A survey on time-varying parameter taylor rule: a model modified with interest rate pass-through

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A

survey

on

time-varying

parameter

Taylor

rule:

A

model

modiﬁed

with

interest

rate

pass-through

Ebru

Yu¨ksel

a,

*

,

Kivilcim

Metin-Ozcan

b,1

,

Ozan

Hatipoglu

c,2

a_Hacettepe_University,_Department_of_Industrial_Engineering,₀₆₈₀₀_Beytepe,_Ankara,_Turkey b_Bilkent_University,_Department_of_Economics,₀₆₈₀₀_Bilkent,_Ankara,_Turkey

c_Bogazici_University,_Department_of_Economics,_Natuk_Birkan_Hall,₃₄₃₄₂_Bebek,_Istanbul,_Turkey

1. Introduction

Recently,NewKeynesianmodelswithmicrofoundations havegainedalotofattention.These modelsraiseinterestinreducinginﬂationvolatilityandaccordinglyinﬂationtargetinginorderto

ARTICLE INFO Articlehistory: Received9August2011

Receivedinrevisedform10July2012 Accepted4August2012 JELclassiﬁcation: E43 E52 E58 Keywords:

ExtendedKalmanﬁlter(EKF) Interestratepass-through Monetarypolicy Taylorrule

Time-varyingparameter(TVP)

ABSTRACT

Today,theprimeaimofcentralbankingistoachievepricestability and,toalesserextent,outputstability.Tothisend,centralbanksuse variousmonetarypolicyrules.Thispaperintendstoprovideabroad surveyoftheliteratureonTaylor-typemonetarypolicyruleswitha time-varying parameter (TVP) specification.To include the TVP feature,somemodificationismadeinthemonetarytransmission mechanismofTaylor-typemonetarypolicymodelstoaccountfor the changing risk preference of individuals. In line with this approach,weintroduceaninterestratepass-throughspecification of the monetary transmission process in a general equilibrium modeltoaccountforthevaryingperceptionsofriskbyindividuals. WeincludeanapplicationforTurkeyandestimatethetime-variable parameters of the model by employing a structural extended Kalmanfilter(EKF).TheresultsindicatethattheEKFperformsbetter thanthestandardKalmanfilterinestimatingthereactionfunction ofthecentralbank.

ß2012ElsevierB.V.Allrightsreserved.

*Correspondingauthor.Tel.:+903122978950;fax:+903122978953.

E-mailaddresses:eyuksel@hacettepe.edu.tr(E.Yu¨ksel),kivilcim@bilkent.edu.tr(K.Metin-Ozcan),

ozan.hatipoglu@boun.edu.tr(O.Hatipoglu).

1

Tel.:+903122902006;fax:+903122665140.

2

Tel.:+902123597640;fax:+902122872453.

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establishmacroeconomicstability.Today,theprimeaimofcentralbankingistoachievepricestability and,toalesserextent,outputstability.AccordingtoNewKeynesianmodels,thedesignofoptimal monetarypoliciesandrulesareessentialinestablishingpricestability.Inthiscontext,assuggestedby

Taylor(1993)andWoodford(2003),short-terminterestrates,usedaspolicyinstruments,arekey variables.Theimportanceoftheuseofinterestratepatternsfordevelopingefﬁcientmonetarypolicy rules,especiallyforinﬂationtargetingcountries,hasbeenfurtherstressedbyTaylor(1999a).Hence,it becomesessentialforcentralbankstodetermineaccurateinterestraterulestoachievepricestability inaneconomy(see,forexample,Claridaetal.,1999;Taylor,1993,1999b).

Inthelastdecade,considerableattentionhasbeengiventotheTVPspeciﬁcationofmonetary policy rules. There are mainly three factors that necessitate the use of dynamic parameter speciﬁcation.First,monetarypolicy rulesarebasedontheattitudeofpolicymakerstowardthe structureoftheeconomyandcontradictingobjectivesofmonetarypolicy.Therefore,theparameters ofinterestraterulesaresubjecttochangeduetothechangingnatureofthebehaviorofpolicymakers andpolicyobjectivesas demonstratedbyFaveroandRovelli(2003),Ozlale (2003)andValente (2003).

Second,centralbanksutilizeawiderinformationsetwhendevisingpolicydecisionsinsteadof relyingonlyonasinglepolicyruleequation.Thus,forexample,ifthepolicyruleisaTaylor-type interestraterule,3thesamelevelsofoutputgapandinﬂationmaynotproducethesamelevelof interestrateindifferentperiodssincetheinformationsetusedbycentralbankswillbedifferentfor eachperiod.Theunstablenatureofthecoefﬁcientsofapolicyrulecantranslateintononlinearitiesin thecentralbank’sreactionfunction,whichisanotherissuethatshouldbeaddressed.Forinstance,

NobayandPeel(2003)discusstheoptimaldiscretionarymonetarypolicyundertheassumptionthat thecentralbankhasanasymmetriclossfunction.FormonetarypolicyintheUK,MartinandMilas (2004) concluded that policymakers use discretionary policy for inflation targeting and that monetary policy responds to inflation nonlinearly. Empirically, commensurate with existing asymmetriesinthepatternsofinterestratesetting,Doladoetal.(2005)arguedthattheEuropean Central Bank’s behavior can beexplained by the nonlinear optimal policy function, unlikethe behavioroftheUSFed.Castro(2011)latersupportedthisfinding,suggestingthattheEuropean CentralBankandtheBankofEnglandfollownonlinearmonetarypolicyruleswhereastheUSFedacts accordingtoa linearTaylorrule.However,Petersen(2007)previouslyfoundthatthemonetary policyoftheUSFedcouldbeassociatedwithanonlinearpolicyruleonceinflationapproachesa certainthreshold.Likewise,Surico(2007)investigatedtheasymmetricbehaviorofthemonetary policyoftheUSFed.

