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FinanceandEconomicsDiscussionSeries
FederalReserveBoard,Washington,D.C.
ISSN1936-2854(Print)
ISSN2767-3898(Online)
TheSlopeofthePhillipsCurve
FrancescoFurlanetto,AntoineLepetit
2024-043
Pleasecitethispaperas:
Furlanetto,Francesco,andAntoineLepetit(2024).“TheSlopeofthePhillipsCurve,”FinanceandEconomicsDiscussionSeries2024-043.Washington:BoardofGovernorsoftheFederalReserveSystem,
/10.17016/FEDS.2024.043
.
NOTE:StafworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.
1
TheSlopeofthePhillipsCurve*
FrancescoFurlanetto*NorgesBank
AntoineLepetitt
FederalReserveBoard
May24,2024
Abstract
WereviewrecentdevelopmentsintheestimationandidentificationofthePhillipscurveanditsslope.Wehavethreemainobjectives.First,wedescribetheeconometricchallengesfacedbytraditionalapproachesofestimatingthePhillipscurve,explainhownewapproachesaddressthosechallenges,andassesswhichlimitationsstillremain.Second,wereviewthefindingsofthosenewapproachesandexaminetheevidenceregardingapotentialflatteningofthePhillipscurveinthepre-pandemicperiod.Third,weprovideanaccountofinflationdynamicsinthepost-pandemicperiodwithaparticularemphasisontheroleofnonlinearities.
JELClassification:C51,E24,E31,E52
1.Introduction
ThePhillipscurvehaslongservedastheworkhorsemodelofinflationandisusedbyeconomiststoanalyzeandforecasttheevolutionofinflation.Initsmodernform,ofwhichwegiveanexampleinequation(
1
),itpositsthatinflationπtdependsonacombinationoffutureexpectedinflationEtπt+1andpastinflationπt−1,ameasureofresourceutilization(heretheoutputgapyt−y),andavarietyofsupplyshocksutincludingthoseaffectingthepricesoffood,energyandothercommodities:
πt=γπt−1+(1−γ)Etπt+1+κ(yt−y)+ut.(1)
Thisparticularspecification,ahybridbetweenatraditionalbackward-lookingPhillipscurveandaforward-lookingNewKeynesianPhillipscurve,isthestartingpointofmanyempiricalexplorations,andwethereforeorganizeourdiscussionoftheliteraturearoundit.
Oneparameterinequation(
1
)istheobjectofconsiderableattention:thecoefficientattachedto
themeasureofresourceslack,κ,thatiscommonlyknownastheslopeofthePhillipscurve.There
*TheviewsexpressedinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsofNorgesBankandoftheBoardofGovernorsoftheFederalReserveSystem.WethankGiovanniRiccoandseminarparticipantsattheFederalReserveBoardforusefulcomments.Thispaperissettobepublished
asrBineaib
se-k
iariandRiccardoTrezzi.
tBoardofGovernorsoftheFederalReserveSystem.Email:
antoine.lepetit@.
2
aretwomainreasonsforthisinterestinκ.First,κisakeydeterminantofthetrade-offbetween
inflationandrealactivityfacedbythemonetaryauthority.Forexample,alargeκimpliesthatinflationcanbereducedatlittlecostintermsofeconomicactivity.Inversely,asmallκentailsthatlargedeclinesinoutputarenecessarytoobtainasignificantreductionininflation.Second,Phillipscurvessuchasequation(
1
)areoneofthemaintoolsusedinpolicyinstitutionstogenerateforecastsofinflation.Inthatregard,givenanassessmentofthevalueoftheoutputgapyt−yanditslikelyevolution,knowingκhelpsforecastthefuturetrajectoryofinflation.
