TheAbsenceofAcceleratingDeflationinJapan
EmmanuelDeVeirmanReserveBankofNewZealand
January14,2007
∗
Abstract
Itisstandardtomodeltheoutput-inflationtrade-offasalinearrelationshipwithatime-invariantslope.Weassessempiricalevidenceforthreetypesofnonlinearityintheshort-runPhillipscurve.Atanempiricallevel,weaimtodiscoverwhylargenegativeoutputgapsinJapanduringtheperiod1998-2002didnotleadtoacceleratingdeflation,butinsteadcoincidedwithstable,beitmoderatelynegativeinflation.WedocumentthatthisepisodeismostconvincinglyinterpretedasreflectingagradualflatteningofthePhillipscurve.Thebroaderrelevanceofouranalysisliesinitsattempttoshedlightonthedeterminantsofsuchtime-variationinthePhillipscurveslope.Ourresultssuggestthat,inanyeconomywheretrendinflationissubstantiallylower(orsubstantiallyhigher)todaythaninpastdecades,time-variationintheslopeoftheshort-runPhillipscurvehasbecometooimportanttoignore.JELcodes:Keywords:
∗
C22,C32,E31,E32
nonlinearPhillipscurve,time-varyingparametermodels.
ThispaperisbasedonthefirstchapterofmydissertationattheJohnsHopkinsUniversity.Iamgratefultomyadvisor,LaurenceBall,andtoAlanAhearne,CarlChrist,RobertDavies,HaliEdi-son,JonFaust,YasuoHirose,MichaelKiley,TakeshiKudo,KennethKuttner,DouglasLaxton,AndrewLevin,LouisMaccini,AthanasiosOrphanides,AdrianPagan,ErwanQuintin,JohnRoberts,JirkaSlacalek,TsutomuWatanabe,IsamuYamamoto,NaoyukiYoshino,andseminarparticipantsattheFederalReserveBankofDallas,theInternationalMonetaryFund,theCanadianEconomicsAssociation,theJapanEco-nomicSeminar,andJohnsHopkinsUniversityforvaluablecommentsandsuggestions.Anyerrorsaremine.IamcurrentlyaneconomistintheResearchDepartmentoftheReserveBankofNewZealand.Contact:ReserveBankofNewZealand,POBox2498,Wellington6140,NewZealand.E-mail:deveirman@jhu.edu
1
1Introduction
TheoriginalPhillipscurvewasnonlinear:AlbanW.Phillips(1958)estimatedanonlinearre-lationshipbetweennominalwageinflationandtheunemploymentrateintheUnitedKingdom.Sincethattime,ithasbecomestandardtomodeltheshort-runPhillipscurveasalinearrela-tionshipwithatime-invariantslope.Thepresentpaperarguesthatthissimplifyingassumptionisnotasinnocentasitseems.
OurpaperassessestheempiricalperformanceofthreeclassesofmodelsinwhichtheslopeofthePhillipscurvevariesendogenouslyovertime.Themodelclassesdifferaccordingtothesetofvariablesdeterminingtheslopeoftheoutput-inflationtrade-off.
InpaperssuchasLaxton,Meredith,Rose(1995),thesizeoftheoutputgapdeterminestheslopeofthePhillipscurve.Inparticular,theoutput-inflationtrade-offbecomessteeperastheoutputgapapproachesthecapacityconstraint,whichisthemaximumpossiblelevelofoutputthatfirmscansupplyintheshortrun.Assuch,theshort-runPhillipscurveisconvex,withaverticalasymptoteatthecapacityconstraint.
InBall,Mankiw,Romer(1988)andDotsey,King,Wolman(1999),trendinflationisamongthedeterminantsofthePhillipscurveslope.Inthesemodelsofcostlypriceadjustment,thefrequencyofpriceadjustmentdependsonfirms’optimizingdecisions.Adecreaseintrendinflation,forone,causesfirmstoadjustpriceslessfrequently,whichinturnimpliesaflatterPhillipscurve.
InLucas(1973),theslopeofthePhillipscurvedependsonthevolatilityofaggregatedemandandsupplyshocks.Forinstance,ifaggregatevolatilitydecreases,alargerfractionofanychangeintheoverallpricelevelismisperceivedbyfirmsasbeingachangeintheirrelativeprice.Inthatscenario,anychangeinaggregatedemandhasalargerimpactonfirms’production,andasmallereffectoninflation.Thatistosay,thePhillipscurveflattens.
2
Throughoutthispaper,werefertothethreeclassesofmodelsasimplyingdifferenttypesofnonlinearityinthePhillipscurve.Strictlyspeakinghowever,onlythefirstoftheabovemodelclassesimpliesthattheshort-runPhillipscurveisnonlinearatagivenpointoftime.Intheothercases,thePhillipscurveislinearatanypointoftime,butitsslopechangesovertimeasaconsequenceofchangesintrendinflationoraggregatevolatility.
Totestthesetheoriesofnonlinearity,wegatherevidencefromJapan.Theperiod1991-2002inJapancanbecharacterizedasasuccessionofrecessions,interruptedonlybybrieforlimitedrecoveries.Standardestimatessuggestthattheoutputgapwasnegativeformostofthatperiod.Initially,inflationdeclined,withcoreCPIinflationreachingthezero-levelinthemid-nineties,andturningnegativeinthesecondhalfofthenineties.After1998however,annualcoreCPIinflationremainedfairlystableatmoderatelynegativelevels,reachingitstroughat-0.79%in2002.
Aswedocumentinourpaper,thefactthatdeflationremainedsurprisinglymildnotwith-standingarelativelylongperiodofnegativeoutputgapspresentsapuzzletoanyonewhotakesastandardlinearPhillipscurveliterally.ThismakesJapanaparticularlyinterestingtestcaseforassessingthenatureoftheoutput-inflationtrade-off.
AnadvantageofusingrecentdataforJapanisthat,unlikethesamplestypicallyusedinearlierempiricaltestsofthethreetypesofnonlinearity,oursampleincludesafairlylargenumberofobservationsfromtheregionofthePhillipscurveatwhichinflationisnear-zeroornegative.Theinclusionoflow-andnegative-inflationobservationsincreasesourchancesofobtainingpreciseresultsastotheexistenceandtypeofnonlinearity.Ourresultsareinstructiveforothereconomiesinwhichacomparablylongdeflationaryperiodhasnotoccurredinthepost-1945period,yetwhichbearsufficientresemblancetoJapaninthatinflationhastendedtodeclineand/orbecomelessvolatileoverthecourseofrecentdecades.
3
Ourmainresults,andtheirrelationshiptopreviouspapers’findings,canbesummarizedasfollows.
Wefindevidenceforastatisticallysignificant,gradualflatteninginalinearPhillipscurvewhichhasbeenoccurringsincebeforethenineties.ThisfindingisrelatedtoexistingresearchontheflatteningoftheJapanesePhillipscurve,1whichhowevertypicallyfocusesondocumentingaone-timestructural’break’inthePhillipscurveundertheassumptionofaknownbreakdate.
GiventhatweobservedagradualflatteningintheJapanesePhillipscurve,weassesswhethersuchtime-variationisconsistentwithanyofthetheoriesofnonlinearity.ThispartofourpaperisrelatedtoearlierempiricalevidenceonnonlinearityinthePhillipscurve.2Wefindthateachofthethreetypesofnonlinearityisconsistentwiththedata.
Ourpapermovesbeyonddocumentingmereconsistencyofthenonlineartheorieswiththedata.Wefindthateachofthenonlinearmodelsperformssignificantlybetter,inaneconometricsense,thananatheoreticalbenchmarkmodelinwhichthePhillipscurveislinear,butitsslopevariesovertimeasarandomwalk.Thisimpliesthatthetime-variationinthePhillipscurveslopehasbeenlargelysystematic.
Moreover,weperformaseriesofnon-nestedmodelhypothesisteststoassesstherelativeper-formanceofthethreetypesofnonlinearity.Ourresultsfavorthehypothesisthatdecliningtrend
NishizakiandWatanabe(2000)andMourouganeandIbaragi(2004).
AvastbodyofpapersincludingLucas(1973),Alberro(1981)andKormendiandMeguire(1984)investigateswhetherthePhillipscurvetendstobesteeperineconomieswithhighaggregatevolatility,withouthoweverexaminingthedeterminantsofchangesinthePhillipscurveslopeovertime.FroyenandWaud(1980)andIlmakunnasandTsurumi(1985)aremorecloselyrelatedtoourpaperinthattheyprovidesomeintertemporalevidence.
DeFina(1991),HessandShin(1999),andKiley(2000)furthertesttheBall-Mankiw-Romertheory.ThefirsttwopapersaswellasBMRprovidesomeintertemporalevidenceontherelationbetweenchangesinthePhillipscurveslopeandchangesintrendinflation.SeeBonomoandCarvalho(2004)forarecenttheoreticalcontribution.
InadditiontoLaxton-Meredith-Rose,paperswhichsupportthepossibleexistenceofasymmetriesinthePhillipscurveincludeTurner(1995),DebelleandLaxton(1996),Laxton,Rose,Tambakis(1999),andDolado,Maria-Dolores,Naveira(2005).SeeSchaling(2004)forarelatedtheoreticalcontribution.
Dotsey-King-Wolmanandsubsequentpapersprovidemodelsimulations,butnoempiricalevidenceontherelationbetweentrendinflationandthePhillipscurveslope.RecenttheoreticalcontributionsincludeGolosovandLucas(2003),Burstein(2006),GertlerandLeahy(2006),andDotsey,King,Wolman(2007).
21
4
inflationcausedfirmstosettheiroutputpriceslessfrequently,whichwouldexplaintheobservedgradualflatteninginthePhillipscurve.Allbutoneofourtestslendequallystrongsupporttothehypothesisthatadeclineinaggregateinflationvolatilityexacerbatedfirms’misperceptionsaboutrelativeprices,implyingaflatterPhillipscurve.Whilestoriesinwhichcapacityconstraintsengenderaconvexshort-runPhillipscurveareconsistentwiththedata,theyperformpoorlyincomparisonwiththetwoothermodels.
AfewofthepapersprovidingempiricalevidenceontherelationbetweenthePhillipscurveslopeandaverageinflation/aggregatevolatilitydosointhetimedimension(seefootnote2).Typically,thesepapersexaminewhetherchangesinthePhillipscurveslopeacrosssubsamplesarepositivelyrelatedtocross-subsamplechangesinaverageinflationand/oraggregatevolatility.Suchproceduresassumethat,ifthePhillipscurveslopechangesovertime,itdoessointheformofasuddenjumpatthesamplesplitpoint.OurpaperiswritteninthebeliefthattheactualPhillipscurveslopeismorelikelytovarygraduallyovertime.Forone,ourfindingthatthePhillipscurvegraduallyflattenedisbasedonatime-varyingcoefficientsmodelwhichyieldsanestimateforthePhillipscurveslopeateverypointoftimeratherthanonlyanestimatepersubsample.Thisislogicallyconsistentwiththefactthatourregressionstestingthenonlineartheoriessimilarlydonotrestricttime-variationinthePhillipscurveslopetooccurasaone-timejump.