Furthermore,variationsinthemonetarypolicytransmissionmechanismcanbethethirdreason fortheunstablenatureofthecoefficientsofapolicyrule.Thus,interestraterulesshouldbetreatedas dynamicinsteadofstatic.Intuitively,duetoshiftsinthecoefficientsofpolicyrules,studiesusing stableparametersmaybemisleadingorinefficientinformulatingpolicyadvice.ParalleltotheLucas (1976)critique,inordertoconductempiricalpolicyanalysis,dynamicparametermodelsaremore appropriateforaccountingforpolicyshiftscontrarytofixedparametermodels.

TheaimofthepresentsurveyarticleistoreviewtheliteratureonmonetarypolicyruleswithaTVP speciﬁcation for a closedeconomy.4 _Following _Taylor₍₁₉₉₃₎_, _numerous _works_have _studied_the

implicationsofvariousversionsoftheTaylorrulefordifferentcountries;asaresult,theuseof Taylor-typeinterestraterulesinanalyzingpolicyshiftshasincreasedsubstantially.Afterareviewofthe literature,thisarticleevaluatestheperformanceoftheTaylorruleinthetransitionofmonetarypolicy

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Taylorrulesaresimplemonetarypolicyrulesthatprescribehowacentralbankshouldadjustitspolicyinstrument,interest rate,inasystematicmannerinresponsetodevelopmentsininﬂationandmacroeconomicactivity.Mostofthesurveypapers reviewthedevelopmentandcharacteristicsofTaylorrulesinrelationtoalternativemonetarypolicyguidesanddiscusstheir roleforpositiveandnormativemonetarypolicyanalysisasinOrphanides(2007)andClaridaetal.(1999).

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Thetheoreticalliteraturehasmainlyassumedaclosedeconomyframework.Literaturethatanalyzestheopeneconomy monetarypolicytoolsalsoexists.Butinthissurveyarticlewewouldliketofocusonlyontheinterestratechannelratherthan theexchangeratechannel,sincethemainopeneconomyalternativesmayperformpoorlyinthefaceofspecifictypesof exchangerateshocks,suchasarulebasedonamonetaryconditionsindex(MCI).SincetheMCIisafunctionoftherealexchange rateitisinfluencedbyeventssuchastermsoftradeshocksandchangesinbusinessandconsumerconfidence,whichdonot necessarilyaffectinterestrates.

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actions over the economy. The Taylor rule suggests that ﬁrms and individuals shape their consumptionandinvestmentdecisionsaccordingtotheshort-termpolicyrate,whichtheyfacemore directly.5 _In_opposition,_we_argue_that_individuals_do _not_face_the_short-term_policy_rate_directly.

Instead,dependingontheirriskandliquiditypreferences,firmsandhouseholdsuseanotherinterest rate,thelong-termmarketinterestrate,6inmakingtheirconsumptionandinvestmentdecisions. Thus,toaccountforthevaryingriskpreferenceofindividuals,wewillconsidertheinterestrate pass-throughspecificationinastructuralmodelwhich,toourknowledge,hasnotyetbeeninvestigated deeply.Theaddedvalueofourrecentsurveyarticleisonthetime-varyingparameterTaylorrule, whichisamodifiedmodelwithinterestratepass-through.Toourknowledgethismodificationhasnot beenincludedintheTaylorrulespecificationbefore.

OurpapercontributestothecurrentdebateontheefficiencyofTaylor-typerulesinexplainingthe monetarytransmissionmechanismin aneconomy.Anotherimportantaspect ofourarticleisthe introductionoftheEKF techniqueasa newestimationmethodology.Thefactthat theEKFisnot widelyemployed for estimating nonlinearsystems in this field makes this study significantfor demonstratingthestrengthoftheEKFinpredictingTVPmodels.Thus,thispapermainlycontributes tothecurrentliteraturebyapplyingamechanicalstatisticaltooltothefieldofmonetaryeconomics. Wehandletheissuewithinasystemofequations,whereweallowthesystemparameterstovaryover time,therebycapturingthevolatilenatureofmacroeconomicvariables andtheunstablerelation betweenthem.Thesecharacteristicsofthemodelinduceustoemployanonlinearstatespacemodel, wheretheunobservedstatevariablesandthetime-varyingparameters,whichappearinthemodelin anonlinearform,canbeestimatedsimultaneously.Inthiscase,theEKFemergesasanappropriate estimationalgorithm.Asimpliedabove,suchanapproachhasnotyetbeenemployedtostudytheTVP Taylorrulemodifiedwithinterestratepass-through.InSection2,weprovidealiteraturereviewon TVPmonetarypolicyrulesindetail.Section3presentsthestructuralmodelanditsdynamics,while Section4introducestheinterestratepass-throughspecificationtoourstructuralmodelanddiscusses theefficiencyofTaylor-typepolicyrules.Section5givessomebriefinformationaboutthestatespace modelandthecharacteristicsofEKF.Section6estimatesthetime-variableparametersofthemodelby employingastructuralEKF.Finally,Section7concludesthestudy.

2. LiteraturereviewonTVPmonetarypolicyrules

Substantialeffort isdevotedtoenactingmonetarypolicychangesandtheTVPspeciﬁcationof monetary policy rules. The changes in policy implementation have been captured by various estimation methods such as subsample analysis, generalized method of moments (GMM), least squares(LS),maximumlikelihoodestimation(MLE),vectorautoregression(VAR),smoothtransition regression,MarkovswitchingandtheKalmanﬁlter.

