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′?

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′?andGambetti

(

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(