Ourpaperisstructuredasfollows.Section2documentsthat,assumingastandardlinearrelationshipbetweentheoutputgapandinflation,thesizeofthenegativeoutputgapsinJapanwouldhavewarrantedacceleratingdeflationintheperiod1998-2002.Section3givesargumentsagainstpopularexplanationsfortheabsenceofacceleratingdeflationinJapanwhichdonotimplytime-variationintheslopeoftheshort-runPhillipscurve.
Theremainderofthepaperfocusesontime-variationintheslopeoftheshort-runPhillips
5
curve.Insection4,wedetectagradual,significantdeclineintheslopeofthePhillipscurvewhichhasbeenoccurringsincebeforethenineties.Sections5through7investigatethedeterminantsoftheflatteningofthePhillipscurve.Insection5,wefindthatallthreeabove-mentionedtypesofnonlinearityareconsistentwiththedata.Insection6,wefindthateachofthetheoriesofnonlinearityoutperformsamodelinwhichthePhillipscurveislinear,yetitsslopeevolvesovertimeasarandomwalk.Section7evaluatestherelativeperformanceofthethreetypesofnonlinearity.Section8concludesandpresentspolicyimplications.
2Background
Thissectiondealswiththreeissues.First,wediscusstheoutputgapseriesusedinthispaperanditsrelationtootheroutputgapestimatesforJapan.Second,wedocumentthatinJapan,theoutputgapandinflationtendedtocomovepositivelythrough1997,tosuchanextentthattheirrelationshipcouldbereasonablywellapproximatedbyastandardlinearPhillipscurve.Third,weshowthat,intheperiod1998-2002,theoutputgapwassufficientlynegativeforalinearPhillipscurvetopredictacceleratingdeflation,apredictionwhichisatoddswiththedata.
Figure1documentstheevolutionofJapan’srealGrossDomesticProduct,alongwithpotentialrealoutputasestimatedforJapanbytheUSFederalReserve.ItisevidentthataverageeconomicgrowthsincethestockmarketcrashofDecember19hasbeenlowerthanitwasinanyoftheprevioustwodecades.
ThepotentialoutputseriesinFigure1correspondstotheFed’sestimatesthrough1998.BecausetheFed’srecentestimatesofpotentialareconfidential,weextrapolatepotentialoutputfor1999Q1-2004Q4.Indoingso,weusetheIMFstaffestimates/forecastsofpotentialgrowth,asquotedinBayoumi(2000),asaguideline.
6
Accordingtoourmeasureofpotential,annualpotentialoutputgrowthhastendedtoslowdowngraduallyfrom3.88%in1990to1.20%in1998.Subsequently,potentialoutputgrowthcontinuedtodecline,butataslowpace,untilitreached0.83%in2004.
ThetoppanelofFigure2graphstheoutputgapseriesimpliedbytheactualandpotentialoutputdatafromthepreviousfigure.Potentialoutputgrowthturnsouttohavebeensufficientlyhighforarelativelylargenegativeoutputgaptoexistovermostoftheperiod1993-2003.However,sinceestimatesofpotentialoutputaretypicallyassociatedwithahighdegreeofuncertainty,wecompareouroutputgapserieswithotherexistingoutputgapmeasures.
TheFed’sestimatesaredirectlycomparabletothoseoutputgapestimatesforJapanwhicharebasedonanestimateofpotentialoutputderivedfromaproductionfunctioninvolvingthecapitalstock,thelaborstock,andtheirrespectivelong-runfactorutilizationrates.Inparticular,theBankofJapan(2006)hasrecentlydevelopedaproductionfunctionbasedprocedure,designedtominimizeanyupwardbiasinpotentialoutputgrowthwhichmayhaveexistedinitsearlierproductionfunctionbasedestimates,asreviewedinKamada(2005).3
LiketheFedestimateswhichweuse,theBankofJapan(2006)estimatessuggestthat,evenwhenaccountingforasizeabledeclineinpotentialoutputgrowthfromtheearlyninetiestothemid-nineties,Japanexperiencedrelativelylargenegativeoutputgapsformostofthenineties.TheBankofJapanoutputgapimpliesthat,ifanything,theninetieswasevenworseadecadeforJapanthantheFedestimatessuggest,relativetopastoutputgaps.
Unliketheproductionfunctionapproach,twootherstandardproceduresforestimatingpo-tentialoutputdonotyieldlargenegativeoutputgaps.However,wedonotconsideroutputgaps
Forinstance,thenewmeasuretreatsthefollowingtwodevelopmentsasstructuralfactors,andinsodoingreducestheestimateofpotentiallaborinputwhichenterstheproductionfunction:adeclineinworkinghours,amongothersduetolaborlawchangesattheendoftheeighties,andadeclineinthelaborforceparticipationratesincethemid-nineties,amongothersduetopopulationaging.
3
7
basedontheseprocedurestobevaluabletoolsforassessingtime-variationintherelationbetweentheoutputgapandinflationinJapan.
First,univariatesmoothingmethodssuchastheHodrick-Prescottfilteryieldanoutputtrendwhichisautomaticallyclosetoactualoutputwheneverthelatterstagnatesforafairlylongtimeattheendofthesample.Unsurprisingly,wefind(notshownhere)thatproxyingpotentialoutputbyaHP-filtertrenddoesnotyieldlargenegativeoutputgapsattheendofthesample,asconfirmedbytheHP-filterbasedoutputgapinKamada(2005).
Second,weappliedthemethodologyofHiroseandKamada(2003)toestimatepotentialoutputasthelevelofoutputatwhichinflationisstable.Wefind(notshownhere)thattheHirose-Kamadaoutputgapmovesaroundzeroattheendofthesample.Thisoutcomeisnotsurprising:attimeswheninflationisfairlystable,outputisbydefinitionnearitsstable-inflationlevel.Ingeneral,therewillbelittletonotime-variationintheslopeoftherelationshipbetweeninflationandanoutputgapmeasurewhichispreciselyconstructedtofitinflationaccuratelyatalltimes.
WearenowreadytogainourfirstinsightsaboutthecomovementoftheoutputgapandinflationinJapan.ThelowerpanelofFigure2graphsannualizedquarterlyinflationintheConsumerPriceIndexexcludingfreshfoods,whichtheBankofJapanadjustedforconsumptiontaxreforms.4Notethatasimplecomparisonbetweentheoutputgapandinflationiscloudedbysupplyshocks,suchastheoilpriceshockswhichledcoreCPIinflationtospikeupin1974Q1and1980Q2.Fornow,acasualinspectionofFigure2suggeststhattherelationshipbetweentheoutputgapandinflationwasfairlywell-behavedthroughouttheseventiesandeighties,inthesensethatinflationdeclinedwhentheoutputgapwasnegative,andtendedtoincreaseinbooms.
Tocharacterizetheoutput-inflationcomovementthrough1997somewhatmoreformally,we
4
Aconsumptiontaxof3%wasintroducedinApril19.Thatsalestaxwasincreasedto5%inApril1997.
8
regressthefollowinglinearPhillipscurveusingdatafor1971Q2-1997Q4:
πt=β1πt−1+β2πt−2+β3πt−3+β4πt−4+γ1ygapt−1+γ2ygapt−2+δimpoilt+et
(1)
Observationsfor1970Q2-1971Q1areusedtoconstructlags.AnnualizedCPIinflationexclud-ingfreshfoodsisafunctionoffourinflationlagsandtwooutputgaplags.Tocontrolforsupplyshocksintheseventies,weincluderelativeinflationintheimportpricesofpetroleum,coal,andnaturalgas.5
Inequation(1),inflationexpectationsareproxiedbylagsofinflation.Insection3.1,wedocumentthatinflationexpectationsinJapanindeedtrackedlaggedinflationrelativelyclosely.
Thelagstructureinequation(1)removesallserialcorrelationfromtheerrortermet,butissufficientlyparsimoniousforourestimationsinvolvingtime-varyingoutputgapcoefficientsand/ornonlinearitiesinthePhillipscurveinsections4through7.Werestrictthesumoftheinflationlagcoefficientstoequalone,andsettheconstanttozero.6
AlinearPhillipscurveestimatedthrough1997Q4fitsthedatawell:theadjustedR-squaredis0.83.Thesumoftheoutputgapcoefficientsispositive(withapointestimateof0.21)andsignificantatthe5%level.Thisconfirmsthat,duringatypicalepisodeintheperiod1971Q2-1997Q4,positiveoutputgapsexertedupwardpressureoninflation,whilenegativeoutputgaps
OilimportpricesareonYenbasis.Inequation(1)asinallPhillipscurvespecificationsbelow,theresultsarecomparablewhenweincluderelativeinflationingeneralimportpricesinstead.BothsupplyshockmeasuresareobtainedfromtheBankofJapan.6
AugmentedDickey-Fullertestsrejectaunitrootintheoutputgap,andinrelativeoilimportprices,atthe1%level.Wecannotstatisticallyrejectaunitrootininflation,butthechangeininflationisstationary.Moreover,inanunrestrictedregressionwithaconstant,thesumoftheinflationlagcoefficientsisnotsignificantlydifferentfromone.Theseconsiderationsleadustorestrictthesumoftheinflationlagcoefficientstoequalone,whichisanalogoustorewriting(1)asanequationforthechangeininflation,withthreelagsofthechangeininflationontheright-handside.SinceourPhillipscurveiseffectivelywrittenintermsofchangesininflation,excludingtheconstantisnecessarytoavoidthepossibilityofalong-runtrendininflation.Ifwedoincludeaconstant,itisvirtuallyzeroandinsignificant.
5
9
tendedtocoincidewithdisinflations.
Therelationshipbetweentheoutputgapandinflationbecamegraduallylesspronounced.Inparticular,wefocusontheepisode1998-2002becauseitconstitutesthemoststrikingpuzzle.Itistheepisodewiththelargestnegativeoutputgaps,yetitisamongtheepisodeswiththemoststableinflationrates.Overtheperiod1998-2002,actualoutputwasonaverage2.97%belowpotential.Meanwhile,annualcoreinflationdidfallfrom0.82%in1997to-0.35%in1998,butfromthatpointondeclinedonlymarginallyuntilitreacheditstroughof-0.79%in2002.
Toillustratethispoint,Figure3showstheresultofadynamicout-of-sampleinflationforecastfromequation(1)fortheperiod1998Q1-2004Q4,contrastedwithactualinflation.Predicteddeflationacceleratesto-8.36%in2002Q3,whileactualannualizedinflationfellbelow-1%inonlytwoquarters,reaching-1.58%in2000Q4.7Thissuggeststhatdeflationwasmilderthanonewouldhaveexpectedconditionalonthelarge,negativeoutputgaps,andassumingalinearrelationshipbetweentheoutputgapandinflation.
Theout-of-sampleforecastofacceleratingdeflationdoesnot,byitself,constituteconclusiveevidenceforastatisticallysignificantbreakinastandardlinearPhillipscurve.WedofindevidenceforstatisticallysignificantstructuralchangeinthePhillipscurveslopeinsection4.BeforeturningourattentiontotheslopeofthePhillipscurvehowever,wefirstevaluatecandidateexplanationsfortheabsenceofacceleratingdeflationwhichdonotrelyontime-variationinthePhillipscurveslope.