Juddand Rudebusch(1998)illustratedhowtheFed’sreactionfunctionhaschangedovertime usingordinaryleastsquares(OLS)andsubsampleanalysis.Thestudyresultedintheparametersofthe Taylor-typeruledifferingsigniﬁcantlyforeachsub-periodconsidered,indicatingthatthemonetary policyregimevariesintime.Thisstudyalsopointedoutthedependencyofmonetarypolicyonthe attitudeofpolicymakerstowardthestructureoftheeconomy.Similarly,Claridaetal.(2000)used GMMtoshowthat theUS monetarypolicychangedsigniﬁcantly afterPaulVolcker became the chairmanoftheFed.Paralleltothesestudies,Orphanides(2004)providedevidenceaboutthechanges

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Thisstudytriestoconnectthepolicyrateandthelong-termratestoaffectconsumptionandinvestmentdecisions.This analysiscanalsobeperformedinclosereferencewiththeexpectationstheoryoftheyieldcurveandacriticalassessmentofthe arbitrageconditionusuallyemployedtoexplaintheshort-termandlong-termrateconnection.However,thisanalysisisleftas subjectmatterforfurtherresearch.

6_The_long-term_interest_rate_plays_an_important_role_in_the_conduct_of_monetary_policy._Especially,_the_recent_ﬁnancial_crisis

highlightedtheimportanceofunderstandingalternativewaystoconductmonetarypolicy.Apotentialuseforlong-term nominalinterestratesisthepossibilityofusingthemasinstrumentsofmonetarypolicy.Infact,previousresearchsuggeststhat long-terminterestraterulessharethedesirablepropertiesofTaylorrules,cansupportuniqueequilibria,andthattheir performanceisbetterthanthatofconventionalTaylorrules(seeMcGoughetal.,2005;Kulish,2007;Gerlach-Kristenand Rudolf,2010;JonesandKulish,2011).IntheUnitedStates,theUnitedKingdom,Canada,Japanandtheeuroarea,shortrates havebeenclosetozeroduringtherecentcrisis,whilelongrateshaveremainedwellabove,suggestingthattheremaybegreater capacitytostimulatetheeconomywithlong-termrates.

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intheinterestrateruleoftheUSusingestimationsofaforward-lookingTaylorrulefortwo sub-periods.

StudiesthatusetheKalmanfiltertoestimateTVPsofTaylorruleincludeElkhoury(2006),Trecroci andVassalli(2006),TrehanandWu(2007)andHatipogluandAlper(2009).Elkhoury(2006)examined theTVPmonetarypolicyruleforanopeneconomy,Switzerland.ThestudyusedtheKalmanfilterto embedpolicyshiftsandstructuralchangesintothemodelandfoundthattheuncertaintyassociated withthepolicyrulewasmostlyduetothetime-varyingcharacterizationoftheparametersand,toa lesserextent,monetaryshocks.TrecrociandVassalli(2006)estimatedaforward-lookingTVPTaylorrule fortheUK,Germany,France,ItalyandtheUSusingtheKalmanfilter.Theresultsdemonstratedthatthe countriesanalyzedhavedifferentinterestraterulesandthatTVPTaylorrulesarepreferredoverfixed parameterrulesincapturingthevariationsinthepolicyrates.Furthermore,thecoefficientsofthepolicy ruleschangeovertimeinagradualfashion.TrehanandWu(2007)employedtheKalmanfiltertopredict aTaylorruleforthebackward-lookingUSeconomy,focusingonatime-varyingequilibriumrealinterest rate.TrehanandWu(2007)concludedthattakingintoaccounttimevariationintheequilibriumreal interestratemakesasubstantialdifferenceintheassessmentofmonetarypolicy.HatipogluandAlper (2009)estimatedanaugmentedTaylorpolicyrulethatrespondstoanexchangerategapinthecontextof emerging markets utilizing Turkish data. To estimate time-varying parameters and unobserved variablessuchastheexchangeratetargetandpotentialoutputsimultaneously,theyemploydualEKF, whichallowsthemtotraceanychangesincentralbankbehavior,includingregimeshifts.

Boivin(2006),Jalil(2004),KimandNelson(2006)andMandler(2007)usedtheKalmanfilterand MLEtogethertoestimateatime-varyingTaylorrulefortheUS.Jalil(2004)estimatedaTVP backward-lookingTaylorrulewithex-postandreal-timedatafor theUS andstated thatthereare gradual adjustmentsinthecoefficientsofthepolicyruleintheUS,whichcannotbecapturedadequatelyby sub-sampleanalysis.Boivin(2006)estimatedaforward-lookingTaylorrulefortheUSemployingthe Kalmanfiltertoconstructalikelihoodfunction.TheconclusionwassimilartothatofJalil(2004)and

Trecroci and Vassalli (2006)in the sensethat the parameters ofthe Taylor rulewere changing gradually.Following Boivin(2006),Kim and Nelson(2006)attemptedtocharacterizea forward-lookingTaylorrulewithTVPusingex-postdataandatwo-stepMLEprocedurewiththeKalmanﬁlter toestimatethemodel.Theirempiricalresultswereinfavorofthedivisionofthemonetarypolicy historyoftheUSintothreeperiodsinsteadoftwo(contrarytoOrphanides,2004).Mandler(2007)

suggestedtheuseoftheTaylorrulewithTVPsandanunobservedcomponentsmodelfortheoutput gaptogethertopredictuncertaintyinthefuturevaluesoftheFedrateusingtheMLEtechniqueviathe Kalmanﬁlter.Mandler(2007)concludedthatthepredicteduncertaintycanbedividedintothree types,namelyuncertaintyduetothetime-dependentcoefﬁcientsoftheTaylorrule,uncertaintyabout futureeconomicevents,andresidualuncertainty.