WhiletherearemanyimportantandinterestingaspectsofPhillipscurvesspecificationandestimationthatdeservediscussion,inthissurveywenarrowlyfocusourattentiononestimatesoftheslopeparameterκ
.1
Wehavethreemainobjectives.First,weprovideanupdateofnewde-velopmentsinestimationandidentificationmethodssincetheauthoritativesurveyof
Mavroeidis,
Plagborg-MollerandStock
(2014)
.Inparticular,webrieflydescribetheeconometricchallengesfacedbytraditionalapproachesofestimatingthePhillipscurvethataredescribedintheaforemen-tionedpaper,explainhownewapproachesproposetoaddressthosechallenges,andexaminewhichlimitationsstillremain.Second,wereviewtheevidenceregardingapotentialflattening—adecreaseinκ—ofthePhillipscurveinthepre-pandemicperiod.Third,weprovideanaccountofinflationdynamicsinthepost-pandemicperiodandlookintoclaimsthatthePhillipscurvehassteepenedinrecentyears.
AsidefromanarrowfocusontheslopeofthePhillipscurve,wealsohadtomakeseveralotherchoicestokeepthissurveyrelativelyshort.First,weonlyconsidercertainapproachestoestimatingthePhillipscurve.Notably,wedonotreviewtheevidencecomingfromfullinformationanalysisofgeneralequilibriummodelswherethePhillipscurveisonlyoneofmultiplestructuralequationswithinasimultaneoussystem.Second,wemainlyfocusonthepricePhillipscurve,althoughtheeconometricchallengesandassociatedsolutionsthatwedescribealsoapplytotheestimationofthewagePhillipscurve.Third,althoughwementionsomeresultsforothercountries,theevidencethatwepresentismainlycenteredontheUnitedStates(forarecentreviewofEuroAreaevidence,see
Eseretal.,
2020
).
Thechapterisstructuredasfollows.Section
2
delvesintotheinterpretationoftheparame-terκ,whatittellsusaboutmonetarypolicytrade-offs,andhowknowingitsvaluecanbeusefulfromaforecastingstandpoint.Section
3
describestheeconometricchallengesfacedbytraditionalapproachesofestimatingthePhillipscurveandexamineshownewapproachesaddressthosechal-lenges.Section
4
reviewstheevidenceuncoveredbythesenewapproaches.Section
5
coverstherecentpost-pandemicperiodandexamineswhetherithasrevealedtheexistenceofsubstantialPhillipscurvenonlinearities.Section
6
concludes.
1Forexample,
Coibion,GorodnichenkoandKamdar
(2018)discusshowincorporatingsurveydataoninflation
expectationscanaddressanumberofshortcomingsofPhillipscurvesunderfull-informationrationalexpectations.
3
2.Afewtheoreticalconsiderations
Beforewebeginoursurveyofrecentdevelopments,webrieflydiscussseveralpointsregardingtheinterpretationofthePhillipscurveslopeκanditsusefulnessforforecastingandassessingmonetarypolicytrade-offs.
TheoverwhelmingmajorityofempiricalexplorationsofthePhillipscurveisbasedonarela-tionshipbetweeninflationandameasureofrealeconomicactivitysuchastheoutputgaportheunemploymentgap.Suchaspecificationalsoformsthebasisofmostpolicydiscussions.However,instructuralmodels,microfoundedversionsofthePhillipscurverelateinflationtoaveragerealmarginalcostmctasfollows:
πt=γπt−1+(1−γ)Etπt+1+ψmct+ut.(2)
Inthethree-equationNewKeynesianmodel(
Gal´ı
2015
),averagerealmarginalcostispro-portionaltotheoutputgapandthePhillipscurvecanthereforebeexpressedasinequation(
1
).However,onlyminordeviationsfromthisbaselinemodel,suchastheintroductionofnominalwagerigidityorcapitalaccumulation,aresufficienttobreaksuchproportionality.Thus,inequation(
1
),theoutputgapshouldbeseenasanimperfectproxyforrealmarginalcost,andweshouldkeepinmindthatκcombinesinformationonthedegreeofpass-throughfromcoststoprices(ψ)togetherwiththeelasticityofrealmarginalcostwithrespecttotheoutputgap.Whileψisastructuralpa-rameterthatcaptures,amongotherthings,thedegreeofpricestickinessandtheextentofstrategiccomplementaritiesinpricesetting,theelasticityofrealmarginalcostwithrespecttotheoutputgapisareduced-formobjectthatcanchangedependingontheshockshittingtheeconomy.