WeequallyobtainamassivedeflationforecastfromananalogousequationwiththeGDPdeflator.WiththeGDPdeflator,bothactualandpredictedinflationaremorenegativethanintheCPIcase.
7
10
3Capturingoutput-inflationcomovementwithouttime-varyingPhillipscurveslope?
WegiveargumentsagainstthreepossibleexplanationsfortheabsenceofacceleratingdeflationinJapan,noneofwhichimpliestime-variationintheslopeoftheshort-runPhillipscurve.
3.1Didinflationexpectationsfailtoturnnegative?
Theforecastofacceleratingdeflationinsection2originatedfromanaccelerationistPhillipscurve,inwhichinflationexpectationswereproxiedbylaggedinflation.Thus,equation(1)implicitlyassumesthatinflationexpectationsturnedmoderatelynegative,alongwithactualinflation.Itispossiblethatinflationexpectationsdidinfactnotturnnegativeintheperiod1998-2002,evenattimesofdeflationintheactualcoreCPI.IfJapaneseinflationexpectationshoveredaroundzero,thePhillipscurvewouldloseitsaccelerationistfeature,asapassageinBlanchard(2000)explains.Underthathypothesis,negativeoutputgapswouldimplynegative,butstableinflation.8Thiswouldaccuratelycapturetheoutput-inflationcomovementinJapanintheperiod1998-2002.
However,everyknownmeasureofinflationexpectationsinJapansuggeststhatinflationex-pectationsdidturnnegative.Theone-shot2002METIsurveyfindsthatonly5.6%offirms,andonly3.0%ofconsumers,expecteddeflationtoendwithinoneyear.TheDecember2001ConsensusforecastspredictheadlineCPIinflationof-0.9%for2002.ThefindingthatinflationexpectationsturnednegativeisconfirmedbyqualitativepriceexpectationsdataintheTankanbusinesssurvey,andbyinflationforecastsfromtheOECDandtheUSFederalReserve.
Toseethis,writethePhillipscurveasπt=β.Et−1(πt)+γ1.ygapt−1+γ2.ygapt−2+δ.impoilt+e,whereEt−1(πt)standsforlaggedexpectationsofcurrentinflation.Ifinflationexpectationsremainatzero,thisimpliesthatEt−1(πt)=0.Fromtheaboveequation,itfollowsthatinthatcase,negativeoutputgapstendtocoincidewithnegative,butstableinflation.
8
11
Basiceconometricanalysisconfirmsthatinflationexpectationscontinuedtotracklaggedin-flationrelativelycloselyevenaslaggedinflationturnednegative.Ourresultssuggestthat,iftherewasanystructuralchangeatallintheprocessofexpectationsformation,inflationexpectationsturnedevenmorenegativeintheperiodsincethemid-ninetiesthanwouldotherwisehavebeenwarrantedbylaggedinflation.9
3.2Didexpansionarymonetarypolicypreventmassivedeflation?
Inatextbookworld,fastmoneygrowthexertsupwardpressureoninflation.BetweenMarch2001andMarch2006,theBankofJapantargetedthereserves(’currentaccountbalances’)ofcommercialbanksattheBankofJapan,whichattimesresultedinmassivegrowthinthemonetarybaseandM1.10Isthisamongthefactorswhichpreventeddeflationfromaccelerating?
Ontheonehand,highgrowthinnarrowmonetaryaggregateshasnottranslatedintohighgrowthratesofbroaderaggregatessuchasM2,afactwhichisplausiblyrelatedtoadeclineinbanklendingwhichcontinuedforseveralyearsafterthebankingcrisesof1997and1998.11Ontheotherhand,wecannotexcludethepossibilitythattheBankofJapan’spolicyofmassivequantitativeeasingdidpreventtheoutputgapfrombecomingevenmorenegative,and/ordidkeepagentsfromexpectingmoreextremedeflationinthefuture.However,anysucheffectswouldalreadybereflectedintheoutputgapandinflationexpectationsdatawhichwediscussedintheprevioustwosubsections.Aswedocumented,inflationexpectationsdidturnmoderatelynegative,notwithstandingexpansionarymonetarypolicy.Similarly,theoutputgapdidgrowsufficiently
WeregressConsensusforecastsorOECDforecastsonaconstantandlaggedinflation,andtestforallpotentialbreakdatesstartingin1995.Theresultissubjecttodatalimitations:quarterlyConsensusforecastsareonlyavailablefromabout1990,andtheOECDforecastspertaintoannualinflation.10
AsitdidbeforeMarch2001,theBankofJapannowusestheuncollateralizedovernightcallrateasitsmainpolicyinstrument.11
Growthinlendingbydomesticcommercialbankshasbeennegativethroughouttheperiod1998-2004,andonlyturnedunambiguouslypositiveinearly2006.
9
12
negativetowarrantacceleratingdeflationinalinearframework.
3.3Downwardnominalwagerigidity?
TheexplanationinthissubsectiondealswiththespecificationofthePhillipscurve,butitaltersthestandardmodelinadifferentwaythanbyallowingfortime-variationintheslopeoftheshort-runPhillipscurve.
Akerlof,Dickens,andPerry(1996)developamodelinwhichdownwardnominalwagerigidityimpliesaconvexlong-runPhillipscurveatinflationratesbelow3%.Thelowertheinflationrate,thelargeristhefractionoffirmswhichcanimplementdesiredrealwagecutsonlythroughareductioninthenominalwage.Inthepresenceofdownwardnominalwagerigidity(DNWR),alowerinflationratethusimpliesthatalargerfractionoffirmsisforcedtopayrealwagesexceedingthewagewhichtheydeemoptimal.InthemodelofAkerlof,Dickens,Perry(1996),thisincreasesthelong-runsustainablelevelofunemployment,aneffectwhichbecomesmorepronouncedasinflationfallsfurtherbelow3%.
ForJapan,thisstoryimpliesthat,ifDNWRexists,actualunemploymentdoesnotexceeditslong-runratebyasmuchasunemploymentgapestimatesbasedontheassumptionofaverticalandlinearlong-runPhillipscurvewouldindicate.
However,wageshavenotbeendownwardlyrigidinJapanduringtheperiodofourfocus.Atamicrolevel,KurodaandYamamoto(2003a,b)findevidenceforDNWRwithdataspanning1992-1998.Inamorerecentstudyhowever,KurodaandYamamoto(2005)findnoevidencefordownwardrigidityinthenominalwagesoffull-timeworkersduringtheperiod1998-2001.Sincefull-timeworkers’nominalwagesstartedbeingcutin1998,downwardnominalwagerigiditycanhardlyexplaintheabsenceofacceleratingdeflation,whichbecameapuzzleatexactlythattime.
13
Atamacrolevel,Japan’swagesareevenlessrigid.AsdescribedinMorgan(2005),thefractionofnon-standardemployees,suchaspart-timeandtemporaryworkers,hasincreasedfrom19.4%in1995to29.0%in2004.Furthermore,thereisalargewagegapbetweenregularandnon-standardemployees.In2004,apart-timeworker’shourlybasewagewasonly40.5%thatofatypicalregularworker.12Hence,evenifnosinglegroupofworkershadexperiencednominalwagecuts,theshiftfromregulartonon-standardworkershadledtoadeclineintheaggregatewage.
Sincebothmicro-economicandmacro-economicdatasuggestthatwageswerenotdownwardlyrigidduringourperiodofinterest,anystoryinvolvingdownwardnominalwagerigidityisunlikelytoexplaintheabsenceofacceleratingdeflationinJapan.
4EvidenceforaflatteningPhillipscurve
Fromthispointon,ourpaperfocusesonthepathanddeterminantsoftheslopeoftheshort-runoutput-inflationtradeoff.
Thepresentsectionpresentstwofindings.First,structuralstabilitytestssuggestthattheslopeofthePhillipscurvehaschangedoverthesampleinastatisticallysignificantfashion.Giventhatresult,weestimatethePhillipscurveslopeasatime-varyingparameterusingtheKalmanfilter.OurresultssuggestthatthePhillipscurvehasflattenedoverthesample,wheremuchoftheflatteningoccurredbeforethenineties.
4.1SignificantstructuralchangeinthePhillipscurveslope
Redefiningγ2=pγ1,werewritethelinearPhillipscurvefromequation(1)as:
Theoverallmonthlycost(includingbonuses,fringebenefits,socialsecuritycontributions,andtrainingexpenses)ofemployingapart-timeworkerwas36.9%thatofemployingafull-timeworker.DataarefromMorgan(2005).
12
14
πt=β1πt−1+β2πt−2+β3πt−3+β4πt−4+γ1(ygapt−1+pygapt−2)+δimpoilt+et
(2)
InordertoassessthepresenceofstructuralchangeintheslopeofthePhillipscurve,wetestforthestabilityofγ1,whileassumingthatpremainsconstantatitsestimatedvalue.Thisprocedureisdirectlycomparabletothatofsubsection4.2.,wherewemodelγ1asatime-varyingparameter,butcontinuetoestimatepasbeingtime-invariant.Wemotivatetheassumptionoftime-invarianceinpinsubsection4.2.
First,weuseastandarddummyvariableproceduretotestforastructuralbreakinthePhillipscurveslope,atahypothesizedbreakdateof1990Q1.13Thetestresultsuggeststhat,conditionalontheabsenceofstructuralchangeintheotherparameters,γ1wassignificantlysmaller,atthe1%level,from1990onwardsthanbeforethattime.EarlierresearchontheflatteningoftheJapanesePhillipscurve,suchasNishizakiandWatanabe(2000)andMourouganeandIbaragi(2004),similarlyimplementeddummyvariabletestsandfoundthattheJapanesePhillipscurvewassignificantlyflatterintheninetiesthanitwasinearlierdecades.
Second,weimplementatestforstructuralchangewhich,unliketheabovetest,doesnotrequireustoassumeanyparticularbreakdate.Inparticular,weapplytheNyblom(19)test,intheversiondevelopedbyHansen(1992).Werejectthenullhypothesisoftime-invarianceinγ1atthe1%level.14Itdeservesemphasisthat,unlikewhatisthecaseforotherstructuralstabilitytestssuchastheabovedummyvariabletest,rejectionofthenullhypothesisdoesnotnecessarily
Weregressπt=β(L)πt+(γ1+γ01breakdum)(ygapt−1+pygapt−2)+δimpoilt+et,wherebreakdum=1forallquartersstartingin1990Q1,and0forallearlierobservations.γ01isestimatedtobenegativeandsignificant.14
ThejointteststatisticforallmodelparameterssuggestssignificantstructuralchangeintheoverallPhillipscurve,atthe1%level.Furthermore,therelevantindividualteststatisticsuggestssignificantchangeinthevarianceoftheerrorterm,atthe1%level.Onthispoint,notethattheHansen(1992)testisasymptoticallyrobusttoheteroskedasticity.Throughoutthepaper,ourOLS/NLSregressionsuseheteroskedasticityrobuststandarderrors.
13
15
implyaone-timejumpinthePhillipscurveslope,yetcouldjustaswellreflectgradualstructuralchange.Infact,theNyblomtesthasoptimalpoweragainstthehypothesisthataparameterfollowsamartingale.Giventhetestresult,wemodelγ1asarandomwalkinthenextsubsection.