Canova and Gambetti (2004), Cogley and Sargent (2001), and Mesonnier and Renne (2007)

employedVARrepresentationwiththeKalmanfiltertomodelaTVPTaylorrule.CogleyandSargent (2001)showedempiricallythatafterWorldWarII,policyactionsvariedsignificantlywithrespectto thestatusoftheeconomy,implyingthatthecoefficientsinthepolicyrulechangewithtime.Asimilar conclusion wasdrawn by Canovaand Gambetti(2004) as a resultof examiningchanges in the structureoftheUS economyviaa structuralVARframework.TheirworkdiffersfromCogleyand Sargent(2001)inthesensethatstructuralshockswerealsoincludedintheiranalysis.Fortheeuro area,MesonnierandRenne(2007)examinedtheTVPpropertyofthenaturalrateofinterest.Thestudy suggestedaTaylor-typepolicyrulewithatime-varyingnaturalrateofinterestfortheeuroareausing theKalmanfilter.

PlantierandScrimgeour(2002)estimatedtheTaylorrulewithaTVPspecificationemployingthe KalmanfilterwithOLStorevealthattheneutralrealinterestrateofNewZealandfollowsadownward trendinrecentyears.Horvath(2006)modeledvariousformsoffixedparametersandTVPTaylor-type rulesfortheCzechRepublicusingGMMandtheKalmanfilter.Theresultsdemonstratedthatthe equilibrium interest rate has decreased steadily over time. In addition to the previous studies involvingtheeuroarea,Kuzin(2006)estimatedabackward-looking(asopposedtoforward-looking) Taylorrulewithtime-dependentcoefficientsusingMarkovswitchingmodelsandtheKalmanfilterfor Germanyonly.TheconclusionwassimilartotheworkofTrecrociandVassalli(2006)inthattheTVP Taylorruleperformedwellincapturingthepolicyshifts.

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Orphanides and Williams (2005) adopted time variation in the parameters of the model by allowingagentstoupdatetheirexpectationsaboutthestructureoftheeconomyandmonetarypolicy. Forthis,theyusedaVARandOLSframeworkandinvestigatedchangesintheviewofthepolicymakers andmonetarypolicyimplementationintheUS.Likewise,SimsandZha(2006)documentedinferences aboutmonetarypolicychangesintheUSbyallowingtimevariationinboththecoefﬁcientsofthe Taylorruleand variancesof shocks totheeconomywithina structural VARframework. Models allowingchangesintheparametersofdisturbancesandthemonetarypolicyfunctionwerefoundto bethebest-ﬁtmodelsfortheUSdata.

Wesche(2003)performedaTVPTaylorruleanalysisforthecountriesconsideredinTrecrociand Vassalli(2006), reaching a similar conclusion despite using a different estimation procedure, a Markov-switchingmodelwithindependentswitchingprocessesfortheTVPsoftheTaylorruleand variances of disturbances. Later, Wesche (2006) demonstrated the changing preferences of policymakersfor interestrate setting in a Markov-switchingframework for theUS, theUK and Germany.OwyangandRamey(2004)alsoemployedaMarkov-switchingmodeltomeasuretheshifts intheparametersofthepolicyruleoftheUSFed.Paralleltopreviousworks,Partouche(2007)also estimatedaforward-lookingTVPpolicyrulefortheUS.InsteadoftheKalmanﬁlterthisstudyadopted adifferenttechnique,whichcombinedtheGMMframeworkwithsmoothingsplines.Suchatechnique is not restrictive on econometric terms in that it imposes no constraints on the form of heteroscedasticityoftheshocktermsandthecorrelationsbetweentheregressorsanddisturbances. Likewise,McCulloch(2007)estimatedaTVPforward-lookingTaylorrulefortheUSusingadifferent method,adaptiveleastsquares(AdaptiveLS),tomodelatime-varyingstructuralVARframework. Recently,GerlachandLewis(2010)usedasmoothtransitionregressionmodeltoshowtheshiftsin theparametersofthemonetarypolicyruleoftheEuropeanCentralBankduringtheﬁnancialcrisis.A summaryoftheliteratureonTVPpolicyrulesispresentedinTable1.

Table1

SummaryofliteratureonTVPpolicyrules.

Methods Articles

Subsample OLS JuddandRudebusch(1998)

Orphanides(2004)

GMM Claridaetal.(2000) Surico(2007)

KalmanFilter TrehanandWu(2007)

TrecrociandVassalli(2006) Elkhoury(2006)

HatipogluandAlper(2009)

MLE Boivin(2006)

Jalil(2004)

KimandNelson(2006) Mandler(2007)

VAR CogleyandSargent(2001) CanovaandGambetti(2004) MesonnierandRenne(2007)

OLS PlantierandScrimgeour(2002)

GMM Horvath(2006)

MarkovSwitching Kuzin(2006)

VAR SimsandZha(2006)

OLS OrphanidesandWilliams(2005)

MLE MarkovSwitching Wesche(2003)

Wesche(2006)

OwyangandRamey(2004)

GMM Partouche(2007)

Castro(2011) Doladoetal.(2005)

AdaptiveLS McCulloch(2007)

Smoothtransition GerlachandLewis(2010)

MartinandMilas(2004) Petersen(2007)

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3. Themodel

Ourbaselinemacroeconomicframeworkisdescribedwithadynamicgeneralequilibriummodel containingmoney.Wewillsimplyconsidertheclosedeconomycase.Frictionsintheeconomyare providedbynominalpricerigidities,whichmake themodelmorerealistic(andexcludeperfectly flexibleprice-settingbehavior).ThisrigidityisprovidedusingCalvo(1983)typestickyprice-setting. Firms are monopolistically competitive and produce differentiated goods, implying that goods marketsarealsomonopolisticallycompetitive.Infinitelylivedhouseholdsaretheownerofthefirms, thatis,wehaveproducer/consumeragents.Thecentralbankusesashort-termnominalinterestrate asthemonetarypolicyinstrument.Therefore,moneysupplyisdeterminedendogenouslytoachieve thedeterminedlevelofnominalinterestrate.

