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首页 Money Demand in Japan and the Liquidity Trap

Money Demand in Japan and the Liquidity Trap.pdf

Money Demand in Japan and the Li…

哈尼 2012-12-16 评分 0 浏览量 0 0 0 0 暂无简介 简介 举报

简介:本文档为《Money Demand in Japan and the Liquidity Trappdf》,可适用于经济金融领域,主题内容包含MoneyDemandinJapanandtheLiquidityTrapYoungsooBaeVikasKakkar†OhioStateUnive符等。

MoneyDemandinJapanandtheLiquidityTrapYoungsooBaeVikasKakkar†OhioStateUniversityCityUniversityofHongKongMasaoOgaki‡OhioStateUniversityDecemberOhioStateUniversityDepartmentofEconomicsWorkingPaper#AbstractInthispaperweestimatelongrunmoneydemandforJapanwithtwofunctionalformsthatallowfortheliquiditytrap,andcomparetheempiricalresultsforthesefunctionalformswiththoseforthestandardloglevelfunctionalformEstimatingdifferentfunctionalformsleadstononlinearcointegrationWecomparetheoutofsamplepredictionperformanceofthethreefunctionalformsOurempiricalresultsindicatethatthefunctionalformswhichallowfortheliquiditytraparebetterthantheloglevelfunctionalformbasedonthepredictionperformanceWethankBillDuporandHuMcCullochforhelpfuldiscussionsGraduateStudent,DepartmentofEconomicsEmail:baeosuedu†AssociateProfessor,DepartmentofEconomicsandFinanceEmail:efvikascityueduhk‡Professor,DepartmentofEconomicsEmail:mogakieconohiostateeduIntroductionThetheoryofmoneydemandimpliesthatthemoneydemandfunctionisorisalmostinfinitelyelasticatloworzeronominalinterestratesThisfeatureofthemoneydemandfunctionhasimportantimplicationsformonetarypolicyForexample,thequantityofmoneythatthecentralbankprintsdoesnothaveanyeffectoninflationoroutputKeynesandmonetaristswereinterestedinthisproblemwhichhasbeencalledtheliquiditytraporthezerointerestboundBecauseofverylowshortterminterestratesinJapantodayandthelowestshortterminterestratesintheUnitedStatesinyears,manyresearchersareinterestedinthisproblemagainForexample,seeKrugman(),OrphanidesandWieland(),Jung,Terashashi,andWatanabe(),Woodford(),EggertssonandWoodford(),andEggertsson()Therefore,itisimportanttoincorporatetheliquiditytrapfeatureinestimatingthemoneydemandfunctionHowever,intherecentliteraturewhichusescointegrationtoestimatelongrunmoneydemand,theloglevel(semilog)functionalformhastypicallybeenused(see,eg,StockandWatson(),andBall())TheloglevelformwithlogmoneyandtheleveloftheinterestratedoesnotincorporatetheliquiditytrapfeatureAnotableexceptionisHoffmanandRasche(),whousealoglogformInthispaperweestimatelongrunmoneydemandforJapanwithtwofunctionalformsthatallowfortheliquiditytrap:theloglogformandtheformimpliedbythemoneyintheutilityfunctionwiththeconstantelasticityofsubstitution(theMUFCESformforshort)WecomparetheresultswiththeloglevelformThesefunctionalformsaremotivatedbytheoryWecomparetheempiricalresultsforthesetwofunctionalformswiththoseforthestandardloglevelfunctionalformBecauseofverylowshortterminterestratesobservedinJapansince,thistaskisimportantDifferentfunctionalformsleadtononlinearcointegrationasdiscussedbyBaeanddeJong(),andweusetheirNonlinearCointegrationLeastSquareestimationtechniqueAndersonandRasche()andBaeanddeJong()estimateandcomparedifferentfunctionalformsoflongrunmoneydemandfortheUnitedStatesMiyao()usesstructuralbreakteststostudythestabilityoflongrunmoneydemandwiththeloglinearandloglogfunctionalformsHisempiricalresultsindicateastructuralbreakfortheloglinearformbutnostructuralbreakfortheloglogformFujikiandWatanabe()usethestabilityoflongrunmoneydemandwiththeloglogformandconfirmedMiyao’sfindingthattheloglogformisstableOurpaperiscomplementarytoThefunctionalformofTaylortypeinterestrulesusedinthesepapersimplicitlydependsontheformoftherelationshipbetweenvelocityandtheinterestrateasinTaylor(),amongotherfactorsTherefore,thefunctionalformdependsontheshapeofthemoneydemandfunctionthesetwopapers,butitisdifferentfromtheminthatweusetheMUFCESforminadditiontotheloglinearandloglogforms,comparedifferentformsintermsofoutofsamplepredictionperformance,andtakeintoaccountnonlinearcointegrationOurempiricalresultsindicatethattheloglogandMUFCESfunctionalformsthatallowfortheliquiditytraparebetterthantheloglevelfunctionalformintermsoftheoutofsamplepredictionTheresultswerequalitativelysimilarbetweentheloglogandtheMUFCESformsandbetweencointegrationandnonlinearcointegrationtechniquesFunctionalFormsofMoneyDemandThissectiondiscussesthethreemainfunctionalformsofmoneydemandthatareestimatedinthispaperThedifferencebetweenthethreeformsarisesbecausetherearevariousplausiblewaysinwhichthenominalinterestrateentersthemoneydemandfunctionMuchoftheempiricalworkonmoneydemandhasestimatedaconventionalmoneydemandfunctionofthefollowingfunctionalformln(MdP)=ββln(Y)βi,()whereMddenotesnominalmoneybalancesPdenotesthepricelevelYisa“scale”variablethatproxiesforthevolumeoftransactionssuchasrealGDPorconsumptionandiisthenominalinterestratewhichmeasurestheopportunitycostofholdingmoneyTheparameterβistheincomeelasticityofmoneydemandandβisthe“semielasticity”ofmoneydemandwithrespecttotheinterestrateAlthoughthisspecificationofmoneydemandhasbeenwidelyusedintheempiricalliteratureonmoneydemand,therearetwoimportantclassesofmodelsthatgiverisetootherspecificationsThefirstclassofmodelsisbasedontheinventorytheoreticapproachtomoneydemandpioneeredbyAllais(,Vol,pp),Baumol()andTobin()ConsideranindividualwhoreceivesanincomeYintheformofbondsThereisafixedtransactionscostbofconvertinginterestbearingbondsintocashLetKdenotetherealvalueofbondsconvertedintocasheachtimethereisaconversionThetotaltransactioncostsγincurredbytheindividualaregivenbyγ=b(YK)i(K),()wherethefirsttermrepresentsconversioncostsandthesecondtermrepresentstheinterestcostonaveragemoneyholdings(K)overtheperiodMinimizingthetransactioncostswithrespecttoKSeeforexample,StockandWatson()yieldsthefollowingsquarerootlawforoptimalrealmoneybalancesMdP=K=(bYi)()ExpressingEquation()inlogarithmicform,weobtainthefollowingloglinearmoneydemandfunctionln(MdP)=ββln(Y)βln(i),()wheretheparametersβandβrepresenttheconstantincomeandinterestelasticitiesofmoneydemandthatareimpliedtobebythemodelMillerandOrr()extendtheAllaisBaumolTobinanalysistothecaseinwhichcashflowsarestochasticwhilemaintainingtheassumptionofafixedtransactioncostinconvertingbondstomoneyInthebasicversionoftheirmodel,cashflowsfollowastationaryrandomwalkwithoutdriftsothatinasmalltimeinterval(t)thecashfloweitherincreasesordecreasesbymdollarswithequalprobabilitiesTheoptimalruleformoneyholdingsisa“triggertarget”ruleWhenevercashbalancesreachthelowerbound(thetrigger)ofzero,zdollarsareconvertedfrombondstocashwhencashbalancesreachtheupperboundofh,(hz)dollarsofcashareconvertedtobondsMillerandOrrshowthattheoptimalsizeofaveragecashbalancesisgivenbyMdP=biσ,()whereσ=mtisthedailyvarianceofthechangesinthecashbalancesTheMillerOrrmodelalsoimpliesaconstantinterestelasticityofmoneydemandbutthevalueisratherthanInmorerecentworkBarIlan()extendstheinventorytheoreticmodelfurthertoallowforthepossibilityofoverdraftingbyrelaxingtheassumptionthatthe“trigger”berestrictedtozeroMoneybalancesmayfallbelowzeroand,whentheydo,theindividualhastopayapenaltyataratep>forusingtheoverdraftingfacilityItisshownthatforanyfinitenominalinterestiandpenaltyrateptheoptimaltriggerpointisnegativeOnlyinthespecialcasewhenthepenaltyrateofusingthecreditisinfinitelyhighrelativetotheinterestratedoesthemodelyieldtheAllaisBaumolTobinresultSincecreditandmoneyareveryclosesubstitutes,evensmallincreasesinthecostofholdingmoneyrelativetocredit(ahigheripratio)resultsinsubstitutionofcreditformoney,therebyyieldingahigherinterestelasticityofmoneydemandthantheearliermodelsAnotherimportantclassofmodelsthathaveimplicationsforthefunctionalformofthemoneydemandfunctionarethosewhererealbalancesentertheutilityfunctiondirectlyThisapproachwasMillerandOrr()alsousetheinventorytheoreticapproachtomodellingtheoptimalamountofmoneyholdingspioneeredbySidrauski()andBrock()andhassincebeenwidelyusedtostudyavarietyofissuesinmonetaryeconomicsMoneyenterstheutilityfunctionbecauseithelpseconomizeonthetimespenttransactingandhencehigherrealbalancesareassociatedwithhigherleisureandhencehigherutilitySupposethattherepresentativehouseholdmaximizesthelifetimeutilityfunctionU=t=βtu(ct,mt),<β<()bychoosingtimepathsforconsumption(ct)andrealbalances(mt)subjecttoanappropriateeconomywidebudgetconstraintThefirstorderconditionsformaximizingutilityyieldum(ct,mt)uc(ct,mt)=(rt)(pit)=itit,()wherertistherealreturnoncapital,φtistheexpectedinflationrateanditdenotesthenominalinterestrateEquation()equatesthemarginalrateofsubstitutionbetweenrealbalancesandconsumptiontotherelativepriceofholdingmoneyIfthehouseholdholdsonelessdollarofmoney,itforegoestheopportunitytoearnaninterestpaymentitSincethispaymentwouldbereceivednextperiod,itisdiscountedbythenominalinterestratetoobtainitspresentvalueThedemandformoneycanbederivedfromEquation()bypositingaspecificutilityfunctionfortherepresentativehouseholdThefollowingconstantelasticityofsubstitution(CES)utilityfunctionhasoftenbeenusedu(ct,mt)=αcβt(α)mβt(β),()where<α<andβ>,β=Withthesepreferences,themarginalrateofsubstitutionbetweenrealbalancesandconsumptionisgivenbyumuc=(αα)(ctmt)β()Equatingthemarginalrateofsubstitutiontotherelativepriceofrealmoneybalances,weobtainthefollowingdemandformoney(inlogform)ln(mt)=βln(αα)ln(ct)bln(itit)()ThismodelimpliesaunitconsumptionelasticityofmoneydemandTheinterestelasticityofmoneydemandimpliedbythismodelisln(mt)ln(it)=bit,()whichisadecreasingfunctionofthenominalinterestrateintermsofabsolutevalueAlternatively,onecouldassumethatrealbalanceshelpreducetransactionscosts,sothathigherrealbalancesleadtoagreaterproportionofincomebeingspentonconsumptionInthiscaserealbalancesentertheindividual’sbudgetconstraintratherthantheutilityfunctionSeeBrock()andFeenstra()fordetailsEstimationResultsofMoneyDemandforJapanCointegrationMethodsInthissectionthefollowingthreefunctionalformsofthelongrunmoneydemandareestimatedbycointegrationmethodsSincethenominalinterestrateshowsapersistentserialcorrelation,theassumptionthatrtisI()isgenerallyacceptedasagoodapproximationWeregardthelongrunmoneydemandfunctionasacointegratingregressionmt=ββitut()mt=ββln(it)ut()mt=ββln(itit)ut()wheremt(=lnMtPtYt)isthelogarithmoftherealmoneybalanceanditisthenominalinterestrateNotethatweimposetherestrictionoftheunitincomeelasticityofthemoneydemandWeallowitanduttobetemporallydependentanduttobeseriallycorrelatedInEquations()and()themoneydemandbecomesanonlinearfunctionoftheinterestrateTousetheconventionallinearcointegrationmethods,suchas“FullyModifiedOLS”(FMOLS)and“DynamicOLS”(DOLS),wemusthavedifferentassumptionsfordifferentfunctionalformsieit,ln(it)andln(itit)mustbeassumedtobeI()forEquations(),()and(),respectivelyHowever,ifitisI(),ln(it)andln(itit)cannotbeI()inanymeaningfulsenseandviceversaBecauseofthisinternalinconsistency,estimationresultsfromtheconventionallinearcointegrationmethodsmightnotbedirectlycomparablewitheachotherTherefore,alongwiththeconventionallinearcointegrationmethods,wealsoconsideranonlinearcointegrationmethodwhichhasbeenproposedrecentlybyBaeanddeJong()Intheir“NonlinearCointegrationLeastSquare”(NCLS)estimationtechnique,itispossibletoestimatedifferentfunctionalformsundertheoneassumptionthatitisI()However,theNCLSestimationmethodusedinthispaperhasnoasymptoticjustificationforEquation()AtheoryhasnotbeenfullydevelopedyetTherefore,wealsoreportbootstrapconfidenceintervalsalongwithasymptoticonesSincetheNCLSestimationtechniqueisrelativelynew,weillustratehowtoimplementtheNCLSestimationtechniquefortheestimationofβinEquation()Letknbeanintegervaluedpositivesequencethatdivergestoinfinityataslowerratethannsuchthatknnppηforsomeη>andp,andnj=njknforj=,,,,knLetzt=ln(inj)fornjtnjforj=,,,knThentheNCLSestimatorβisdefinedasanIVestimatorthatusesztastheinstrumentalvariableforln(it)Notethatalthoughβisaconsistentestimator,itcannotbeusedforstatisticalinferenceunlessthelimitingBrownianprocessesassociatedwithitandutareorthogonal,whichisunlikelyinthecaseofthelongrunmoneydemandfunctionTherefore,thefollowingfullymodifiedtypeNCLSestimationtechniqueisusedTheestimationprocedureisasfollowsCalculatetheresidual,ut,fromaregressionbytheNCLSestimationmethodGetaHACestimateforthelongruncovariancematrixof(ut,it),Ω,byusing(ut,it)Calculatem†tinawayanalogoustotheFMOLS,m†t=mtΩ′ΩitThefullymodifiedversionoftheNCLSestimatorβisdefinedastheNCLSestimatorthatiscalculatedusingthemodifieddependentvariablem†tinsteadofmtNotethatnowtheusual“tandFstatistics”arevalidbecausetheyachievethecorrectsignificancelevelconditionallyonitDataandEmpiricalResultsFortheestimationoftheJapaneselongrunmoneydemandfunctionthequarterlydatasetfrom:to:isusedSincethedatafrequencyisquarterly,weaddquarterlyseasonaldummiesintheregressionMCD,theConsumerPriceIndex(CPI),boththeGrossDomesticProduct(GDP)andthePrivateConsumption(CON),andthelendingrateof“CityBanks”areusedformoney,price,output,andnominalinterestrate,respectivelyDuetothefinancial“BigBang”inJapan,weincludeforeignbanks’accountsinMCDbeginningin:Tablereportscoefficientestimates,anditsasymptoticandbootstrapconfidenceintervalsSincenoasymptoticandbootstrapconfidenceintervalscontainzero,coefficientestimatesarestatisticallyThefollowingassumptionneedstobemaderegardingpLetutanditbelinearprocessesgivenbyut=Xi=φ,iε,tiit=Xi=φ,iε,tiwhereεt=(ε,t,ε,t)isasequenceofindependentandidenticallydistributed(iid)randomvariableswithmeanzeroE|εj,t|p<forsomep>forj=,fordetails,seeBaeanddeJong()ShinichiNishiyamaintheBankofJapankindlyprovidedthedataofMCDandthelendingrateof“CityBank”ForCPI,GDP,andthePrivateConsumptiontheDatastreamwasusedsignificantinallcombinationsoffunctionalformsandestimationmethodsAsymptoticandbootstrapconfidenceintervalsaregenerallysimilar,thoughbootstraponeislargerthanasymptoticoneWhenwecomparetheestimationresultsacrossthedifferentfunctionalforms,therearesignificantdifferences,asexpectedHowever,theestimationresultsarerobustacrossthedifferentestimationmethods,includingtheNCLSestimatorTofurtheraddressthequestionofwhichfunctionalformismostappropriatefortheJapaneselongrunmoneydemand,weinvestigateoutofsamplepredictionperformancesforthethreedifferentfunctionalformsTablereportsthesumofsquarederrorfortwodifferentmethodsofoutofsamplepredictionperformanceEquations()and(),whicharenonlinearfunctionsoftheinterestrate,clearlyoutperformEquation(),thelinearone,inallestimationmethodsexceptDOLSThesepredictionperformanceresultssupportempiricallyourconvictionthatthenonlinearfunctionalforms,suchasEquations()and(),aremoreappropriatefortheJapaneselongrunmoneydemandConclusionsInthispaperweestimatedlongrunmoneydemandforJapanwithtwofunctionalformsthatallowfortheliquiditytrapandcomparedtheempiricalresultsforthesefunctionalformswiththoseforthestandardloglevelfunctionalformEstimatingdifferentfunctionalformsleadstononlinearcointegrationHowever,wefoundthattheempiricalresultsarerobusttoestimationmethodsthatassumelinearandnonlinearcointegrationWethencomparedtheoutofsamplepredictionperformanceofthethreefunctionalformsOurempiricalresultsindicatedthatthefunctionalformswhichallowfortheliquiditytraparebetterthantheloglevelfunctionalformReferencesAllais,Maurice()EconomieetInteset(Paris:ImprimerieNationale)Bae,Youngsoo,andRobertMdeJong()‘Moneydemandfunctionestimationbynonlinearcointegration’manuscript,OhioStateUniversityBall,Laurence()‘Anotherlookatlongrunmoneydemand’JournalofMonetaryEconomics,–BarIlan,Avner()‘Overdraftsandthedemandformoney’AmericanEconomicReview(),–Baumol,WJ()‘Thetransactionsdemandforcash:Aninventorytheoreticapproach’QuarterlyJournalofEconomics,–Brock,WA()‘Moneyandgrowth:Thecaseoflongrunperfectforesight’InternationalEconomicReview(),–deJong,RobertM()‘Nonlinearestimatorwithintegratedregressorsbutwithoutexogeneity’MichiganStateUniversity,mimeoEggertsson,GautiB()‘Thedeflationbiasandcommittingtobeingirresponsible’JournalofMoney,Credit,andBankingFeenstra,RC()‘Functionalequivalencebetweenliquiditycostsandtheutilityofmoney’JournalofMonetaryEconomics(),–Fujiki,H,andKWatanabe()‘Japanesedemandformanddemanddeposits:Crosssectionalandtimeseriesevidencefromjapan’MonetaryandEconomicStudies,–Hoffman,DennisL,andRobertHRasche()‘Longrunincomeandinterestelasticitiesofmoneydemandintheunitedstates’TheReviewofEconomicsandStatistics(),–Hofman,D,RRasche,andMTieslau()‘Thestabilityofmoneydemand

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