供应链约束和通货膨胀 Supply Chain Constraints and Inflation

NBERWORKINGPAPERSERIESCONSTRAINTSANDINFLATIONDiegoACominobertCJohnsonmJJonesWorkingPaper31179http//papers/w31179NATIONALBUREAUOFECONOMICRESEARCHCambridgeMA8April2023WethankBrentNeiman,SebastianGraves,RobertKollmann,andWernerRoegerforhelpfuldiscussions,andseminarparticipantsatBostonUniversity,theFederalReserveBankofDallas,theNBERconferenceon“TheRiseofGlobalSupplyChains”(December2021),theInternationalResearchForumonMonetaryPolicyConference(May2022),theCEPR/EC/EERconferenceon“TheCOVID-shockandtheNewMacroeconomicLandscape”(October2022),andtheBOJ-CEPR7thInternationalMacroeconomicsandFinanceConference(March2023)forcomments.WeespeciallythankDiegoAnzoategui,whoassistedusduringintermediatestagesofthisresearch.ThismaterialisbaseduponworksupportedbytheU.S.DepartmentofHomelandSecurityunderGrantAwardNumber18STCBT00001-03-00.Theviewsandconclusionscontainedinthisdocumentarethoseoftheauthorsandshouldnotbeinterpretedasnecessarilyrepresentingtheofficialpolicies,eitherexpressedorimplied,oftheU.S.DepartmentofHomelandSecurity.TheviewsexpressedarethoseoftheauthorsandnotnecessarilythoseoftheFederalReserveBoardortheFederalReserveSystem.TheviewsexpressedhereinarethoseoftheauthorsanddonotnecessarilyreflecttheviewsoftheNationalBureauofEconomicResearch.NBERworkingpapersarecirculatedfordiscussionandcommentpurposes.Theyhavenotbeenpeer-reviewedorbeensubjecttothereviewbytheNBERBoardofDirectorsthataccompaniesofficialNBERpublications.©2023byDiegoA.Comin,RobertC.Johnson,andCallumJ.Jones.Allrightsreserved.Shortsectionsoftext,nottoexceedtwoparagraphs,maybequotedwithoutexplicitpermissionprovidedthatfullcredit,including©notice,isgiventothesource.SupplyChainConstraintsandInflationDiegoA.Comin,RobertC.Johnson,andCallumJ.JonesNBERWorkingPaperNo.31179April2023JELNoE,E3,E5,F40STRACTWedevelopamultisector,openeconomy,NewKeynesianframeworktoevaluatehowpotentiallybindingcapacityconstraints,andshockstothem,shapeinflation.WeshowthatbindingconstraintsfordomesticandforeignproducersshiftdomesticandimportpricePhillipsCurvesup,similartoreduced-formmarkupshocks.Further,dataonpricesandquantitiestogetheridentifywhetherconstraintsbindduetoincreaseddemandorreductionsincapacity.ApplyingthemodeltointerpretrecentUSdata,wefindthatbindingconstraintsexplainhalfoftheincreaseininflationduring2021-2022.Inparticular,tightcapacityservedtoamplifytheimpactofloosemonetarypolicyin2021,fuelingtheinflationtakeoff.DiegoA.CominCallumJ.JonesDartmouthCollegeFederalReserveBoardEconomicsDepartmentConstitutionAveNW&20thStNW6106RockefellerHall,Room327Washington,DC20551Hanover,NH03755jonescallum@andCEPRandalsoNBERin@obertCJohnsonUniversityofNotreDamepartmentofEconomicskinsNanovicHallNotreDame,IN46556andNBERrjohns