2
Thiselas-ticityalsodependsontheconceptoftheoutputgapunderconsideration.Itislikelythatmarginalcostismorecloselyrelatedtothedeviationofoutputfromitsflexible-pricelevel,whichfluctuatessubstantiallyinresponsetosupplyshocks,thanitistothedeviationofoutputfrommeasuresofpotentialoutputcomputedby,forexample,theCongressionalBudgetOfficeorcentralbanksandinternationalorganizations,whicharegenerallyestimatedasrathersmoothtrendmeasuresofGDP.
AnotherpointworthnothingisthattheslopeofthePhillipscurveκprovidesonlyapartialcharacterizationofthetrade-offsfacedbythemonetaryauthority.Infact,itmeasurestheimpactresponseofinflationtoachangeinaggregatedemandholdinginflationexpectationsconstant.
BarnichonandMesters
(2021)proposeametric,thePhillipsmultiplier,whichgivesamorecomplete
characterizationofmonetarypolicytrade-offsandisdefinedasfollows:
Ateachhorizonh,thePhillipsmultiplierPhisequaltothecumulativeresponseofinflation
toamonetarypolicyshockdividedbythecumulativeresponseoftheoutputgaptothesame
2Manyfactorsasidefrompricestickinessandstrategiccomplementaritiescanaffectψ.Forexample,whensteady-stateinflationispositive,ψbecomesafunctionoftrendinflation:see
AscariandSbordone
(2014)
.Forempiricalevidenceonstructuraldriversoftrendinflation,see
AscariandFosso
(2024)
.
4
shock.Itsummarizeswhatacentralbankcaresabout:byhowmuchinflationdeclineswhenachangeinpolicylowerstheoutputgapbyagivenamount.Inthecontextofthethree-equationNewKeynesianmodel,κisequaltothePhillipsmultiplieronlywhenshocksareindependentlyandidenticallydistributed.Whenshocksarepersistent,thePhillipsmultiplierdependsalsoonthepersistenceoftheshocks.AwayfromthesimpleNewKeynesianmodel,thePhillipsmultiplierdependsonotherfeaturesofthePhillipscurvesuchastheimportanceoflaggedinflationbutalsoonfeaturesembeddedinotherequationsofthemodelsuchasinertiainaggregatedemand.
Finally,wenotedintheintroductionthatinformationonthevalueofκisoftenusedaspartofestimatedPhillipscurverelationshipstoproduceforecastsofinflationinpolicyinstitutions.Inpractice,however,Phillipscurve-basedforecastshavebeenfoundinferiortotheonesproducedbysimpleunivariatemodelsofinflation,asshownby
AtkesonandOhanian
(2001)and
Dotsey,
FujitaandStark
(2018)
.WhilethisfindingseemstosuggestthatPhillipscurvesshouldnotfeatureprominentlyinthetoolboxofforecasters,thereareseveralreasonstobecautiousindrawingsuchconclusions.AfirstreasonthatweelaborateonbelowisthatthePhillipscurveshouldnotbeexpectedtoperformwellunconditionally:indeed,thePhillipscurvetracesouttheresponseofinflationtoshiftsindemand.Ifthedataareinsteaddrivenbysupplyshocks,weshouldnotexpecttoseethepositiverelationshipbetweeninflationandrealactivitythatischaracteristicofthePhillipscurve.AsecondreasonisthattheaferomentionedstudiesdonotattempttoaddressthemanyendogeneityissuesthatariseintheestimationofPhillipscurves.Wediscussthoseendogeneityissuesnext.