Householdsbuyconsumption goods, supply laborand holdbonds(viaa ﬁnancial agent) and money.Firmshirelabor,producedifferentiatedgoodsandselltheminmonopolisticallycompetitive goodsmarketsasgiveninDixitandStiglitz(1977).UsingthenotationofWalsh(2003),theutility functionofthehouseholdisdescribedasafunctionofconsumptionofdifferentiatedgoodsCt,real

moneybalancesMt/Pt,andtimeallocatedtoemploymentNt.Theobjectiveofthehouseholdisto

maximizethepresentworthoftheexpectedfutureutilitygivenby

EX 1 t¼0

b

t Ct1s 1

s

þ

g

1b Mt Pt 1b

x

N 1þh t 1þ

h

" # (1)

subjecttothebudgetconstraint

CtþMt Pt þBt Pt ¼ Wt Pt NtþMt1 Pt þð1þit1Þ Bt1 Pt þ

P

t (2)

whereBtisthenominalholdingsofone-periodbonds,Wtisthenominalwage,

P

tistherealproﬁt

transferredfromﬁrmsanditisthenominalinterestratefacedbyhouseholds.

Therepresentativeﬁrm,ontheotherhand,maximizesitsproﬁtgivenby

max pjt Et X1 i¼0

v

i

_b

i Ctþi Ct s _p jt Ptþi

cj;tþi

’

tþicj;tþi

(3)

where

v

i_is_the_probability_of_unchanging_price_of_good_j_from_period_t_to_period_{t + i,}_and

_w

tistheﬁrm’s

realmarginalcost.

Attheequilibrium,thePhillip’scurveisderivedasafunctionofoutputgapxt¼ytytwhereytis

theactualoutputandy

tisthepotentialoutputrespectively,andtheanticipatedinﬂationisasfollows:

p

t¼

k

xtþ

b

Et

p

tþ1þmt (4)

wheremtisacost-pushshocktotheNewKeynesianPhillipscurve.

Theaggregatedemandcurvecanbeexpressedby

xt¼Etxtþ1

1

s

ðitEt

p

tþ1Þþut (5)

whereutisanexogenousproductivityshock.

Thefactthatthemonetarypolicyinfluenceseconomicactivityintheshorttermhasbeenwidely discussedintheliterature(see,forexample,BernankeandBlinder,1992;BernankeandMihov,1997; Bernankeetal.,1997;Christianoetal.,1996,1998;Gali,1992).Monetarypolicydecisionsareusedto establishastableeconomyintermsofpricesandoutputgrowth.Inthisrespect,itisnecessaryto transmitmonetarypolicyactionstomacroeconomicvariablessuchasinflationandoutputsothatthe interrelationsamongthesevariablescanproducethegroundsofasteadyeconomy.Forthispurpose, differenttransmissionmechanisms(interestrate,exchangerate,assetprices)areusedtodisseminate changesinthepolicyvariablestootherrealandnominalvariables.Inourmodel,weusedinterestrate asthemonetarypolicytoolthattransmitstheactionsofmonetaryauthoritytothefinancialsystem andrealactivity.

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In order to specify the monetarytransmission mechanism, it is necessary to determine the behaviorofmonetarypolicyimplementedbythecentralbank.Intheliterature,itiscommontousea

Taylor(1993)typemonetarypolicyrule,whichrelatestheshort-terminterestratetobothinﬂation andoutputgap.Therefore,theTaylorruleisexpressedbelowtoclosethemodel:

itp¼iþ

d

pðEt

p

tþ1

p

Þþ

d

xEtxtþ1þ

n

t (6)

wherei*isthedesiredrate,

p

*isthetargetedinﬂationand

v

tstandsfortheshockstotheshort-term

interestrate.

Typically,theinterestratefacedbyhouseholdsandﬁrms(inEq.(5))istakenequaltothepolicy interestratesetbythecentralbank(inEq.(6)).Then,thecommonpracticeinempiricalstudiesisto performasimulationand/orempiricalstudyforconductingamonetarypolicyanalysisandextracting policysuggestionsusingtheaforementionedstructuralequationsandmonetarypolicyrule(see,for instance,Ball,1997;Claridaetal.,1999;LeitemoandLønning,2006;RudebuschandSvensson,1998; Schmitt-GroheandUribe,2002).

4. Interestratepass-through

In astructuralmodelofmonetarypolicyanalysis,themonetarytransmissionmechanismisof paramount importance. Since policy decisions affect the economy through these transmission channels,thedynamicsofpropagationmechanismsshouldbeincludedinapolicyanalysis.Inthe literature,itisproposedthatpolicydecisionsaretransmittedtotheeconomyviatheshort-termpolicy interestrate.Suchaconstructionimplicitlyassumesthathouseholds/firmsrealizethepolicyinterest ratewithoutresortingtoinformationfromanymediasource,andthatmacroeconomicvariablessuch asinflationandaggregateoutputaredirectlyaffectedbythepolicyrate.Nevertheless,households/ investorsin theeconomydo notrealize policyratesdirectly. Onthecontrary, short-termpolicy interestratesareindirectlyrecognizedbyagentsthroughtheactionsoffinancialinstitutions(e.g. banks)thatcollectdepositsfromhouseholdswithdifferentmaturitiesandbuybondsfromthecentral bankusingthesedeposits.Sincethesedepositsandcreditsspreadonlonghorizons,investorsrequire highinterestratestocompensatefordecreasedliquidityandhighercreditrisk.Hence,theinterest ratefacedbyhouseholdsisnottheshort-termpolicyinterestratebutinfactthelong-termmarket interestrate.Changesinthepolicyrateleadtochangesinthelong-termrate,whichresultsinchanges in investment, consumption and finally aggregate output. Thus, the direction of the monetary transmissionmechanismisfrompolicyratetolong-termrateandthentooutputandinflation.7