24@1tiveicandveinusetchkitkulanddeSoyresSantacreuandYoung2InInternationalMonetaryFund(2021),GitaGopinathwrites:“PandemicoutbreaksincriticallinksofglobalowsJeromePowell2seintothroughmarginalcosts.ItisalsoprimafacieconsistentwiththatfactthatUSprofitmarginsousexampletheal3eTolayoutthestructureofthepaper,westartbycollectingdatafactsinSection1,whichimportsidepricesforimportedindustrialmaterialsinputsroserapidlyin2021,whilepricesheryntsis(2017))thatuseinversionfilterstoconstructthelikelihoodfunctionarenotapplicableinour4ofofbindingconstraintsisanequilibriumoutcomeinourmodel,unlikepriorapplicationsoftheeriodsocksWendthattightcadindeaintisthezeroealizedringromesa5hinneJoussier,MartinandMejean(2021),Gourinchasetal.(2021),Alessandriaetal.(2022),andivepredictivepowerforpiricalframeworkdiGiovannietaloutputframework.12Amitietal.(2023)studyhowthecombinationofdomesticlabormarketontheimpactsoffiscalpolicyoninflation,includingdiGiovannietal.(2023)anddeSoyres,tivetothisliteratureourpaperisthersttoourknowledgetoanalyzeoccasionallyhrist11SeealsoadiscussionoftheimpactofChineseshutdownsonUSsourcingfromChinabyHeise(2020).hnsonWhileceof6centagePointsyearonyear-50510lescentagePointsyearonyear-50510les20172018201920202021202220231CollectingFactstionrosethintheedbygoodspriceinationdown7atyearonyearWhilethepriceofoilandderivativefuels(whichdoubledduringthisperiod)playedalargeroleindrivingthisincrease,thepriceionforimeregionThefinalsetoffactspointtopotentialsupply-sideconstraints.InFigure4a,weplotrealantspriceinflation.tivesectorwasalsoverylowandinationforfoodstrackedtotalimportpriceinationcloselyThusthes8centagePointsyearonyear-2002040riceInflationtotalalMaterialsSuppliesIndustrialMaterialsSupplies(ex.fuels)ConsumerGoodsexautos)centagePointsyearonyear-2002040riceInflationtotalalMaterialsSuppliesIndustrialMaterialsSupplies(ex.fuels)ConsumerGoodsexautos)2017201820192020202120222023PCEGoodsShare.4PCEGoodsShare.7.68.69GoodsServices.7.68.69GoodsServices201720212022202320182017202120222023PCEPCEServicesShareRealQuantityIndex80100120140160GoodsRealQuantityIndex80100120140160Services201720182019202020212022202391.2RealQuantityIndex(2017Q1=1)11.191.2RealQuantityIndex(2017Q1=1)11.19 Goods Services2017201820192020202120221.6RealQuantityIndex(2017Q1.6RealQuantityIndex(2017Q1=1)11.21.48 ConsumerGoods(ex.autos) ConsumerGoods(ex.autos) IndustrialMaterials&Suppliesdofw2Modelmdomesticfirms.Inwritingdownthemodelhere,weallowtheseconstraintstobepotentiallyinputproducingfirms.Lookingforward,wethenrestrictattentiontoparticularconstraintsinms2.1ConsumersU({Ct,Lt}0)=E0tptIt{_X?withCt=│ζt(s)1/8Ct(s)(8_1)/8←8/(8_1)andCt(s)=│y(s)1/ε(s)CHt(s)(ε(s)_1)/ε(s)+(1_y(s))1/ε(s)CFt(s)(ε(s)_1)/ε(s)←ε(s)/(ε(s)_1),datetandtsisatimevaryingparameterthatcontrolstastesforgoodsfromPtCt+Et[St,t+1Bt+1]sBt+WtLt,(2)ticdiscountfactor(definedbelow).Further,sectoralconsumptionexpenditureisPt(s)Ct(s)=PHt(s)CHt(s)+PFt(s)CFt(s),wherePHt(s)andPFt(s)arethepricesofthehomeandforeigncon-Ct(s)=ζt(s)│←_8CtCHt(s)=y(s)│←_ε(s)Ct(s)CFt(s)=(1_y(s))│←_ε(s)Ct(s)1=Et!St,t+1P1(1+it)?whereSt,t+1=p╱、_βisthestochasticdiscountfactor,Pt=╱Esζt(s)Pt(s)1_8、1/(1_8)istheaggregatepriceindex,Pt(s)=╱y(s)(PHt(s))1_ε(s)+(1_y(s))(PFt(s))1_ε(s)、1/(1_ε(s))isthe2.2DomesticProducersdfirms.2.2.1CompositeDomesticGoodcomposite.Theproductionfunctionfortheintermediaryis:Yt(s)=╱)01Yt(s,0)(ε_1)/εd0、ε/(ε_1),demandsYt(s,0)=╱、_εYt(s),wherePHt(s)=|)01Pt(s,0)1_εd0ì1/(1_ε)isthepriceofthe2.2.2DomesticFirmsYt(s,0)=Zt(s,0)A(s)(Lt(s,0))1_a(s)(Mt(s,0))a(s)Mt(s,0)=!E\s╱a(s\,s)/a(s)、1/kMt(s\,s,0)(k_1)/k!k/(k_1) n(s\)input,Zt(0)isproductivity,andA(s)=a(s)_a(s)(1_a(s))_(1_a(s))isanormalizationconstant.ticMHtssandForeignMFtss,0))compositeinputs.Theparametersn(s)20areelas-ermedtheArmingtonschooses|Lt(s,0),Mt(s,0),Mt(s\,s,0),MHt(s,0),MFt(s\,s,0)÷tominimizethecostofproduc-ingYt(s,0),whichisWtLt(s,0)+PMt(s)Mt(s,0),withPMt(s)Mt(s,0)=Es\Pt(s\,s)Mt(s\,s,0)tothisWtLt(s,0)=B(s)MCt(s,0)Yt(0)PMt(s)Mt(s,0)=(1_B(s))MCt(s,0)Yt(s,0)Mt(s\,s,0)=│←_kMt(s,0)MFtssssnsMtssthepriceofMt(s,0),andthefirm’smarginalcostisMCt(s,0)=(Zt(s,0))_1Wt1_B(s)(PMt(s))B(s).{a,x0)}E0{Pt(s,0)Yt(s,0)_MCt(s,0)Yt(s,0)_│_1←2PHt(s)Yt(s)?s.t.Yt(s,0)st(s),ut(s,0)[Yt(s,0)_t(s)]=0.(17)Andwerequireut(s,0)20andtheconstrainttoholdinequilibrium(Yt(s,0)st(s))asusual.Whentheconstraintbinds,thenut(s,0)>0.InEquation16,weseethisisequivalenttoan2.3ForeignProducersrate2.3.1CompositeForeignGoodsforeigncompositeaccordingtotheproductionfunction:Y(s)=╱)01Y(s,ō)(ε_1)/εdō、ε/(ε_1).PuFt(s,ō)isthepriceofvarietyōandPuFt(s)=╱)01PuFt(s,ō)1_εdō、1/(1_ε)isthepriceofthe2.3.2ForeignFirmsEachforeignfirm(insectors,producingforenduseu)isabletosupplyoutputuptoapre-{P)}E0{PuFt(s,ō)Y(s,ō)_EtMC(s)Y(s,ō)_│_1←2PuFt(s)Y(s)?s.t.Y(s,ō)s(s),ut(s,ō)[Y(ō)_]=0.Andut(ō)20andtheconstraintY(ō)sarerequiredtoholdinequilibrium.2.4ClosingtheModelXt(s)=│←_σ(s)Xt*(s),(20)Yt(s)=CHt(s)+s.01MHt(s,s\,0)d0+Xt(s)+.01{│_1←2Yt(s)?d0.(21)Yt(s)=CFt(s)+0s)(ⅡCFt(s)_1)2Yt(s)s\Yt(s)=EMFt(s,s\)+0s)(ⅡMFt(s)_1)2Yt(s).s\Lt=Lt(s)withLt(s)=.01Lt(s,0)d0.(24)It│←_βQt=z,licyperiodsandtheapproximateinationrateisgivenbytEslnPts)_lnPt_1(s)],licy1+it=(1+it_1)βiⅡ¯(1_βi)(Yt/Y0)(1_βi)βyatregaterealgrossoutputandatisamonetarypolicyshockThe2.5EquilibriumwithSymmetricFirmsBss(s\,s)}s,s\.Further,valuesfordomesticvariables{It,{ζt(s),Zt(s)}s,at},foreignvari-ring{Ct,Lt},sector-levelquantities,Ct(s),CHt(s),CFt(s),Lt(s),Yt(s),Mt(s),Xt(s),Yt(s),Yt(s)←s,in-levelpricestsCFtsMFtsPts)/Pt,MCt(s)/Pt,PMt(s)/Pt,PHt(s)/Pt,PCFt(s)/Pt,PMFt(s)/Pt}s,inputprices{{Pt(s\,s)/Pt}s\}s,and(normalized)multipliers,ut(s)/Pt,ut(s)/Pt*,ut(s)/Pt*←sAllocationCt_βAllocationCt(s)=ζt(s)╱、_8CtCHt(s)=y(s)╱、_ε(s)Ct(s)CFt(s)=(1_y(s))╱、_ε(s)Ct(1=│Esζt(s)╱、1_8←1/(1_8=│y(s)╱、1_ε(s)+(1_y(s))╱、1_ε(s)←1/(1_ε(s))Lt(s)=(1_B(s))(s)Yt(s)(s)Mt(s)=B(s)(s)Yt(s)Mt(s\,s)=╱、_kMt(ssnsMtsMFt(s\,s)=(1_ξ(s\,s))╱、_n(s\)Mt(s\,s)Bs╱、B(s)=│Es\╱、╱、1_k←1/(1_k)=!