4.2State-spaceformofmodelwithtime-varyingPhillipscurveslope
Wewritethemodelinstate-spaceform.Themeasurementequation,intheformofHarvey(1994):
πt=[ygapt−1+pygapt−2]γ1,t+[β(L)πt+δimpoilt]+et
(3)
Whereγ1,tisthestatevariable.Theerrortermetisnormallydistributedwithmeanzeroandvarianceσ2e.
Inequation(3),weimposetherestrictionthatthetwooutputgapcoefficientsareproportionalatanypointoftime,i.e.γ2,t=pγ1,t,wherepisatime-invariantparametertobeestimatedbyMaximumLikelihood.Theestimationresultsaresimilarwhetherweimposeproportionalityornot,exceptforthefactthatthesumoftheoutputgapcoefficientsisimpreciselyestimatediftheassumptionofproportionalityisnotimposed.Wesimplydonothaveenoughobservationstoobtainpreciseestimatesforthesumoftwodistincttime-varyingcoefficients.Inanycase,weareprimarilyinterestedinthesumoftheoutputgapcoefficients,andlesssointheprecisewayinwhichthissumisallocatedoverthetwoindividualoutputgapcoefficients.
Whileequation(3)representsthemeasurementequation,thetransitionequationisasfollows:
γ1,t=γ1,t−1+v1,t
(4)
2Wherev1,tisnormallydistributedwithmeanzeroandvarianceσ2v1=σeq1.Theparameter
16
q1isthesignal-to-noiseratioforthecoefficientontheoutputgap’sfirstlag.Thepathofthecoefficientonthesecondoutputgaplagfollowsfromγ2,t=pγ1,t.
4.3Estimationprocedureandresults
WeapplyMaximumLikelihoodtoestimatethemodelconstitutedbyequations(3)and(4).AsinHarvey(1994)andKimandNelson(1999),wecomputetheloglikelihoodfunction,initspredictionerrordecompositionform,fromtheKalmanfilterpredictionerrorsandtheirvariances.Wemaximizetheloglikelihoodfunctionwithrespecttothehyperparameters.15Finally,weusetheKalmanfilterrunthatmaximizedthelikelihoodinordertocomputeKalmansmoothedestimatesofthetime-varyingoutputgapcoefficientsandtheirsum.
Table1comparestheresultsofthetime-varyingcoefficientslinearPhillipscurvewiththoseofalinearPhillipscurveestimatedbyOLS.Bothestimations,aswellasallotherestimationsintheremainderofthispaper,arecarriedoutover1971Q2-2004Q4,wheredatafor1970Q2-1971Q1areusedtoconstructlags.TheMLEestimatesofthetime-invariantparametersarecomparabletotheirOLScounterparts.Similarly,theaverageofthesumoftheoutputgapcoefficientsisvirtuallyidenticaltothesumoftheoutputgapcoefficientsimpliedbytheOLSestimation.Thesacrificeratio’sareplausibleinbothcases.IntheMLEcase,adisinflationofonepercentagepointrequiresoutputtobe1.39%belowpotentialforfourquarters.ThisisinlinewithearlierestimatesoftheJapanesesacrificeratioinBall(1994)andZhang(2005).16
Figure4graphsKalmansmoothedestimatesoftheoutputgapcoefficientsandtheirsum,alongwitha95%confidenceinterval.Thesumoftheoutputgapcoefficientsdeclinesgradually
WeusetheMatlab-functionfminunctooptimizetheloglikelihoodfunction.Wesetthesignal-to-noiseratio,q1,to1/1600inthebaseline.TheparameterestimatesreportedinTable1arerobustforallvaluesofq1upto1/25.16
Ball(1994)computesasacrificeratioforJapanof0.93%.OurslightlylargerestimateisinlinewithacontinuedflatteningofthePhillipscurveafter1994.Zhang(2005)computesasacrificeratioof1.85%whenaccountingforlong-livedeffects.
15
17
overthesample.Theresultssuggestthatmuchoftheflatteningoccurredbeforethenineties.Theabsenceofacceleratingdeflationin1998-2002isonlyoneamongtheepisodesconsistentwiththetime-pathofthePhillipscurveslope.Forexample,thefindingthatthePhillipscurvewasalreadyrelativelyflatduringthebubbleperiodinthelateeightiesisinlinewiththefactthatinflationremainedsurprisinglymoderateatthattime,notwithstandinglargepositiveoutputgaps.
5WhydidthePhillipscurveflatten?Candidatetypesofnon-linearity
TheflatteningofalinearPhillipscurvemaysuggestthattheoutput-inflationtrade-offshouldac-tuallybemodeledasanonlinearrelationship.Inthissection,weassesstheempiricalperformanceofthreetypesofnonlinearity.ThecoefficientestimatesfromnonlinearPhillipscurveregressionsareinlinewitheachofthenonlineartheories.Moreover,whilesection4detectedstatisticallysignificantstructuralchangeintheoutputgapcoefficientsofalinearPhillipscurve,thereisnosignificantstructuralchangeinthecoefficientsforanyofthethreetypesofnonlinearity.
5.1Aconvexshort-runPhillipscurveduetocapacityconstraints?
Laxton,Meredith,Rose(1995)andrelatedpapers17allowforconvexityintheshort-run
Phillipscurve.InLaxton,Meredith,Rose(LMR),capacityconstraintsconstitutetheeconomicrationalefornonlinearity.Supposethatatthecurrentlevelofoutput,firmsareoperatingnearthecapacityconstraint.Insuchasituation,anyincreaseinaggregatedemandcanhardlybemetbyincreasedproduction.Assuch,theincreaseindemandtranslatesalmostuniquelyintoanincreaseininflation,evenintheshortrun.Hence,thePhillipscurveisnearlyverticalnearthe
17
Seefootnote2forreferencestopapersrelatedtoanyofthetheoriesofnonlinearity.
18
capacityconstraint,wheretheslopebecomesgraduallysteeperastheeconomymovestowardsthecapacityconstraint.ThisstoryimpliesaverticalasymptoteinthePhillipscurveatthecapacityconstraint.ThebaselinefunctionalformwhichLMRuseimpliesthat,ifconvexityispresent,itexistsalongtheentirePhillipscurve.
NotethatitisnotobviouswhetherthepresenceofcapacityconstraintscanbearationaleforconvexityinthePhillipscurveinregionswhicharefarawayfromthecapacityconstraint.Theanswertothisquestionisparticularlyimportantforourpurposes:theLMRmodel’spredictionsforJapanarethat,sincetheeconomywasfarfromthecapacityconstraintin1998-2002,JapanwasonaflatterpartofaconvexPhillipscurveduringthatperiod.Thatwouldexplaintheflatteningwhichweobservedinsection4.Yet,ifconvexityisnotpresentatnegativeoutputgaps,theJapaneseeconomywouldhavemovedalongalinearpartofthePhillipscurveformostofthenineties,suchthattheLMRmodelcouldnotexplainanytime-variationinthePhillipscurveslopeduringthatperiod.Therearesurelywaystomotivateconvexityatnegativeoutputgaps,18butsuchreasoningsarenotcontainedinLMR’soriginalpaper.
WefollowLMRinusingafunctionalformwhichimpliesthatthePhillipscurveiseitherconvexinallregions,orlineareverywhere.Theabsenceofacleartheoreticalmotivationforconvexityatnegativeoutputgapswillenterouroverallmodelassessmentinsection7.2.
WeestimateapotentiallynonlinearPhillipscurvebyNonlinearLeastSquares,wherethefunctionalformoftheoutputgaptermsisequivalenttothatinLMR:
∙µ
¶
µ
¶¸
πt=β(L)πt+γ1
18
φygapt−1φ−ygapt−1
+p
φygapt−2φ−ygapt−2
+δimpoilt+et
(5)
Inthepresenceofsectoralheterogeneity,itispossiblethatevenatnegativeoutputgaps,asmallfractionoffirmsoperatesnearfullcapacity.Ifso,itisplausiblethatthefractionofcapacity-constrainedfirmsincreasesastheoutputgapbecomeslessnegative(ormorepositive).
19
Whereγ1istime-invariant.Forequation(5),theNyblomtestfailstorejectthenullhypothesisofstructuralstabilityinγ1,atthe10%level.Thatis,thereappearstobelittletonotime-variationinthePhillipscurveslopebeyondthatimpliedbythenonlinearityofthefunctionalform.
Thecrucialparametertobeestimatedisφ.Thisparameterindicatestheleveloftheoutputgapatwhichtheeconomyreachesthecapacityconstraint.Bythesametoken,φgovernsthedegreeofnonlinearityinthePhillipscurve.Thesmallerthepointestimateforφis,thesmallerthedistancebetweenthezerooutputgapandthecapacityconstraintwillbe.Thisinturnyieldsahigherdegreeofconvexity.
TherightmostcolumnofTable2presentsestimationresultsforequation(5).WealsoincluderesultsfromapurelylinearPhillipscurve,whichessentiallyimposestherestrictionthatφ=∞.Inthepotentiallynonlinearcase,φispreciselyestimated,withapointestimateofexactly10.00.Thissuggeststhattheeconomywouldreachthecapacityconstraintifactualoutputweretoexceedpotentialoutputby10%.
Toillustratethedegreeofconvexityimpliedbytheestimatesforγ1,p,andφinequation(5),Figure5graphsthesumoftheoutputgaptermsasafunctionoftheoutputgap.Inparticular,theboldcurveinFigure5graphsγ1[(φygapt−1/(φ−ygapt−1))+p(φygapt−2/(φ−ygapt−2))]withrespecttotheoutputgap,whereweimposethatygapt−1=ygapt−2.Forcomparison,thethinsolidlineinthesamefiguregraphsthesamefunction,withexactlythesamevaluesforγ1andp,butimposingthatφ=∞.Visually,weseeafairlystrongdegreeofnonlinearityinthePhillipscurve.19Inotherwords,boomsinrealactivityincreaseinflationbymorethanrecessionsdecreaseit.Theasymmetryintheeffectsofdemandshiftsbecomesmorepronouncedasonemovesfurtherfromthezerooutputgapineitherdirection.Forinstance,anoutputgapof-5%tendstoleadto
Thedottedlinealsousesthesamevaluesforγ1andp,butassumesavalueforφwhichistheupperboundofthe95%confidenceintervalaroundtheestimatednonlinearityparameter.
19
20
adisinflationof0.53percentagepointsaftertwoquarters,whilethetotalimpactofa5%outputgapistoincreaseinflationby1.60percentagepoints.
5.2AflatterPhillipscurveduetoalowerfrequencyofpriceadjustment?
Inthissubsection,weassesstheempiricalvalidityoftwotheoriesinwhichcostsofpriceadjustmentleadfirmstoadjusttheiroutputpricesinfrequently:Ball,Mankiw,Romer(1988),andDotsey,King,Wolman(1999).Inbothmodels,lowertrendinflationdecreasesthefrequencyofpriceadjustment.Lessfrequentpriceadjustmentinturnreducestheeffectofaggregatedemandshiftsoninflation.Thatistosay,thePhillipscurveisflatteratlowerratesoftrendinflation.