AsinNelson(2002),applicationoftheexpectationstheoryofthetermstructurealsoleadsustothe conclusionthattheaggregatedemandfunctionincludesthelong-terminterestrateinsteadofthe short-termrate.IterationsonEq.(5)generate

xt¼Etxtþ1 1

s

ðitEt

p

tþ1Þþut ¼Etxtþ2 1

s

ðEtitþ1Et

p

tþ2Þ 1

s

ðitEt

p

tþ1ÞþEtutþ1þut¼ xt ¼ 1

s

ðilt

p

ltÞþut whereil

t¼EtP1j¼0itþj

p

lt¼EtP1j¼0

p

tþ1þj andut¼EtP1j¼0utþj; which isthesumof theexpected

futuredemandshocks(productivityshocks).

Itiswidelyacceptedthataggregatedemandisdependentonlong-terminterestratesratherthan short-terminterestrates(see,forinstance,Bascietal.,2007;Coricellietal.,2006;Rotembergand Woodford,1999;Taylor,1995;Woodford,1999). Sincethecentralbankonlyusestheshort-term

7

However,eventhoughaggregatedemandisdependentonlong-terminterestratesratherthanshort-terminterestrates,the short-terminterestrate,orpolicyrate,alsohasitsdirecteffectsonoutputandinﬂation,asiswidelyrecognizedintheliterature onTaylorrules.

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interestrateasamonetarypolicytool,thereshouldbeatransitionequationbetweenthemarket interestrateandthepolicyrate,withtheintentionthatbychangingthelatter,thecentralbankcan impacttheeconomyaccordingtothisconnection.Althoughtheliteratureontheinterestrate pass-throughandthetermstructureoftheinterestratehaselaboratedonthisissue,toourknowledgeno attempthasbeenmadetoapplytheinterestratepass-throughspecificationinastructuralmodelof monetarypolicyanalysis.Therefore,themaincontributionofthepresentpaperistheinclusionofthe interestratepass-throughspecificationwithaTaylor-typemonetarypolicyruleinaNewKeynesian model.Particularly,aTVPinterestratepass-throughspecificationisaddedtothestructuralmodelina simplewaytoaccountforthemonetarytransmissionmechanismintheeconomy.Thisspecificationis alsofunctionalinaccountingforthechangingattitudeofinvestorstowardrisk.Itwouldnotbewrong toclaimthatsuchadesigncouldalsoprovidethemeansforexaminingthetransitionfromshort-term tolong-terminterestratesunderdifferentmonetarypolicies.

Consequently,ourcontributiontotheabovemodel,givenbyEqs.(4)–(6),istheinclusionofthe interest ratepass-throughas adifferentmonetarytransmission mechanism.The transitionfrom policyratetoaggregateoutputandinﬂationisrealizedbymeansofthelong-terminterestrate.In ordertocompletetheabovemodel,weincorporatetheinterestratepass-throughrelationship,which toourknowledgehasnotyetbeenimplementedintheliterature.Theinterestratepass-through relationshipestablishesthelinkbetweentheshort-termpolicyrateandthelong-terminterestrate. SimilartoKwapilandScharler(2006)andSørensenandWerner(2006),thelong-terminterestrateis modeledasafunctionofitslag,thepolicyrateandariskcomponent,whichisgivenbelow:

it¼

l

1it1þ

l

2itpþ

e

t (7)

whereitpstandsfortheshort-termpolicyinterestrateandit1capturesthedegreeofthemonetary

policyinertia.The interest ratepass-throughliterature statesthat the long-terminterestrate is positivelydependentonitslagandpolicyrate.Hence,allthecoefﬁcientsinthisequationareexpected tobepositive.Theerrorcomponent,

e

t,capturestheriskpreferenceofhouseholdsandﬁrms.

4.1. Empiricalstudiesonriskmodeling

TheerrorterminEq.(7)canberegardedastheriskpremiumcomposedofdefaultrisk,liquidityfactor andinflationriskpremium.Defaultriskaccountsforthepossibilityofaborrowerfailingtorepaythe principal and interest payments of a credit on time. Liquidity is another factor that affects the determinationofinterbankandmarketinterest rates(Hubbard,2001). Theperceptionofinvestors towardinflation,whichistheinflationriskpremium,istheelementof

e

tthatconstitutestheinﬂation

expectationsofinvestors.Sincechangeintheinflationrateisanimportantdeterminantofthedeposit/ loanrate(marketinterestrate),theinflationriskpremiumturnsouttobeasignificantpartoftheinterest rateriskconsideredintheinterestratepass-throughrelationship.Therefore,defaultrisk,liquidityand inflationriskpremiumshouldbeseriouslytakenintoaccountinempiricalmodelsofmonetarypolicy. Theimpactofdefaultriskandliquidityonthetransitionfrompolicyratetomarketratewasshown byMartinandMilas(2008)indetail.Theyinvestigatedtheinfluenceofthe2007sub-primecrisison thegapbetweenthepolicyrate,setbythecentralbank,andthemarketinterestrate,whichaffects aggregatedemand,fortheUK.Theydemonstratedthatthedifferencebetweenthepolicyrateandthe marketratewidenedduringthesub-primecrisisandexplainedthisgapasthecombinationofmainly unsecuredlendingriskandtheliquidityfactor.MartinandMilas(2008)highlightedtheincreasing differencebetweenthepolicyrateandthemarketinterestrateduringthe2007sub-primecrisis.They thenshowedthatthisdifferencewasmostlyaresultofunsecuredlendingrisk(defaultrisk)andthe liquidityfactor.Similarly,MichaudandUpper(2008)empiricallyillustratedtheimpactofcreditrisk andliquidityfactorsonthegapobservedininterbankinterestrates.Theyconcludedthatinterestrate riskishighlyinfluencedbycreditriskandliquidityfactors.