3.Econometricchallengesandnewapproaches3.1.Econometricchallenges
ThissectiondiscussesthedifferentsourcesofendogeneitythatarepresentinPhillipscurveequa-tionsandthemethodsusedtoaddressendogeneityissuesthatwerepredominantintheliteratureuntilthesurveyof
Mavroeidis,Plagborg-MollerandStock
(2014)
.Theexpositionheredrawsfrom
BarnichonandMesters
(2020)
.
NotethatthebaselinePhillipscurve,equation(
1
),includestwounobservedvariables:expec-tationsoffutureinflationEtπt+1andpotentialoutputy.Afirststepisthereforetoreformulateequation(
1
)intermsofobservables,whereisanobservableproxyforpotentialoutput:
、尺
πt=γπt−1+(1−γ)πt+1+κ(yt−)+t+(1−γ)(Etπt+1−πt+1)+κ(−y–).(4)
et
Thereareseveralpotentialsourcesofendogeneityinequation(
4
).First,thecost-pushshockutmayaffectπtandytsimultaneously:E(ytut)0.Forthistohappen,itsufficesthattheincreaseininflationinducedbythecost-pushshockleadstoashiftinrealinterestrates(forexample,becauseoftheresponseofmonetarypolicytoinflation)which,inturn,affectsrealactivity(forexample,becauseanIS-typerelationshiprelatesrealinterestratestodemand).Second,ifanunexpectedshockmaterializesbetweentimetandtimet+1,expectedinflationEtπt+1willdifferfromrealized
5
inflationπt+1,inwhichcasewewillhavethatE(πt+1et)0.Third,theremightbemeasurement
errorinpotentialoutput,inwhichcasewewillhavethatE(et)0.
Tomakeitworse,endogeneityissuesarisingfromthecorrelationbetweencost-pushshocksandrealactivityareexacerbatedbygoodmonetarypolicy.Underoptimalpolicy,acentralbankwillseektofullystabilizeinflationandtheoutputgapinresponsetoshocksthatdonotcreateatrade-offbetweenthosetwoobjectives—thisincludesdemandshocksaswellascertainsupplyshocks.Ifthecentralbankissuccessfulindoingso,theremainingvariationininflationandtheoutputgapinthedatawillbedominatedbycost-pushshocksandwillbecharacterizedbythenegativecorrelationthatistypicaloftheoptimalpolicyresponsetothoseshocks(foranexpositionofthisargument,see
McLeayandTenreyro
(2019)andarelatedcommentby
Rognlie
(2019))
.Thus,anegativecorrelationintheobservedequilibriumvaluesofinflationandtheoutputgapisnotthesignofaflatteningordisappearingPhillipscurve;rather,itistheexpectedoutcomeiftheunderlyingdatageneratingprocessfeaturesapositively-slopedPhillipscurvesuchasequation(
1
),andifmonetarypolicyisconductedwiththeaimsofstabilizinginflationandthewelfare-relevantoutputgap.
Untilrecently,thestandardapproachforhandlingendogeneityissuesintheestimationofthePhillipscurvewastouselagsofmacroeconomicvariablesasinstruments.Forthisapproachtobesuccessful,theinstrumentsztusedbytheeconometricianmustbebothexogenouswithrespecttothedifferentelementsofetandstronglycorrelatedwithπt+1andyt.Inparticular,theexogeneityconditionissatisfiedifthefollowingconditionsaremet.First,cost-pushshocksutmustnotbecorrelatedwithzt,whichhappensifuthasnoserialcorrelationoriftheinstrumentsaresufficientlylagged.Second,ztmustnotbecorrelatedwiththeinflationforecasterrorEtπt+1−πt+1,whichhappensundertheassumptionofrationalexpectationssincetheinflationforecasterrorarisesonlybecauseoftimet+1shocksthatareorthogonaltozt.Third,ztmustnotbecorrelatedwith
themeasurementerrorinpotential−y,whichhappensifthemeasurementerrorhasnoserial
correlationor,again,iftheinstrumentsaresufficientlylagged.