InBall,Mankiw,Romer(BMR),firms,whensettingtheirprice,alsochoosethelengthoftimeoverwhichtheirpricewillbeineffect.Firmsminimizealossfunctionwhichdependsontheaveragecostofpriceadjustmentperperiod,andondeviationsoftheiractualnominalpricefromtheprofit-maximizingnominalpriceoverthecourseoftheperiodthatthepriceisineffect.Whentrendinflationishigh,anyfirmexpectsitsrelativepricetochangerapidlyovertime,whichinturnleadsthefirmtoexpectarapidchangeinitsprofit-maximizingnominalprice.Thus,theforward-lookingfirmwillnotfixitsactualpriceforalongtime.Instead,thefirmoptsformorefrequentpriceadjustment,thuspayingahigherper-periodcostofpriceadjustment,inordertoavoidlargedeviationsofitsfuturepricesfromtheirprofit-maximizinglevels.
InDotsey,King,Wolman(DKW),highersteady-stateinflationimpliesthatanyfirm’srela-tivepricehasbeenerodedtoalargerextentsinceitslastpriceadjustment.Thisimpliesthatforalargerfractionoffirms,thebenefitofpriceupdatingwillexceedthe(labor)costofpriceadjustment.Inconclusion,highersteady-stateinflationleadstohighersteady-stateprobabilitiesofpriceadjustment.
21
Thesetwomodels’predictionforJapanisthat,astrendinflationgraduallydecreasedoverthesample,thefrequencyofpriceadjustmentdeclined,whichinturnledtoagraduallyflatteningPhillipscurve.Atthetimeofwriting,wearenotawareofanypubliclyavailabletimeseriesdataontheaveragefrequencyofpriceadjustmentforJapan.Wethereforecannotmodelthefrequencyofpriceadjustmentexplicitly,muchlikewhatwasthecasefortheempiricalanalysesintheearlierstudiesreferencedintheintroduction.However,wecantestwhethertheslopeofthePhillipscurvedependspositivelyontrendinflation.
InspiredbyDeFina(1991),weadoptaone-stepapproach.20Thatistosay,weestimateaPhillipscurveinwhichtheslopedependsontheabsolutevalueoftrendinflation:21
πt=β(L)πt+[a+b|πt|][ygapt−1+pygapt−2]+δimpoilt+et
(6)
WegeneratetrendinflationattimetasageometricaverageofJquartersofpastinflation:
J
1−θXj
πt=θπt−j
θ−θJ+1j=1
(7)
Inthebaseline,θ=0.93andJ=71.Notethattrendinflationdoesnotdependoncurrentinflation,soastoavoidendogeneityissuesinequation(6).Thefactorinfrontofthesummationsignensuresthatthesumoftheweightsonthepastinflationtermsisequaltoone.
Inequation(6),theNyblomtestdoesnotdetectanystructuralchangeinaorbindividually,
EmpiricalfindingsontherelationshipbetweentheslopeofthePhillipscurveandtrendinflationoraggregatevolatility,asreferencedintheintroduction,havemostlybeenbasedonatwo-stepapproach.Inatime-seriessetting,itisundesirabletoenterthePhillipscurveslopeasaleft-handsidevariableinasecond-stageregression,amongothersbecausethetime-varyingPhillipscurveslope(obtained,say,fromrollingwindowsregressions)islikelytobenonstationary.21
Wetaketheabsolutevalueoftrendinflationbasedontheintuitionthattheeffectsofmorepronounceddeflationshouldaffectfirms’relativeprices,andhencethefrequencyofpriceadjustment,inmuchthesamewayasanincreaseininflationdoes.NeitherDKW,BMR,norDeFina(1991)taketheabsolutevalue,yetthiscanbeattributedtotheirdealingwitheconomiesinwhichnegativetrendinflationcouldhardlybeimaginedatthattime.
20
22
oraandbjointly,atthe10%level.Thissuggeststhatthereislittletonotime-variationintheoutputgapcoefficientsbeyondthatassociatedwithchangesintrendinflation.
Table3displaystheestimationresultsforequation(6).Forcomparison,weincluderesultsfromaPhillipscurveinwhichthecoefficientontrendinflationissettozero.Inequation(6),thecoefficientontrendinflation,b,ispositiveandsignificantatthe1%level.ThisresultisinlinewiththeBall-Mankiw-RomerandDotsey-King-Wolmantheories.
Fromtheestimatesfora,b,andp,andourseriesfortrendinflation,wecomputedtheimpliedoutputgapcoefficientsandtheirsum.GiventhatthePhillipscurveslopeisalineartransformationoftrendinflation,itdisplaysasimilarpatternovertimeastrendinflationitself.Inparticular,thesumoftheoutputgapcoefficients(notgraphedhere)increasesuntil1976,anddecreasesquicklythroughthelateeighties.Fromtheearlyninetieson,thePhillipscurveslopestilltendstodecrease,butataslowerpace.Itfallsbelowzeroin1994,yetfrom1996onremainsfairlystableatmoderatelynegativelevels.
5.3AflatterPhillipscurveduetoadeclineinaggregatevolatility?
InLucas(1973),theslopeofthePhillipscurvedependsonthevolatilityofaggregatedemandandsupplyshocks.Firmssetquantitiesproducedbasedontheirperceivedrelativeprice.Asthevarianceofaggregateshocksdecreasesrelativetothevarianceoffirm-specificshocks,alargerfractionofanychangeintheoverallpricelevelismisperceivedbyfirmsasbeingachangeintheirrelativeprice.Inthatway,loweraggregatevolatilityimpliesthatanychangeinaggregatedemandhasalargereffectonatypicalfirm’sproduction,andthusonaggregateoutput.Correspondingly,demandshiftshaveasmallerimpactoninflation.Inconclusion,lowlevelsofaggregatevolatilityimplyaflatterPhillipscurve.
23
AtestableimplicationofthismodelforJapanisthatadecreaseinthevarianceofaggregatedemandand/orsupplyshockswouldhavebeenassociatedwiththeflatteningofthePhillipscurvewhichwedocumentedinsection4.22
Wecaptureaggregatevolatilitybythevarianceofinflation.23WeestimateaPhillipscurveinwhichtheslopeisexplicitlymodeledasafunctionofthevarianceofinflation:
πt=β(L)πt+[c+dvart(π)][ygapt−1+pygapt−2]+δimpoilt+et
(8)
Wegeneratethevarianceofinflationattimetasageometricallyweightedaverageofpastsquareddeviationsofinflationfromitstrend:
J
1−θXj
vart(π)=θ(πt−j−πt)2
J+1θ−θj=1
(9)
Wheretrendinflationπtiscomputedasinequation(7).Again,thebaselinevaluesareθ=0.93andJ=71.
Inequation(8),theNyblomtestrejectsthenullofnostructuralchangeincindividually,andincanddjointly,butonlyatthe10%level.Itfailstorejectthehypothesisoftime-invarianceind.Thissuggeststhatchangesinthevarianceofinflationexplainmost,butnotall,ofthetime-variationinthesumoftheoutputgapcoefficients.
Table4containstheestimationresultsforequation(8).AspredictedbytheLucas-theory,thecoefficientdoninflationvolatilityispositiveandsignificantatthe1%level.
Ball,Mankiw,Romer(1988)equallyimpliesthatadecreaseinthevarianceofaggregateshocksleadstoaflatter
Phillipscurve.Yet,inBMR,themechanismworksthroughthefrequencyofpriceadjustment:decliningaggregatevolatility,whichreducesuncertaintyaboutfutureoptimalprices,enablesfirmstosettheirpricesforalongerperiodoftime.AlowerfrequencyofpriceadjustmentinturnimpliesaflatterPhillipscurve.23
Theotherstandardcandidate,thevarianceofnominalGDP,wouldnotbeasappropriateameasuretocapturebothsupplyanddemandshocks.Forinstance,ifaggregatedemandisunit-elastic,aggregatesupplyshockshavenovisibleimpactonnominalGDP,sincetheireffectonpricesisexactlyoffsetbytheireffectonrealactivity.
22
24
Thesumoftheoutputgapcoefficientsimpliedbyequation(8)increasessteeplyfrom1973to1975,thendecreasesquicklythroughthelateeighties.Fromtheearlyninetieson,theimpliedPhillipscurveslopedecreasesonlyslightly.Itstayspositiveatalltimes.
6Dothenonlinearmodelsbeattherandomwalkmodel?
Inthepresentsection,weestimatemodelsinwhichthePhillipscurveslopedependsonarandomwalktermaswellasonafunctionimpliedbyaparticulartheoryofnonlinearity.
Inthecaseswherewetestforit,wefindthatwecanomittherandomwalktermfromtheencompassingmodelwithoutengenderingasignificantdeclineinthevalueofthelikelihoodfunction.Thisisrelatedtoourfinding,insection5,ofnostructuralchangeinthecoefficientsontheoutputgaptermsforeachofthenonlinearmodels.Beyondthat,thepresentsection’sresultsimplythataddinganyofthethreetypesofnonlinearitytoapurerandomwalkmodelyieldsasignificantimprovementinthefit.
6.1Thetrendinflationmodelbeatstherandomwalkmodel
WeestimateamodelwhichencompassestherandomwalkmodelandtheBall-Mankiw-Romer/Dotsey-King-Wolman(BMR/DKW)trendinflationmodel,andtestforthestatisticalrelevanceoftherandomwalktermontheonehand,andthetrendinflationtermontheotherhand.
ThePhillipscurve,aliasmeasurementequationofthestate-spacemodel,isexactlythesameasequation(3):
πt=[ygapt−1+pygapt−2]γ1,t+[β(L)πt+δimpoilt]+et
(10)
Thenoveltyliesinthetransitionequation.Intheencompassingmodel,theoutputgapcoeffi-25
cientγ1,tisallowedtodependbothonitsownlagandontrendinflation.Inthepurerandomwalkmodel,γ1,t=γ1,t−1+v1,t.Ontheotherhand,inthepureBMR/DKWmodel,γ1,t=a+bπt.Nestingthesetwoyieldsthefirstrowofthestateequation:
γ1,t=λ(γ1,t−1+v1,t)+(1−λ)(a+bπt)
(11)
Notethattrendinflationappearsasanexogenousvariableinthefirstrowofthetransitionequation.TextbooktreatmentsoftheKalmanfiltersuchasHarvey(1994),Hamilton(1994),orKimandNelson(1999)donotdiscusssolutionsforhowtoenteranexogenousvariableinthestateequation.Ifwewishtoenterπtinthetransitionequation,weneedtospecifyatransitionprocessfortrendinflation,andenterthisprocessinthesecondrowofthestateequation.Wederivesuchprocessfromthedefinitionoftrendinflationinequation(7).ForθsufficientlysmallandJconvergingtoinfinity,wefind:
πt+1=(1−θ)πt+θπt
(12)
Thetransitionequationthusbecomes:
⎡
⎤
⎡
⎤
⎡
⎤⎡
⎤
⎡
⎤
⎢γ1,t⎥⎢(1−λ)a⎥⎢λ(1−λ)b⎥⎢γ1,t−1⎥⎢λv1,t⎥
⎥.⎢⎥=⎢⎥+⎢⎥+⎢⎥⎢
⎦⎣⎦⎣⎦⎣⎦⎣⎦⎣
(1−θ)πt0θπt+1πt0
(13)
First,weestimatetheencompassingmodel,consistingofequations(10)and(13).Intheunrestrictedmodel,λisestimatedtobe-0.51.Essentially,theweightontheBMR/DKWmodelinthetransitionequationexceedsunity.