Ho¨rdahl and Tristani (2007) estimated the inflation risk premium for the euro area using a structuralmacroeconomicmodelandtermstructuredynamics.Theydemonstratedthattheinflation riskpremiumisasignificantingredientinconstructinginflationexpectationsofinvestorsintheeuro area.Ho¨rdahl(2008),inasubsequentstudy,measuredtheinflationriskpremiumbothintheUSand

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theeuroareabyemployingthetermstructuremodeldescribedinHo¨rdahlandTristani(2007).The linkbetweentheinﬂationriskpremiumandtheinﬂationexpectationsofinvestorswashighlightedin

Ho¨rdahl(2008)anditwassuggestedthatchangesintheinﬂationriskpremiumaremostlydrivenby changesinoutput.Angetal.(2008)providedanotherstudythatillustratesthecorrelationbetween theinﬂationriskpremiumandinterestratesusingatermstructuremodel.

Therecentstudiesaboverevealthatitisimportanttoconsidertheinterestraterisk,whichis includedintheinterestratepass-throughrelationship,andthatmonetarypolicymodelsshouldtake intoaccounttheinterestrateriskwhilebuildingmonetarytransmissionmechanisms.Hence,the introductionoftheinterestratepass-throughrelationshipaswellastheinterestrateriskandits componentswillsubstantiallyimprovemonetarypolicymodels.

5. Astatespacemodel

ThemodelgivenbyEqs.(4)–(7)isacomputablegeneralequilibriummodel,whichiscomposedof bothlinearandnonlinearequationsillustratingthebehaviorofallhouseholds,ﬁrmsandthecentral bankintheeconomyaswellasequilibriumconditions(Bergman,1990).Inthissection,weproposea structuralnonlinearEKFalgorithmasanewmethodfortheestimationoftime-variablemonetary policyparameters.

The studieslisted inthe literaturereview sectionrevealedthat monetarypolicy changesare sensitivetothemethodsemployedtomodeltimevariationinthecoefficientsoftheinterestraterule andtheestimationtechniquesused.While initialstudieswereusingsubsample analysistochart changesinmonetarypolicies, differenttechniqueswerelater adopted,suchasMarkov-switching models,GMM,andtheKalmanfilter.TheKalmanfilter(Kalman,1960)especiallyiswidelyutilized duetoitsaptnessinestimatingthepast,presentandfuturestatesofamodeleveniftheexactformof themodelarenotknown.AlthoughthestandardKalmanfilterisaninfluentialtechniqueinestimating lineartransformations(Harvey,1990),itfailstobea reliabletechniquefornonlinearstatespace forms.WhenmodelingpolicyrulesandstructuralequationswithTVPssimultaneously,thesystem takesanonlinearform,andEKFbecomesnecessaryastheappropriateestimationtool.Totheextentof ourknowledge,theuseofEKFisnotascommoninmonetarypolicyanalysisusingTVPs.

InordertofacilitateEKF,themodelneedstobewritteninstatespaceform.Astatespacemodelis composedoftwosetsofequations,thesystemequationsrepresentingtheevolutionofstatevariables andtheobservationequationstomodeltheobservedstatevariables.8_An_appropriate_state_space

setupforthemodelweproposedabovecanbewrittenasfollows:

Wtþ1¼AtWtþBtUtþutþ1 (8)

Yt¼CtWtþDtVtþ

v

t (9)

whereWtisanrx1vectorofunobservedstatevariablesandYtisannx1vectorofobservedsignals,Ut

and Vt are kx1and jx1 predeterminedvariables. At,Bt,Ct and Dt are time-dependentparameter

matrices.Ifoneallowsfortime-variablecoefﬁcients,thesystemcanberewrittenas

itp¼itþ

d

p;tðEt

p

tþ1

p

tÞþ

d

x;tEtðytþ1ytþ1Þþ

n

t (10) Et

p

tþ1¼

rp

t

u

xtþkt (11) Etxtþ1¼xt 1

s

ði tEt

p

tþ1Þþut (12) it¼

l

1it1þ

l

2itpþ

e

t (13) yt¼ytþxt (14)

8_Explanations_about_the_EKF_are_standard_and_adopted_from_Pasricha₍₂₀₀₆₎_,_Ribeiro₍₂₀₀₄₎_,_Welch_and_Bishop₍₂₀₀₆₎_and

(10)

wherei

t,Et

p

t+1andEtxt+1areunobservablestatevariables,itp,

p

*,ytanditareobservedsignals,and

d

p,t and

d

x,taretime-variablepolicyparameters.Eqs.(10)–(12)arederivedfromEqs.(4)–(7) and

Eqs.(11)and(13)areslightlymodiﬁedbymakingthelong-termratesequaltothedesiredratesto includetheeffectofinterestratepass-throughonpolicyrates.Eq.(14)isanidentity.Moreover,

r

= 1/

b

,

u

=

k

/

b

andkt= mt/

b

.InadditiontoEqs.(10)–(14),wespecifythetime-variableparametersasa

randomwalkinlinewiththeliterature.9

d

p;t¼

d

p;t1þ

e

t (15)

d

x;t¼

d

x;t1þ

e

t (16)