ξ(s\,s)╱、1_n(s\)+(1_ξ(s\,s))╱、1_n(s\)?1/(1_n(s\))0=1_ε│1_←_0(s)(ⅡHt(s)_1)ⅡHt(+Et{x0(s)(ⅡHt+1s()_1)ⅡHt+1()s2?0=1_ε│1_←_0(s)(ⅡCFt(s)_1)ⅡCFt(s)+Et{x│←_β0(s)(ⅡCFt+1s()_1)ⅡCFt+1()s2?0=1_ε│1_←_0(s)(ⅡMFt(s)_1)ⅡMFt(s)+Et{x│←_β0(s)(ⅡMFt+1s()_1)ⅡMFt+1()s2?min{ut(s),t(s)_Ytmin{ut(s),t(s)_Yt(s)}=0min{ut(s),t(s)_Yt(s)}=0Yt(s)=CHt(s)+Es\MHt(s,s\)+Xt(s)+0s)╱_1、2Yt(s)Xt(s)=╱、_σ(s)Xt*(s)Yt(s)=CFt(s)+0s)(ⅡCFt(s)_1)2Yt(Yt(s)=Es\MFt(s,s\)+0s)(ⅡMFt(s)_1)2Yt(s)It╱、_βQt=zEsLt(s)=LtAuxiliaryInflation1+it=(1+it_1)βiⅡ¯(1_βi)(Yt/Y0)(1_βi)βyatwithYtAuxiliaryInflation=│Esζ0(s)╱、1_8←1/(1_8)2.6Discussion2.6.1SolvingtheModelrtsinanleadsromtheunconstrainedraintisbindingaswellsaXt=J(Xt_1,εt;9)+Q(Xt_1,εt;9)Xt_1+G(Xt_1,εt;9)εt,(27)2.6.2DomesticandImportPricePhillipsCurvesordomesticandimportedgoods.Notingthatut(s)/Ptandut(s)/Pt*foru∈{C,M}takeonzerolnPFt(s)_lnPFt_1(s),rmct(s)=ln(MCt(s)/Pt),rmc(s)=lnlnPFt(s)_lnPFt_1(s),rmct(s)=ln(MCt(s)/Pt),rmc(s)=ln(MC(s)/Pt*),rpHt(s)=ln(PHt(s)/Pt),rpuFtslnPuFtsPtandqtlnQtEquationsaresector-leveldomesticandimportttsBindingConstraintsasMarkupShocksAnimportantconceptualpointisthatbindingcon-ducedformsdeedizationggletoexplainthehighlycompetitiveenvironmentpersehasenmarkupisequaltoprofitsperunitofoutputinthesteadystate:Pt(s)_MCt(s)=,wherezt(s)三Pt(s)Yt(s)_MCt(s)Yt(s)istheprofitoftherepresentativeproducerinsectors.23Thus,InFigure5,weplotindexesofUScorporateprofitsperunitofgrossoutputforboththeaintsinuencermconductholdingmarketstructurexedisnotuniquetoourparticularmonopolisticcompetitionmodel.Forexample,inoligopolymodelswithsymmetricfirms,itisdpricingleadstocompetitivepricingequilibriumpricesatmarginalcostwhenrmsaretitivetstdexQ1.522.5dexQ1.522.5ingingAllSectors201720182019202020212022Kerr3ImpulseResponseAnalysispayyof3.1QuantitativeSetupstraintswenowhoneinonaparticulartwosectorstructurewithtwopotentiallybindingcon-sst3.2AnalyzingaDemandShock26Takingtheconstraintsforsector2toinfinity–i.e.,t(2)→g,t(2)→g,andt(2)→g–issufficienttontsthenYt(1)=t(1).Thisimpliesthatt(1)=lnt(1)_lnY0(1),soimportedinputsarequantityconstrained,3.2.1UnconstrainedBenchmarkHtstsnTHt(s)=(1_a(s))│←prEt[t+r_Ht+r(s)]+a(s)│←prEt[Mt+r(s)_Ht+r(s)]realwagetermrealinputpricetermselconsumerpriceinationisgivenbyTtsTHtsTCFtswhereTt(s)=t(s)_t_1(s)isinflationinsectors. ation (f)ImportQuantitysInallwhilethedemandshockraisesoverallinationityieldsamixofresultsthatarein3.2.2BindingConstraints (f)ImportQuantityeadtoabouttwiceasmuchinationos (f)ImportQuantityly3.3ShockstoConstraintsnby:t(1)=入t_1(1)+εt,t(1)=入t_1(1)+ε*twithvar(εt)=σandvar(ε*t)=σ,ation(f)ImportQuantitypation(f)ImportQuantityve3.4SummingUpichleadgoodspriceinationtooutstripins4AccountingforRecentInflationExperience4.1EstimationFrameworkngivenpointintime:Rt={1(Yt(1)=t(1)),1(Yt(1)=t(1))},wheretheindicatorfunctionsAfordetails.cunobservedstateasinStHtXtvtwherevtisaniidvectorofnormallydistributedmea-kelihoodfunctiondsthisproperty,weverifyitholdsnumericallyinthemodelinpractice,andwecandemonstratethatimposingthise31Asanextension,weintendtoexplorevariantsonthesebaselineresultsinwhichconstraintsareallowedto4.2DataandParametersetoriceinationforimportedindustrialmaterialsexle ghminingandelectricalgast(2016):/cqer/research/wu-xia-shadow-federal-funds-rate.Changes ches4.3ModelFitllssng4.4ExplainingtheInflationSurgecks4.4.1MultipliersonConstraintsofhusowbetweenaggregateinationinthemodelanddataislikelyduetodifferingindexnumberconcepts.Specifically,ntheintonegativeterritoryattimesinthesimulationsThisreectstwofactorsFirstthereisapproximationPercentagePoints-6-4-2024PercentagePoints-6-4-2024DataDataMedianSmoothedValue5th-95thPercentiles2017201820192020202120222023PercentagePoints-50510PercentagePoints-50510DataDataMedianSmoothedValue5th-95thPercentiles2017201820192020202120222023PercentagePoints-10-505PercentagePoints-10-505 Data2017 DataPercentagePoints-20-10010PercentagePoints-20-100102030DataMedianSmoothedValue5th-95thPercentiles2017DataMedianSmoothedValue5th-95thPercentilesedosesticConstraintut6LogDeviation6LogDeviationfromSteadyState-.20.2.4 MedianSmoothedValue5th-95thPercentiles2017 MedianSmoothedValue5th-95thPercentilesonstraintut3LogDeviation3LogDeviationfromSteadyState012 MedianSmoothedValue5th-95thPercentiles2017 MedianSmoothedValue5th-95thPercentilesoninFigurewhichforeshadowsthe4.4.2RelaxingConstraintssWeorlowerboundonthemultipliers,whichisrequiredinthefullnon-linearsolutiontothemodel.Instead,multipliersareimplicitlycalculatedviaresidualsinthePhillipsCurve–theirvalueispinneddownbyexcessinflationoverthatconstraintsarepotentiallybindinginlinewithposteriordurationestimatesUsingtheseeorutvicesinFigure13b.WhileservicespriceinflationinitiallyacceleratesduetotheunderlyingnkagesPercentagePoints-50510DataMedianCounterfacualValue5th-95thPercentilesPercentagePoints-50510DataMedianCounterfacualValue5th-95thPercentiles2017201820192020202120222023nPercentagePoints-4-2PercentagePoints-4-2024 Data MedianCounterfacualValue5th-95thPercentiles Data MedianCounterfacualValue5th-95thPercentilesPercentagePoints-4-2024PercentagePoints-4-2024DataDataMedianCounterfacualValue5th-95thPercentiles20172018201920202021