Satisfyingthoseexogeneityconditionsisalreadyatallorder.However,astheliteraturehasshown,meetingtherelevancecondition—thatis,findinginstrumentsthatarestronglycorrelatedwithπt+1andyt—isevenmorechallenging
.3
Putdifferently,evenifonefindsinstrumentsthatsatisfytheexogeneityconditions,thoseinstrumentsarelikelytobeweak
.4
Thisweakinstrumentproblemleadstolargesamplinguncertaintyand,as
Mavroeidis,Plagborg-MollerandStock
(2014)
show,itcanexplainthelargedispersionofresultsintheliteratureasseeminglyinnocuousandapriorireasonablespecificationchangescanleadtobigdifferencesinpointestimates.Theseauthorsconclude:“...theliteraturehasreachedalimitonhowmuchcanbelearnedabouttheNewKeynesianPhillipscurvefromaggregatemacroeconomictimeseries.Newidentificationapproachesandnewdatasetsareneededtoreachanempiricalconsensus.
”5
Inrecentyears,researchershaverespondedtothischallengebyproposingnewapproaches,whichwereviewinthenextthreesubsections.
3Tobeprecise,itisfindingstronginstrumentsforfutureinflation,notoutput,thatisparticularlychallenging.
4Usinglongerlagsofmacroeconomicvariables,whichwesuggestedaboveasawayofmeetingtheexogeneityrequirement,willonlyexacerbatetheweakinstrumentissue.
5Suchapessimisticconclusionischallengedby
Inoue,RossiandWang
(2022)whoproposeanewflexibletime
-varyinginstrumentalvariableapproachthatpassesseveralweakinstrumentstests.
6
3.2.Newapproach:conditioningondemandshocks
Afirstapproach,putforwardby
BarnichonandMesters
(2020),consistsinusingsequences
ofindependentlyidentifiedstructuraldemandshocksasinstruments.Toseehowthisapproach
works,denoteby{ε−h}=0asequenceofcurrentandpaststructuraldemandshocks.Asbefore,
theinstrumentsmustverifyboththeexogeneityandtherelevanceconditions.Startingwiththe
exogeneitycondition,itissatisfiedifthesequence{ε−h}=0isorthogonaltoalltheelementsofet
inequation(
4
).Toseehowlikelythisistohappen,weevaluatetheexogeneityconditionsforeachofthecomponentsofetonebyone.First,aslongasthedemandshocksareproperlyidentified,theyshouldbeorthogonaltothecost-pushshockutanditslags.Second,underrationalexpectations,theforecasterrorforfutureinflationdependsonlyontimet+1shocksandisthereforeorthogonaltodemandshocksoccurringattimetorbefore.Third,themeasurementerrorinpotentialoutputmustbeindependentofdemanddisturbances.Ifpotentialyisindependentofdemandfactors,ascommonlyassumedinmacroeconomictheory,thisimpliesthateconomistsmustbeableto
parsedemandfromsupplyfactorswhenconstructingmeasuresofpotentialoutput.Asshownby
Coibion,GorodnichenkoandUlate
(2018),commonly-usedproxiesforpotentialoutputdonotverify
thisproperty.Instead,ifyisnotindependentofdemandfactors,asintheoriesofhysteresis,this
impliesthattheproxyforpotentialoutputmustreactinthesamewaythanpotentialoutputto
demanddisturbances.Turningtotherelevancecondition,
BarnichonandMesters
(
2020
)establishthatitholdsifandonlyiftheimpulseresponsesoflaggedinflation,futureinflation,andtheoutputgaptotheidentifiedstructuralshocksarenotlinearfunctionsofoneanother,aconditionthatislikelytobemetinpractice.