Next,werestrictλ=0,inwhichcasethemodelreducestotheBMR/DKWtrendinflation
26
model.Wetestthatrestrictionbymeansofalikelihoodratiotest.Sincewearetestingonerestriction,thelikelihoodratiostatistichasaχ2(1)distribution.Accordingtothetestresult,relaxingtherestrictionthatλ=0doesnotsignificantlyimprovethefit,notevenatthe10%level.
Finally,werestrictthemodelsuchthatequation(11)reducestoarandomwalk.Inthiscase,thelikelihoodratiohasaχ2(3)distribution.24AbstractingfromtheBMR/DKWtermsignificantlydeterioratesthefitatthe1%level.
Ontheonehand,wefoundthatthepureBMR/DKWmodeldoesnotperformsignificantlyworsethantheencompassingmodel.Ontheotherhand,thepurerandomwalkmodeldoesperformsignificantlyworsethantheencompassingmodel.WeconcludethattheBMR/DKWmodelprovidesamoreaccuratedescriptionofthedatathantherandomwalkmodeldoes.
6.2Themisperceptionsmodelbeatstherandomwalkmodel
ThissubsectionimplementsasimilarprocedurefortheLucasmisperceptionsmodelastheprevioussubsectiondidforBMR/DKW.Themeasurementequationisexactlythesameasequation(10).
Thestateequationisanalogoustoequation(13),butissomewhatcomplicatedbythefactthatthetransitionprocessforthevarianceofinflationismoreinvolvedthantheprocessfortrendinflation.Thefirstrowofthetransitionequationisanalogoustoequation(11):
γ1,t=λ(γ1,t−1+v1,t)+(1−λ)[c+dvart(π)]
(14)
Fromthedefinitionofthevarianceofinflationinequation(9),wederiveitstransitionprocess,
Atfirstsight,thedistributionappearstobenonstandard,sinceaandbpotentiallyactasnuisanceparameters.Yet,rewriteequation(11)asγ1,t=γ1,t−1+v1,t+(λ−1)(γ1,t−1+v1,t)+(1−λ)a+(1−λ)bπt.Redefining(1−λ)aand(1−λ)bsuchthattheyareparametersintheirownright,thisequationisineffectlinearintheparameters.Itreducestotherandomwalkmodelafterimposingthreerestrictions:(λ−1)=0,(1−λ)a=0,and(1−λ)b=0.
24
27
tobeincludedinthesecondrowofthestateequation.ForθsufficientlysmallandJconvergingtoinfinity,wefindthat:
vart+1(π)=(1−θ)Xt+θvart(π)
θ
WhereXt=(2−θ)(πt−πt)2−21−θ(πt−πt)
JXj=1
(15)
θj(πt−j+1−πt).
Thetransitionequationthusbecomes:
⎡⎢
⎢⎣
⎤
⎡
⎤
⎡
⎥⎢(1−λ)c⎥⎢λ(1−λ)d⎥⎢γ1,t−1⎥⎢λv1,t⎥
⎥.⎢⎥+⎢⎥=⎢⎥+⎢⎥⎦⎣⎦⎣⎦⎣⎦⎣⎦
0θ(1−θ)Xtvart+1(π)vart(π)0γ1,t
⎤⎡⎤⎡⎤
(16)
WhereXtisasdefinedunderequation(15).
Intheencompassingmodel,whichconsistsofequations(10)and(16),thenestingparameterλisnotsignificantlydifferentfromzero,withapointestimateof-0.13.ThisisevidenceinfavoroftheLucasmodel,relativetotherandomwalkmodel.Asintheprevioussubsection,wefindthatimposingtherestrictionthatλ=0doesnotsignificantlyworsenthefit,whileimposingrestrictionssuchthatequation(14)reducestoarandomwalkleadstoasignificantdeclineintheloglikelihoodfunctionvalueatthe1%level.
Inconclusion,therandomwalkmodelprovidesasignificantlylessaccuratefitthantheen-compassingmodel,whilethefitoftheLucasmodelisstatisticallyindistinguishablefromthatoftheencompassingmodel.Hence,themisperceptionsmodelbeatstherandomwalkmodel.
6.3Convexityevenwithindependenttime-variationinthePhillipscurveslope
Insection5,wedetectedastrongdegreeofnonlinearityinaPhillipscurvemodeledasinLaxton,Meredith,Rose(LMR).However,thatsection’sprocedureisnotdesignedtodeterminewhetherthenonlinearityisstatisticallysignificant.Inthepresentsubsection,wedofindthatamodel
28
whichallowsforLMR-stylenonlinearitycapturestheevolutionofthePhillipscurveslopeinasignificantlybetterfashionthanapurerandomwalkmodeldoes.
WespecifyaPhillipscurvewhichneststhelineartime-varyingcoefficientmodelofequations(3)and(4),andthenonlinearLMRmodelofequation(5):
∙µ
¶
µ
¶¸
πt=β(L)πt+γ1,t
φygapt−1φ−ygapt−1
+p
φygapt−2φ−ygapt−2
+δimpoilt+et
(17)
Whereγ1,tevolvesasarandomwalk:
γ1,t=γ1,t−1+v1,t
(18)
Thismodelcollapsestothelineartime-varyingcoefficientsmodelifφ=∞,andreducestothenonlinearmodelwithtime-invariantcoefficientsifv1,t=0forallt.
Weestimatetwomodels,oneinwhichthenonlinearityparameterφisrestrictedtobeaverylargenumber,25andoneinwhichφisfreelyestimated.
Intheunrestrictedmodel,thenonlinearityparameterissmallandpreciselyestimated,beitsomewhatlargerthaninsection5.
Weapplyalikelihoodratiotesttoexaminewhetherthemodelinwhichφisfreelyestimatedperformssignificantlybetterthanthemodelinwhichlinearityisimposed.Thelikelihoodratiostatisticisdistributedχ2(1).Thetestresultsuggeststhatrelaxingtheassumptionoflinearitysignificantlyincreasesthevalueofthelikelihoodfunctionatthe1%level.
Inconclusion,theLMRmodeladdsinformationbeyondthatcontainedinthelineartime-varyingcoefficientsmodel.
25
Weimposeφ=1E20.
29
7WhichtypeofnonlinearityinthePhillipscurve?
Sofar,wehavefoundthateachofthethreemodelsofnonlinearitynotonlyisconsistentwiththedata,butalsooutperformsthebenchmarkrandomwalkmodel.Inthepresentsection,wecomparethethreenonlineartheories’successinexplainingtheflatteningofJapan’sPhillipscurve.
7.1Non-nestedmodelfitcomparison
Weperformthreehypothesistestingprocedurestocomparetheperformanceofthenonlinearmodels.
First,weregressPhillipscurveswhichnesttwononlinearmodels.Forexample,thefollowingequationneststheLaxton,Meredith,Rose(LMR)modelfromequation(5)andtheBall-Mankiw-Romer/Dotsey-King-Wolman(BMR/DKW)modelofequation(6):
∙µ
¶
µ
¶¸
πt=β(L)πt+[a+b|πt|]
φygapt−1φ−ygapt−1
+p
φygapt−2φ−ygapt−2
+δimpoilt+et
(19)
Asitturnsout,thecoefficientontrendinflationbispositiveandsignificantatthe1%level,whichisinlinewiththeBMR/DKWmodel.Thenonlinearityparameterφisestimatedtobe12.94,withasomewhatlargerstandarderrorthaninsections5or6,whichallinallsuggeststhattheLMR-convexitystillplaysarole.
TheresultswithaPhillipscurvenestingtheLMR-andLucas-modelsaresimilar:thereisevidenceforbothmodels.Ontheotherhand,regressingaPhillipscurveinwhichtheoutputgapcoefficientsdependonbothtrendinflationandthevarianceofinflationdoesnotyieldcon-clusiveresults.Toseewhy,notethatthecorrelationbetweentrendinflationandthevarianceofinflationis0.96.Inthepresenceofmulticollinearity,itisnotsurprisingthatbothvariablesenter
30
insignificantly.
Second,wediscussresultsfrompairwisenon-nestedtestsasdevelopedbyDavidsonandMacK-innon(1981).TheLMRconvexityturnsouttoperformpoorlyrelativetotheothertwomodels.ThecoefficientonthefittedvaluefromtheBMR/DKWmodel,whenaddedtoaLMRregres-sion,issignificantatthe5%level.ThissuggeststhattheBMR/DKWmodeladdsinformationbeyondthatcontainedintheLMRmodel.AnanalogousresultholdswhenweaddthefittedvaluefromtheLucasmodeltotheLMRmodel.Ontheotherhand,Davidson-MacKinnontestsfavortheBMR/DKWandLucasmodels.ThefittedvaluefromtheLMRmodeldoesnotentersignificantlyineithermodel.
Third,toassesswhichamongthemodelsinourmodelspaceismostlikelytocorrespondtothetruth,weapplyBayesianmodelaveragingmethodsasinBrock,Durlauf,andWest(2004).Inparticular,weusetheprocedureinKiley(2005)tocomputepseudo-posteriormodeloddsbasedonacomparisonoftheBayesianInformationCriteriafromthethreenonlinearmodelsandthelinearmodel.Thisprocedureassumesauniformpriordistributionoverthemodelspace.AsTable5documents,theresultsstronglyfavortheBMR/DKWendogenouspricingmodel.Accordingtothepseudo-posteriordistribution,theprobabilitythattheBMR/DKWmodelisthetruemodelis81.42%.Thepseudo-posteriormodeloddsfortheLucasmodelare18.58%.TheprobabilityforeithertheLMRmodelorthelinearmodeltobethetruemodelisvirtuallyzero.
7.2Assessment
Twooutofthreeproceduresyieldedconclusiveresults.Davidson-MacKinnontests,aswellasthecomputationofpseudo-posteriormodelodds,suggestedthattheLaxton,Meredith,Rose(LMR)modelprovidesalessaccuratedescriptionofthedatathanthetwoothermodels.
31
Inthissubsection,wetakeamoredetailedlookattheregressionresultsfromsection5,soastoexaminewhytheLMRmodelperformedpoorlyinthenon-nestedmodelhypothesistests.Beforedoingso,rememberfromsection5.1thatitisdoubtfulwhethercapacityconstraintscanbearationaleforconvexityatregionsofthePhillipscurvewhicharefarfromthecapacityconstraint.
