者=a(1−xc)andUc,tisanexogenousconsumptiondemandshockwhichisassumedtofollowanAR(1)process:Inequation(2),0<6c≤1isthediscountingparameterinthespiritofthebehavioralNewKeynesianmodelofGabaix(2020)anditsopeneconomyextension(Kolasaetal.,2022).1Themarginalutilityofconsumptionvariesinverselywithcurrentconsumption,butriseswithpastconsumptionwiththelatterreflectinghabitpersistenceinconsumption,入c,t=−1(ct−xcct−1−Uc,t),Uc,t=pUUc,t−1+ec,t.Takentogether,theseequationsimplythatconsumptiondemanddependsonalong-termrealinterestrateTt,butwithanimportantcaveatthatthisborrowingratedependsonadiscountedsumoffutureshort-termrates:Theinclusionofdiscounting(i.e.,allowingfor6c<1)impliesthatfutureshort-termrealinterestrateshavemoremutedeffectsoncurrentconsumptiondemand.2byassumingthattheborrowingratefacinghomeconsumersincludesatime-varying“privateHenceTistheeffectivelongtermrealinterestrateongovernmentbonds,andtheinterestratei.e.,Ψt=Et∑06(ib,t+j−it+j)=Et∑06wt+j=wtwherethelastequalityfollowsfromthefactthatweassumethattheshort-termborrowingspreadfollowsanAR(1)process:wt=pwwt−1+ew,t.(7)Fisher(2015)showsthatthisSmetsandWouters(2007)domesticrisk-premiumshockcanbeinterpretedasastructuralshocktothedemandforsafeandliquidassets.Inthetheoreticaltwo-countrymodelbyAdrianetal021),aspreadbetweeninterestratesfacedbyhouseholds(ib,t)andthecentralbankpolicyrate(it)onlyariseswhenthehomeeconomyhitstheborrowinglimit.specificationineqallowsthisspreadtobepositiveevenwhenthehomeeconomyisnotIngeneralassumingbehavioralexpectationsasinGabaix(2020)mayintroduceadditionaltermstotheintertemporaloptimalityconditions.Forexample,Kolasaetal.(2022)showthateq.(2)shouldalsocontainnetforeignassets.Topreservetractabilityofthemodel,wedisregardtheseadditionalfeatureswhenevertheirquantitativeimplicationsaresmall.2Accordingly,forwardguidanceaboutfuturemonetarypolicyactionswouldhavemuchsmallereffectsinthissetupthaninthestandardworkhorseNewKeynesianmodel.IMFWORKINGPAPERSAnEstimatedDSGEModelforIntegratedAnalysisINTERNATIONALMONETARYFUND10bankingsector,forexample(e.g.,GertlerandKaradi,2011).Wenowturntodiscussthecontributionofnetexportstoaggregatedemandytineq.(1).FollowingChristianoetal.(2011),andasnotedearlier,weallowexportingfirmstocombinedomesticallyproducedgoodsandimportedgoodsintheproductionofexportgoods.Thus,exportsinvolveacontinuumofexporterswithsomedegreeofmonopolypowerwhocombineahomogeneousdomesticallyproducedgoodandahomogeneousgoodfromimports.Toafirst-orderapproximation,demandfordomesticallyproduced(m,t)andimported(m,t)goodsusedtoproduceexportsisthengivenbym,t=y−7xytx,∗+业x7xy,d,m,t=y−7xytx,∗−7x(1−业x)y,d+m∗,t,where业xistheshareofimportedgoodsdirectedtowardstheexportsectorinthesteadystate,ytx,∗istherelativepriceofexportedgoods(producedbyhomeexporters)tothatoftheirforeigncompetitors,andy,distherelativepricebetweenimportedanddomesticgoods,i.e.y,d=pm,t−pt.Intheexportdemandforimportedgoods,weallowforastationaryexogenousshockm∗,t=d?m∗,t/1,where?m∗,tfollowsanAR(1)process(asdeviationfromitsdeterministicmeanofunity):?m∗,t−1=pm∗(?m∗,t−1−1)+em∗,t,0≤pm∗<1,em∗,t~i.i.d.N(0,G∗).Thisshockwilltendtoshiftbothexportsandimportsinparallel,withoutaffectingthetradebalance.Thedemandequationsaboveimplythattotalexportdemandm=(1−业x)m,t+业xm,tcanbebeexpressedas:yxytxxmtHence,totalexportdemandmriseswithforeignoutputyandfallswiththerelativepriceofgoodsexportedtotheforeigneconomy,i.e.,ytx,∗=px,t−p.So,allowingforimportedgoodstobeusedintheexportsectordoesnotaffectthefinalexportdemandequation,butrelativepriceimportedanddomesticallyproducedgoodswouldchangetherelativeshareofthosetwotypesofgoodsusedinproducingexports.Finally,noticethatinthespecialcasewhenforeigncurrencypricesofhomeproductsmoveinverselyone-to-onewiththenominalexchangeratewehaveytxequaltothenegativeoftheproductrealexchangerateqp,t,whichisgivenbyqp,t=st+p−pt.(11)Similarly,totalimportsequalmt=(1−业x)mc,t+业xm,twhereimportdemandfordomesticconsumptionpurposesexpandsasdomesticconsumptionrisesandfallsinresponsetoanreaseintheirrelativepriceIMFWORKINGPAPERSAnEstimatedDSGEModelforIntegratedAnalysisINTERNATIONALMONETARYFUND11mc,t=ct−7cy,c+m,t,reycpmtpctisthepriceofabundleofimportedgoodsrelativetothatofaconsumptionbasketcomprisingbothdomestically-producedandimportedgoodsandm,t=d?m,t/1.Thecationwithprivateconsumptionratherthangovernmentspendingmeansthatwemaintaintheassumptionthatgovernmentspendinghasanegligibleimportcontent.Importantly,domesticimportdemandisalsosubjecttoanexogenoustransientpreferenceshifter,?m,twhichfollowsanAR(1)process(asadeviationfromitsdeterministicmeanofunity):?m,t−1=pm(?m,t−1−1)+cm,t,0≤pm<1,cm,t~i.i.d.N(0,G).fromexchangeratestoimportpricesreducestotheconsumption-basedrealexchangerateqc,t=st+p−pc,t.(13)II.2.AggregateSupplyTurningtothesupplyside,theprice-settingequationfordomesticallyproducedgoodstakestheformofamodifiedNewKeynesianPhillipsCurve:几t−Ld几t−1=F6cEt(几t+1−Ld几t)+Kpmct+c几,t.(14)ThisspecificationisbasedonCalvo-stylepricesetting,withthesensitivityofdomesticproducerpriceinflationttomarginalcostmctdeterminedbytheslopecoefficientKp=(1−新pwhichvariesinverselywiththemeandurationofpricecontracts新p.ThePhillipsCurvespecificationin4)allowsforthepossibilityofsomestructuralpersistencethatisdeterminedbytheindexationparameter0≤Ld≤1.ThispersistencemaybeinterpretedasreflectingdynamicingfirmsindextheirnewpricetopastinflationandtheinflationtargetaccordingtoP=(1+几)1−Lp(1+几t−1)LpPt−1,whichimpliesthatthesteady-stateembedsnopricedistortions.Butitisalsoempiricallyconsistentwiththeviewthatinflationexpectationsfeatureanadaptivecomponent,asinClaridaetal.(1999).Eitherway,whenLp>0i.i.d.cost-pushshockslikec几,tmayexertpersistent“secondround”effectsoninflation.Marginalcostmctriseswithanincreaseintheproducerrealwage3t,andfallswithadeclineinthemarginalproductoflabormpltmct=3t−mplt,(16)IMFWORKINGPAPERSAnEstimatedDSGEModelforIntegratedAnalysisINTERNATIONALMONETARYFUND

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