BarnichonandMesters
(2020)usetheexternallyidentifiedmonetarypolicyshocksof
Romer
andRomer
(2004)and
GertlerandKaradi
(2015)asinstruments
.
Inoue,RossiandWang
(2022)
extendtheirapproachtoasettingwithtime-varyingparameters.Afirstlimitationofthisapproachisthat,becausetheroleofcentralbanksistomakemonetarypolicyasendogenoustothestateoftheeconomyaspossible,trulyexogenousmonetarypolicyshocksaresmallandconstituteweakin-struments,thusleadingtolargeweak-IVrobustconfidenceintervalsfortheparametersofequation
(1)
.Asecondlimitationrelatestotheuncertaintyassociatedwiththeidentificationofthestruc-turalmonetarypolicyshocks.Whilethissurveyisnottheplacetodiscusstheliteratureontheidentificationofmonetarypolicyshocks,itisworthnotingthatboththespeedandthemagnitudeoftheeffectsoftheidentifiedshocksoninflationandrealactivityvaryconsiderablydependingonthemethodologyused
.6
ArelatedapproachistoidentifyshocksinastructuralVectorAutoRegression(VAR)modelandestimatePhillipscurvesconditionaloncertainshocks.
Gal´ıandGambetti
(
2020
)identifyshocksthroughacombinationofzeroandsignrestrictionsandestimatewagePhillipscurvesusingtimes
seriesofwageinflation,priceinflationandunemploymentthatarepurgedfromthecomponentasso-
6Severalrecentstudies
(Jaroci´nskiandKaradi,
2020;
Miranda-AgrippinoandRicco,
2021;
BauerandSwanson,
2023
)arguethatthestandardhigh-frequencyapproachusedby
GertlerandKaradi
(2015)mixestruemonetarypolicy
surpriseswithinformationaboutthestateoftheeconomyoraboutthecentralbank’sreactionfunctiondisclosedthroughthepolicyannouncement.Afterpurgingmeasuresofmonetarypolicyshocksfromthoseinformationeffects,thesepapersfindlargerandfastereffectsofmonetarypolicyoninflationand,toalesserextent,output.
7
ciatedwithwage-markupshocks.
DelNegroetal.
(2020)estimatepricePhillipscurvesconditional
oninnovationstotheexcessbondpremiumof
GilchristandZakrajˇsek
(2012),whichtheyinterpret
asaproxyfordemandshocks.
Bergholt,FurlanettoandVaccaro-Grange
(2024)developabivariate
VARininflationandtheoutputgap,identifydemandandsupplyshocksusingsignrestrictions,andcomputeinflation-outputgapcorrelationsconditionalondemandshocks.TheseVARstudieshaveonepotentialadvantageovertheliteratureusingmonetarypolicyshocksasinstruments:theshocksthattheyidentifytendtoexplainalargershareofthevarianceininflationandrealactivityinthedatathanmonetarypolicyshocks.Nonetheless,weshouldpointoutthat,inthecaseofsignrestrictions,themodelsareonlyset-identifiedandtheuncertaintyaroundtheestimatescanthereforebeconsiderable.Moreover,aswasthecasewithmonetarypolicyshocks,thoseVARap-proachesarevalidonlyinsofarastheidentifyingassumptionsarecorrectandsufficienttoidentifytheshockofinterest
.7
Lastly,weshouldalsomentiontheworkof
Angeletos,CollardandDellas
(2020),whoprovide
evidenceonthedynamicrelationshipbetweeninflationandrealactivityconditionalona‘mainbusiness-cycleshock’,identifiedasashockthatmaximizesthecontributiontothevolatilityofeitherGDP,unemployment,hoursworked,orinvestmentatbusiness-cyclefrequencies.Theseauthorsfindthatthisshockaccountsforasmallshareoffluctuationsininflation,whichissuggestiveofaflatPhillipscurve.However,itispossiblethattheshockcapturesbothsupplyanddemandforces,inwhichcaseitwouldnotnecessarilybeinformativeabouttheslopeofthePhillipscurve.Moreover,
Bianchi,Nicol`oandSong
(2023)arguethatfixed-coefficientsVARs,suchastheoneused
by
Angeletos,CollardandDellas
(2020),maybeunabletodisentanglebusiness-cyclevariationsfrom
low-frequencymovementsoverperiodsoftimefeaturingstructuralbreaks.WhenusinginsteadaTrend-CycleVAR,whichseparatestrendsfromcyclespriortotheidentificationofshocks,theyfindthatthemainshockdrivingcyclicalfluctuationsinunemploymentoroutputisalsoanimportantdriverofcyclicalinflation.