ItturnsoutthattheaccuratefitoftheLMRmodelinaregressionofequation(5)over1971Q2-2004Q4ismostlydrivenbyitssuperiorfitaroundthetimeofthefirstoilpriceshock.Muchofthenonlinearityseemstospringfromthe1974Q1observation,whenoilimportpricessurged,annualizedcoreCPIinflationspikedto32%,andthepre-1974boomsuddenlyhalted.Asarobustnesstest,weperformregressionsforthethreenonlinearmodelsasinsection5,butoverasamplewhichexcludesallpre-1975observations.ItturnsoutthatthereisnoevidenceforLMR-typeconvexityoverthesample1975Q1-2004Q4.Moreprecisely,thestandarderroronthenonlinearityparameterφisthatlargethatnoinferencecanbedrawnastowhetherthePhillipscurveisconvexorlinear.Incontrast,theresultsfortheBMR/DKWandLucasmodelsarerobusttotheexclusionofobservationsfromtheoilshockepisode.Trendinflationandthevarianceofinflation,respectively,entersignificantlyatthe1%levelevenwhenpre-1975observationsareexcluded.
8Conclusion
Atadirectempiricallevel,ourpaperinvestigateswhydeflationdidnotaccelerateinJapannotwithstandinglargenegativeoutputgapsduringtheperiod1998-2002.Wefindthattheabsenceofacceleratingdeflationcannotbeadequatelyaddressedbypopularexplanationswhichassumealinearshort-runrelationbetweentheoutputgapandinflationwithatime-invariantslope.Giventhatfinding,thebodyofourpaperfocusesonthepathanddeterminantsofthePhillipscurve
32
slope.Wedocumentagradual,significantflatteningoftheJapanesePhillipscurvewhichpredatesthenineties.
Asforthedeterminantsofsuchtime-variationinthePhillipscurveslope,ourresultsfavortheBall-Mankiw-Romer/Dotsey-King-Wolmanhypothesisthatdecliningtrendinflationcreatedanenvironmentinwhichpricesbecamestickier,whichinturncausedthePhillipscurvetoflatten.AllbutoneofourtestslendequallystrongsupporttotheLucashypothesisthatadeclineinaggregateinflationvolatilityexacerbatedfirms’misperceptionsaboutrelativeprices,implyingaflatterPhillipscurve.WhilestoriessuchasLaxton-Meredith-Roseinwhichcapacityconstraintsengenderaconvexshort-runPhillipscurveareconsistentwiththedata,theyperformpoorlyincomparisonwiththetwoothermodels.
Onabroaderlevel,ourresultsareindicativefortheappropriatetheoreticalframeworktomodeltheoutput-inflationtrade-off.IfitisindeedageneralrulethatthePhillipscurveflattensastrendinflationdeclines,weseetwoimplicationsformonetarypolicymakersineconomieswheretrendinflationislowtodayrelativetopastexperience.
First,theBall-Mankiw-Romer/Dotsey-King-WolmanmodelimpliesthatthePhillipscurveinthosecountriesiscurrentlyflatterthanthestandardlinearmodelwouldsuggest.Allotherthingsbeingequal,thisimpliesahighersacrificeratio:ifthecentralbankbringsaboutadisinflation,theassociatedreductioninoutputwillbelargerthanitwouldappearfromthelinearmodel.
Second,althoughtheendogenouspricingmodelsimplythatthePhillipscurveturnsflatterastrendinflationdeclinestozero,thesemodelsdonotpredictthattheriskofadeflationaryspiralisnegligible.Onthecontrary,boththeBall-Mankiw-RomerandDotsey-King-Wolmanmodelsaresymmetricaroundzero.Oncetrendinflationturnsnegative,thesemodelsimplythatanyfurtherdecreaseintrendinflationisassociatedwithanincreaseinthefrequencyofpriceadjustment.
33
Thisinturnmeansthatanynegativeoutputgaphasstrongerdeflationaryeffects,thusincreasingtheriskofamorepronouncednegativeinteractionbetweendeflation,realactivity,andfinancialsectorvulnerabilities.
OuranalysisalsolendssomeempiricalsupporttotheLucasmodel.Thismodelimpliesthat,ineconomieswhereinflationiscurrentlymorestablethaninearlierdecades,thePhillipscurveisflatterthanthestandardlinearmodelwouldsuggest.Hence,thismodelimpliesthatinsucheconomies,theshort-runoutputcostsofdisinflationarehigherthantheywouldappearfromalinearmodel.
34
References
[1]Akerlof,GeorgeA.,WilliamT.Dickens,andGeorgeL.Perry(1996).“TheMacroeconomics
ofLowInflation.”BrookingsPapersonEconomicActivity1,1-76.
[2]Alberro,Jose(1981).“TheLucasHypothesisonthePhillipsCurve:FurtherInternational
Evidence.”JournalofMonetaryEconomics7,239-250.
[3]Ball,Laurence(1994).“WhatDeterminestheSacrificeRatio?”InMonetaryPolicy,edited
byN.GregoryMankiw,pp.155-193.Chicago,IL:UniversityofChicagoPress.
[4]Ball,Laurence,N.GregoryMankiw,andDavidRomer(1988).“TheNewKeynesianEco-nomicsandtheOutput-InflationTrade-Off.”BrookingsPapersonEconomicActivity1,1-82.[5]BankofJapan(2006).“TheNewEstimatesofOutputGapandPotentialGrowthRate”,
BankofJapanReviewSeriesNo.3.
[6]Bayoumi,Tamim(2000).“WhereAreWeGoing?TheOutputGapandPotentialGrowth.”In
Post-BubbleBlues;HowJapanRespondedtoAssetPriceCollapse,editedbyTamimBayoumiandCharlesCollyns,pp.-106.Washington,DC:InternationalMonetaryFund.
[7]Blanchard,Olivier(2000).“Bubbles,LiquidityTraps,andMonetaryPolicy.”InJapan’sFi-nancialCrisisanditsParallelstoU.S.Experience,editedbyMikitaniandPosen,pp.185-193.Washington,DC:InstituteforInternationalEconomics.
[8]Bonomo,Marco,andCarlosCarvalho(2004).“EndogenousTime-DependentRulesandIn-flationInertia.”JournalofMoney,Credit,andBanking36,1015-1041.
[9]Brock,WilliamA.,StevenN.Durlauf,andKennethD.West(2004).“ModelUncertainty
andPolicyEvaluation:someTheoryandEmpirics.”NBERWorkingPaperNo.10916.
35
[10]Burstein,ArielT.(2006).“InflationandOutputDynamicswithState-DependentPricing
Decisions.”JournalofMonetaryEconomics53,1235-1257.
[11]Davidson,Russell,andJamesG.MacKinnon(1981).“SeveralTestsforModelSpecification
inthePresenceofAlternativeHypotheses.”Econometrica49,781-793.
[12]Debelle,GuyandDouglasLaxton(1996).“IsthePhillipsCurveReallyaCurve?Some
EvidenceforCanada,theUnitedKingdom,andtheUnitedStates.”IMFStaffPapers44,249-282.
[13]DeFina,RobertH.(1991).“InternationalEvidenceonaNewKeynesianTheoryofthe
Output-InflationTrade-Off.”JournalofMoney,Credit,andBanking23,410-422.
[14]Dolado,JuanJ.,RamonMaria-Dolores,andManuelNaveira(2005).“AreMonetaryPolicy
ReactionFunctionsAsymmetric?TheRoleofNonlinearityinthePhillipsCurve.”EuropeanEconomicReview49,485-503.
[15]Dotsey,Michael,RobertG.King,andAlexanderL.Wolman(1999).“State-DependentPric-ingandtheGeneralEquilibriumDynamicsofMoneyandOutput.”QuarterlyJournalofEconomics114,655-690.
[16]Dotsey,Michael,RobertG.King,andAlexanderL.Wolman(2007).“AggregateDynamics
ofInflationandRealActivitywithFirm-LevelProductivityShocks.”Mimeo.
[17]Froyen,RichardT.,andRogerN.Waud(1980).“FurtherInternationalEvidenceonOutput-InflationTradeoffs.”AmericanEconomicReview70,409-421.
[18]Gertler,Mark,andJohnLeahy(2006).“APhillipsCurvewithanSsFoundation.”NBER
WorkingPaperNo.11971.
36
[19]Golosov,Mikhail,andRobertE.Lucas(2003).“MenuCostsandPhillipsCurves.”NBER
WorkingPaperNo.10187.
[20]Hamilton,James(1994).TimeSeriesAnalysis.Princeton,NJ:PrincetonUniversityPress.[21]Hansen,BruceE.(1992).“TestingforParameterInstabilityinLinearModels.”Journalof
PolicyModeling14,517-533.
[22]Harvey,Andrew(1994).TimeSeriesModels.Cambridge,MA:MITPress.
[23]Hess,GregoryD.,andKwanhoShin(1999).“SomeIntranationalEvidenceonOutput-InflationTrade-offs.”MacroeconomicDynamics3,187-203.
[24]Hirose,Yasuo,andKoichiroKamada(2003).“ANewTechniqueforSimultaneousEstimation
oftheOutputGapandPhillipsCurve.”BankofJapanMonetaryandEconomicStudies21,93-112.
[25]Ilmakunnas,Pekka,andHirokiTsurumi(1985).“TestingtheLucasHypothesisonOutput-InflationTrade-offs.”JournalofBusinessandEconomicStatistics3,43-53.
[26]Kamada,Koichiro(2005).“Real-TimeEstimationoftheOutputGapinJapananditsUse-fulnessforInflationForecastingandPolicymaking.”NorthAmericanJournalofEconomicsandFinance16,309-332.
[27]Kiley,MichaelT.(2000).“EndogenousPriceStickinessandBusinessCyclePersistence.”
JournalofMoney,Credit,andBanking32,28-53.
[28]Kiley,MichaelT.(2005).“AQuantitativeComparisonofSticky-PriceandSticky-Information
ModelsofPriceSetting.”ComputinginEconomicsandFinance2005No.183.
37
[29]Kim,Chang-JinandCharlesNelson(1999).State-SpaceModelswithRegimeSwitching.Cam-bridge,MA:MITPress.
[30]Kormendi,RogerC.,andPhilipG.Meguire(1984).“Cross-RegimeEvidenceofMacroeco-nomicRationality.”JournalofPoliticalEconomy92,875-908.
[31]Kuroda,Sachiko,andIsamuYamamoto(2003a).“AreJapaneseNominalWagesDownwardly
Rigid?”BankofJapanMonetaryandEconomicStudies21,1-30.
[32]Kuroda,Sachiko,andIsamuYamamoto(2003b).“AreJapaneseNominalWagesDownwardly
Rigid?”BankofJapanMonetaryandEconomicStudies21,31-68.
[33]Kuroda,Sachiko,andIsamuYamamoto(2005).“WageFluctuationsinJapanaftertheBurst-ingoftheBubbleEconomy:DownwardNominalWageRigidity,Payroll,andtheUnemploy-mentRate.”BankofJapanMonetaryandEconomicStudies23,1-29.
[34]Laxton,Douglas,GuyMeredith,andDavidRose(1995).“AsymmetricEffectsofEconomic
ActivityonInflation.”IMFStaffPapers42,344-374.
[35]Laxton,Douglas,DavidRose,andDemosthenesTambakis(1999).“TheU.S.PhillipsCurve:
TheCaseforAsymmetry.”JournalofEconomicDynamicsandControl23,1459-1485.[36]Lucas,RobertE.(1973).“SomeInternationalEvidenceonOutput-InflationTrade-Offs.”
AmericanEconomicReview63,326-334.