Given our model, we specify the system matrices for the EKF as follows: WT t ¼

½i

t;Et

p

tþ1;Etxtþ1;

d

p;t;

d

x;t;YtT¼½i p

t;yt;0;0;0;UtT¼½it1;

p

t;0;0;0; and VtT¼½

p

t;yt;0;0;0; where T

denotesthetranspose.ParametermatricesaregivenbyAt= diag{

l

2,0,0,1,1},whereAisadiagonal

5 5matrixwiththeexceptionsA(1,2) =

l

2

d

p,t,A(1,3) =

l

2

d

x,t,A(2,3) =

u

,A(5,2) = A(5,3) = (1/

s

),

Bt= diag{

l

1,

r

,0,0,0},Ct= diag{1,0,0,0,0}withtheexceptionsC(1,2) =

d

p,tand C(1,3) =

d

x,t and

Dt= diag{

d

p,t,1,0,0,0}.

6. Dataandestimationresults

WeestimatethemodelusingTurkishdataasacaseinpoint.WebelievethattheTurkishcaseis particularlyinterestingbecauseatime-variablerulecanresemblethebehaviorofanemergingmarket centralbankmoreclosely.Bothassetandliabilitydollarization,shallowfinancialmarkets,aswellasa highcurrentaccountdeficitcanleadtofearofsuddencapitalflights,whichmightcauseanemerging marketcentralbanksuchastheCentralBankofTurkey(CBT)toshiftpoliciessignificantlyandmore frequently.

Forthepolicyrateweusethemonthlyaverageofthedailyovernightinterbankborrowingrate from2001:01until2012:01.OutputiscalculatedasthelogarithmofseasonallyadjustedrealGDP. InﬂationistakentobethelogarithmicdifferenceofmonthlyannouncedannualCPIafterseasonal adjustment.ActualinterestratesaremarketratesannouncedbytheCBT.Alldataareprovidedbythe CBT.

Ourestimationinvolvesseveralsteps.SincetheKalmanfilterisarecursiveprocedure,oneneedsto specifyplausibleinitialvalues.Todoso,wefirstestimatetheparametersofEq.(10)usingOLS.Weuse theseparametersaswellasfittedvaluesofthestatevariablesobtainedfromregressionsasinitial values.Next,toshowtherelevanceofthemethodologyemployed,wecompareefficiencyresultsof theEKF tothestandard Kalmanfilter,where we keepthepolicy parametersconstant. We then estimatetheTVPbyexperimentingwithseveralinitialcandidatestocheckfortherobustnessofthe results.Table2reportsboththeefficiencyresultsandthevaluesoftheparameters.TheEKFparameter isreportedatthelastobservation.Accordingtomeansquareerror(MSE)criteria,EKFperforms15% better than the standard Kalman filter. The interest rate pass-through is significant and more pronouncedundertheTVPrule.AnotherinterestingfacttonoteisthatundertheTVPestimation,the

Table2 Estimationresults. Standard EKF Inﬂationgap 1.301(0.492) 1.022(0.704) Outputgap 0.039(0.335) 0.012(0.133) l1 0.622(0.061) 0.767(0.049) l2 0.371(0.059) 0.229(0.052)

Meansquareerror 5.653 4.441

Note:StandarderrorsinparenthesesexceptEKF,whereMSEisreported.InEKFtheparametervalueisreportedatthelast observation.

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CBTseemstohavefoughtinflationlessaggressively,astheaveragecoefficientoftheinflationgapfor theinflation-targetingperiodis1.09.10_This_result_might_be_due_to_the_presence_of_a_high_interest_rate

pass-througheffect.

7. Conclusion

For years, themonetary policiesimplemented by central banksand their inﬂuence over the economy and the monetary transmission mechanism have been the research topic of several academicsandpolicymakers.Forcarryingoutmonetarypolicyanalysisandexaminingitsimpactover theeconomy,differentdirections/questions/motivationswereadoptedforvariousinvestigations.

Thispaperreviewedmonetarypolicyrules withaTVPspecification.Thechangingbehaviorof policymakers,fullorpartialuseoftheinformationsetavailable,andtheunstablestructureofthe economyarethemainreasonsforrequiringtheemploymentofTVPcharacterization.Inthelightof thisanalysis,weclaimedthatchangesintheriskpreferencesofhouseholdsandfirmsshouldalsobe reflectedinsuchaworld.Oneofthewaysofdoingthisistoincludetheriskattitudeofhouseholdsin theformationofthemarketinterestratefacedbyinvestorsandcreditors.Forthis,wedifferentiated theshort-terminterestratedeterminedbythecentralbankandthelong-terminterestratefacedby households. This differentiation should be made especially in empirical studies to increase the robustnessoftheconclusions.Next,westressedthatthechangingbehaviorofinvestorstowardrisk shouldbeconsideredasacomponentinthedeterminationofthelong-termmarketinterestrate.This construction is given by the interest rate pass-through specification. Through this method, the changingriskpreferencesofhouseholdsandfirmscanbeconsideredinastructuralmodel,which couldbeworthwhileforreal-timedataapplications.

Finally,wespecifiedastatespacemodelwiththeinterestratepass-throughwithinwhichwecan utilizetheEKF toestimateaTVP Taylorrule. ByutilizingTurkish datawe showedthat theEKF performedbetterthanthestandardKalmanfilterinestimatingtheCBTreactionfunction.Afuture studymightlookintotheroleoftheexchangeratepass-throughtogetherwiththeinterestrate pass-throughinaTaylor-typereactionfunction.Webelievetheroleofexchangeratesindeterminingthe expectedinflationaswellastheoutputgapinaTVPruleisnotadequatelyanalyzed.

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