3.3.Newapproach:regionaldata
AsecondapproachdevelopedinrecentyearsistoestimatethePhillipscurveusingregionaldata.Anon-exhaustivelistofstudiesinthisliteratureincludes
Kiley
(2015),
BabbandDetmeister
(2017),
McLeayandTenreyro
(2019),
Beraja,HurstandOspina
(2019),
Hooper,MishkinandSufi
(2020),
Hazelletal.
(2022),
Fitzgeraldetal.
(2024),and
Smith,TimmermannandWright
(2023)
.Themotivationforusingregionaldataistwo-fold.First,thereispotentiallymorevariabilityintheregionaldatathanintheaggregatedata,whichfacilitatesinference.Second,changesintheaggregateenvironmentcanbecapturedbytime-fixedeffects.Asweshownext,thiseliminatestheendogeneitybiasinducedbytheresponseofmonetarypolicytocost-pushfactors(apointforcefully
emphasizedby
McLeayandTenreyro,
2019;
Fitzgeraldetal.,
2024)andpermitstocontrolfortime
-
7Inthecaseofsignrestrictions,itiswellknownthatlinearcombinationsofotherstructuralshockscanmasqueradeastheshockofinterestandthusleadinferenceastray(
Wolf,
2020)
.Similarly,onemaybeworriedthatfinancialmarketdisruptionscapturedbyshockstotheexcessbondpremiumcouldhavesubstantialsupply-sideimplicationsandthat,asaconsequence,theestimatedPhillipscurvemaynotbeparticularlyinformativeabouttheinflation-outputtrade-offfacedbythemonetaryauthority.
8
variationinaggregateinflationexpectationsandaggregatepotentialoutput.Accordingto
Hazell
etal.
(2022),thisabilitytousetime-fixedeffectstocontrolforaggregateinflationexpectationsisthe
mainadvantageofusingregionaldata.Indeed,theyarguethatthecentralissuewithPhillipscurveestimationsisthatshiftsininflationexpectationscorrelated,butnotnecessarilycausallyrelated,withshiftsintheoutputgapimpartanupwardbiasonestimatesoftheslopeofthePhillipscurve.Wenowexplainingreaterdetailshowtheuseofregionaldatacanhelpsharpenidentification.
Theexpositiondrawsfrom
McLeayandTenreyro
(2019)
.ConsideramonetaryunioncomposedofNregionsindexedbyi.Weassumethat,ineachregion,dynamicsaresimilarandaregovernedbyaEulerequationandaPhillipscurve:
yi,t−y,t=Etyi,t+1−Ety,t+1−(it−Etπi,t+1−ri,t),(5)
πi,t=γπi,t−1+(1−γ)Etπi,t+1+κ(yi,t−y,t)+ui,t,(6)
whereitisthenominalinterestsetbythemonetaryauthoritythatiscommonacrossregions.Thecost-pushshocksui,tanddemandshocksri,tarepotentiallyautocorrelated.Furthermore,aggregatevariablesareaweightedaverageofregion-specificvariablesxt=Σ1αixi,tforxt=πt,yt,wheretheregion-specificweightsαisatisfyΣ1αi=1.Thisimpliesthatwecanaggregateequations
(5)and(
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