[37]Mourougane,Annabelle,andHideyukiIbaragi(2004).“IsThereaChangeintheTrade-Off
betweenOutputandInflationatLoworStableInflationRates?SomeEvidenceintheCaseofJapan.”OECDEconomicsDepartmentWorkingPaperNo.379.
38
[38]Morgan,Peter(2005).“Employment-theShifttoFlexibility.”HSBCspecialreport,February
2005.
[39]Nishizaki,Kenji,andTsutomuWatanabe(2000).“Output-InflationTrade-OffatNear-Zero
InflationRates.”JournaloftheJapaneseandInternationalEconomies14,304-326.[40]Nyblom,Jukka(19).“TestingfortheConstancyofParametersOverTime.”Journalofthe
AmericanStatisticalAssociation84,223-230.
[41]Phillips,AlbanW.(1958).“TheRelationbetweenUnemploymentandtheRateofChange
ofMoneyWageRatesintheUnitedKingdom,1861-1957.”Economica25,283-299.[42]Schaling,Eric(2004).“ThenonlinearPhillipsCurveandInflationForecastTargeting:Sym-metricVersusAsymmetricMonetaryPolicyRules”,JournalofMoney,Credit,andBanking36,361-386.
[43]Turner,Dave(1995).“SpeedLimitandAsymmetricInflationEffectsfromtheOutputGap
intheMajorSevenEconomies.”OECDEconomicStudies24,57-87.
[44]Zhang,LawrenceHuiyan(2005).“SacrificeRatioswithLong-LivedEffects.”International
Finance8,231-262.
39
Figuresandtables
Actual and Potential GDP (trillion 1995 yen), 1970Q1-2004Q4
600550
500
Actual real GDP450
Potential real GDP400
350
300
250
200
15019701975198019851990199520002005Source: US Federal Reserve, Board of Governors
Figure1
Note:sincetheFed’srecentpotentialoutputestimatesareconfidential,weextrapolatepoten-tialoutputfor1999Q1-2004Q4usingIMFstaffestimates/forecastsforpotentialoutputgrowth,asquotedinBayoumi(2000),asaguideline.
40
10
Output Gap (%), 1970Q1-2004Q4
5
0
-51970403020
Source: US Federal Reserve, Board of Governors
1975198019851990199520002005
Annualized Core CPI Inflation (%), 1970Q2-2004Q41050-5-101970
Source: Bank of Japan
1975198019851990199520002005
Figure2
Note:’AnnualizedCoreCPIinflation’standsforannualizedquarterlyinflationintheCon-sumerPriceIndexexcludingfreshfoods,whichtheBankofJapanadjustedforconsumptiontaxreformsinApril19andApril1997.
41
403020
Dynamic Out-Of-Sample Forecast from Linear Phillips Curve
Forecasted core CPI inflationActual core CPI inflationEstimation100-101970
Projection197519801985
Figure3
1990199520002005
Note:ThelinearPhillipscurveisestimatedover1971Q2-1997Q4;theforecastwindowis1998Q1-2004Q4.Theresultsuggeststhat,assumingastandardlinearrelationshipbetweentheoutputgapandinflation,thesizeofthenegativeoutputgapsinJapanwouldhavewarrantedacceleratingdeflationintheperiod1998-2002.
42
LinearModel:Time-invariantvs.Time-varyingOutputGapCoefficients
πt=β(L)πt+γ1,t(ygapt−1+pygapt−2)+δimpoilt+etSample:1971Q2-2004Q4β1β2β3β4γ1,tγ2,t=p.γ1,tδσepSumoutputgapcoefficientsSacrificeratioFitOLS(linear)0.67***(0.17)0.17(0.16)0.39***(0.15)-0.23(0.16)0.87**(0.36)-0.70**(0.35)0.018*(0.009)--0.81***(0.10)0.17**(0.07)1.47R2=0.85R=0.84Standarderrorsareinparentheses.
***indicatessignificanceatthe1%level;**at5%level;*at10%level.
Table1
Note:Therightmostcolumnshowstheresultsfromestimatingthestate-spacemodelconsistingofequations(3)and(4)bymeansoftheKalmanfilterandMaximumLikelihood.ThePhillipscurveislinear,yettheoutputgapcoefficientsareallowedtovaryovertimeasarandomwalk.’avg’indicatestheaverageofatime-varyingcoefficientanditsstandarderroroverthesample.Forcomparison,themiddlecolumnshowstheresultsfromestimatingastandardlinearPhillipscurvewithtime-invariantoutputgapcoefficients.
2MLE(linearTV)0.67***(0.08)0.17**(0.08)0.37***(0.08)-0.21***(0.07)0.75***(0.16)avg-0.58***(0.12)avg0.018***(0.004)1.33***(0.04)-0.77***(0.10)0.18***(0.04)avg1.39LLF=-255.9443
Random Walk Model: Time-Varying Output Gap Coefficients
21010-1TV coefficient on ygap(-2)TV coefficient on ygap(-1)-1197019801990200020100.6
-219701980199020002010
Sum of output gap coefficients0.40.20.0
19701980199020002010
Figure4
Note:ThisfiguregraphstheKalman-smoothedtime-varyingoutputgapcoefficientscorre-spondingtotheestimationresultsinTable1,alongwiththeir95%confidenceinterval.Notethatthesumoftheoutputgapcoefficientsisgraphedonadifferentscalethantheindividualoutputgapcoefficientsinthetoprow.
44
LinearPhillipsCurvevs.Laxton-Meredith-RosePhillipsCurve
h³φygapt−1φ−ygapt−1
πt=β(L)πt+γ1
´+p
³φygapt−2φ−ygapt−2
´i+δimpoilt+et
Sample:1971Q2-2004Q4β1β2β3β4γ1γ2=pγ1δφpFitQ-stat[withp-value]:4thlagQ-stat[withp-value]:12thlagOLS(linear)0.67***(0.17)0.17(0.16)0.39***(0.15)-0.23(0.16)0.87**(0.36)-0.70**(0.35)0.018*(0.009)∞-0.81***(0.10)R2=0.85/R=0.845.61[0.23]6.74[0.16]2NLS(LMR)0.70***(0.14)0.15(0.14)0.37**(0.15)-0.22(0.17)0.69**(0.30)-0.54*(0.29)0.019**(0.008)10.00***(1.83)-0.77***(0.12)R2=0.87/R=0.865.26[0.26]9.27[0.68]2Huber-Whitestandarderrorsareinparentheses.
***indicatessignificanceatthe1%level;**at5%level;*at10%level.
Table2
Note:TherightmostcolumnshowstheresultsfromestimatingaLaxton-Meredith-RosePhillipscurve.Thenonlinearityparameterφispreciselyestimated.AsFigure5demonstrates,itspointestimateimpliesafairlystrongdegreeofconvexityinthePhillipscurve,withaverticalasymptoteatanoutputgapof10%.Forcomparison,themiddlecolumninthetableabovegraphstheresultsfromestimatingalinearPhillipscurve.
45
43210
LMR Phillips Curve and Linear Phillips Curve
LMR Phillips curveEstimate phi=10.00Output gap term in Phillips curveLMR Phillips curveUpper bound 95% CI: phi=13.59Imposing linearity-1
-2-8
-6-4-20Figure5
2468
Output gap (%)
Note:Thisfiguregraphsγ1[(φygapt−1/(φ−ygapt−1))+p(φygapt−2/(φ−ygapt−2))],asestimatedinTable2,withrespecttotheoutputgap.Thedottedlinegraphsthesamefunctionimposingavalueforφwhichequalstheupperboundofthe95%confidenceintervalaroundthepointestimateforφ.
46
StandardPhillipsCurvevs.Ball-Mankiw-Romer/Dotsey-King-WolmanPhillipsCurve
πt=β(L)πt+[a+b|πt|][ygapt−1+pygapt−2]+δimpoilt+et
Sample:1971Q2-2004Q4β1β2β3β4γ1γ2=pγ1δabpFitQ-stat[withp-value]:4thlagQ-stat[withp-value]:12thlagOLS(linear)0.67***(0.17)0.17(0.16)0.39***(0.15)-0.23(0.16)0.87**(0.36)-0.70**(0.35)0.018*(0.009)γ10.00-0.81***(0.10)R2=0.85/R=0.845.61[0.23]6.74[0.16]2OLS(BMR/DKW)0.77***(0.10)0.18(0.12)0.22**(0.09)-0.17*(0.10)0.76avg-0.63avg0.019**(0.008)-0.53***(0.19)0.34***(0.05)-0.82***(0.07)R2=0.90/R=0.0.61[0.96]4.29[0.98]2Huber-Whitestandarderrorsareinparentheses.
***indicatessignificanceatthe1%level;**at5%level;*at10%level
Table3
Note:TherightmostcolumncontainstheresultsfromestimatingaPhillipscurveinwhichtheslopedependsontheabsolutevalueoftrendinflation.InlinewithBall-Mankiw-RomerandDotsey-King-Wolman,thecoefficientbontrendinflationispositiveandsignificantatthe1%level.Forcomparison,themiddlecolumnprovidestheresultsfromastandardPhillipscurveinwhichthecoefficientontrendinflationissettozero.
47
StandardLinearPhillipsCurvevs.LucasPhillipsCurve
πt=β(L)πt+[c+dvart(π)][ygapt−1+pygapt−2]+δimpoilt+et
Sample:1971Q2-2004Q4β1β2β3β4γ1γ2=pγ1δcdpFitQ-stat[withp-value]:4thlagQ-stat[withp-value]:12thlagOLS(linear)0.67***(0.17)0.17(0.16)0.39***(0.15)-0.23(0.16)0.87**(0.36)-0.70**(0.35)0.018*(0.009)γ10.00-0.81***(0.10)R2=0.85/R=0.845.61[0.23]6.74[0.16]2OLS(Lucas)0.83***(0.12)0.14(0.11)0.22**(0.09)-0.19*(0.10)0.66avg-0.52avg0.020**(0.008)-0.05(0.20)0.04***(0.01)-0.79***(0.10)R2=0.90/R=0.0.27[0.99]2.79[1.00]2Huber-Whitestandarderrorsareinparentheses.
***indicatessignificanceatthe1%level;**at5%level;*at10%level.
Table4
Note:TherightmostcolumncontainsresultsfromaPhillipscurveinwhichtheslopedependsonthevarianceofinflation.InlinewiththeLucasmisperceptionstheory,thecoefficientdonthevarianceofinflationispositiveandsignificantatthe1%level.
48
BayesianModelAveraging:Pseudo-PosteriorModelOdds
Ball-Mankiw-Romer/Dotsey-King-WolmanLucasLaxton-Meredith-RoseLinearTable5
81.42%18.58%1.95E-06%1.84E-09%Note:Thistabledisplaysthepseudo-posterioroddsforeachofthefourlistedmodelstobethetruemodel,accordingtoaBayesianModelAveragingprocedureasinBrock,Durlauf,West(2004).Thisprocedureplacesequalpriorprobabilityoneachofthemodels.
49
因篇幅问题不能全部显示，请点此查看更多更全内容
Copyright © 2019- baomayou.com 版权所有 赣ICP备2024042794号-6
违法及侵权请联系：TEL:199 18 7713 E-MAIL:2724546146@qq.com
本站由北京市万商天勤律师事务所王兴未律师提供法律服务