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Thisarticlewasdownloadedby:[K.U.Leuven-Tijdschriften]On:09May2012,At:08:38Publisher:RoutledgeInformaLtdRegisteredinEnglandandWalesRegisteredNumber:1072954Registeredoffice:MortimerHouse,37-41MortimerStreet,LondonW1T3JH,UKAppliedEconomicsPublicationdetails,includinginstructionsforauthorsandsubscriptioninformation:http://www.tandfonline.com/loi/raec20TheeffectsofmonetarypolicyusingstructuralfactoranalysisabDandanLiu&DennisW.JansenaDepartmentofEconomics,478BusinessAdministrationBuilding,KentStateUniversity,POBox5190,Kent,OH44242,USAbDepartmentofEconomics,4228TAMU,TexasA&MUniversity,CollegeStation,TX77843-4228,USAAvailableonline:20Apr2012Tocitethisarticle:DandanLiu&DennisW.Jansen(2013):Theeffectsofmonetarypolicyusingstructuralfactoranalysis,AppliedEconomics,45:18,2511-2526Tolinktothisarticle:http://dx.doi.org/10.1080/00036846.2012.669462PLEASESCROLLDOWNFORARTICLEFulltermsandconditionsofuse:http://www.tandfonline.com/page/terms-and-conditionsThisarticlemaybeusedforresearch,teaching,andprivatestudypurposes.Anysubstantialorsystematicreproduction,redistribution,reselling,loan,sub-licensing,systematicsupply,ordistributioninanyformtoanyoneisexpresslyforbidden.Thepublisherdoesnotgiveanywarrantyexpressorimpliedormakeanyrepresentationthatthecontentswillbecompleteoraccurateoruptodate.Theaccuracyofanyinstructions,formulae,anddrugdosesshouldbeindependentlyverifiedwithprimarysources.Thepublishershallnotbeliableforanyloss,actions,claims,proceedings,demand,orcostsordamageswhatsoeverorhowsoevercausedarisingdirectlyorindirectlyinconnectionwithorarisingoutoftheuseofthismaterial. AppliedEconomics,2013,45,2511–2526Theeffectsofmonetarypolicyusingstructuralfactoranalysisa,bDandanLiu*andDennisW.JansenaDepartmentofEconomics,478BusinessAdministrationBuilding,KentStateUniversity,POBox5190,Kent,OH44242,USAbDepartmentofEconomics,4228TAMU,TexasA&MUniversity,CollegeStation,TX77843-4228,USAThetraditionalVectorAutoregression(VAR)methodiswidelyusedtotraceouttheeffectsofmonetarypolicyinnovationsontheeconomy.However,thismethodsuffersfromthecurseofdimensionality,sothatinpracticeVARsareestimatedonalimitednumberofvariables,leadingtoapotentialmissinginformationproblem.Inthisarticleweusethemethodofstructuralfactoranalysistoevaluatetheeffectsofmonetarypolicyonkeymacroeconomicvariablesinadatarichenvironment.ThismethodologyallowsustoextractinformationonmonetarypolicyanditsimpactontheeconomyfromamuchlargerdatasetthanispossiblewiththetraditionalVARmethod.Weproposetwostructuralfactormodels.OneistheStructuralFactorAugmentedVectorAutoregressive(SFAVAR)modelandtheotheristheStructuralFactorVectorAutoregressive(SFVAR)model.ComparedtothetraditionalVAR,bothmodelsincorporateinformationfromhundredsofdataseries,seriesthatcanbeandaremonitoredbythecentralbankinsettingpolicy.Moreover,thefactorsusedarestructurallymeaningful,afeaturethataddstotheunderstandingofthe‘blackbox’ofthemonetarytransmissionmechanism.Bothmodelsgeneratequalitativelyreasonableimpulseresponsefunctions.FortheSFVARmodel,boththepricepuzzleandtheliquiditypuzzleareeliminated.Keywords:monetarypolicy;VAR;structuralfactor;SFAVAR;SFVARJELClassification:C32;C43;E50;E52I.IntroductionThetraditionalVARapproachisstraightforwardandDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012familiar.Italsosuffersfromthecurseofdimensionality.TherehasbeenagreatdealofinterestinidentifyingandThisandthedesiretopreservedegreesoffreedom,leadsinmeasuringtheeffectsofmonetarypolicyshocksonmacro-practicetoVARswithrelativelysmallnumbersofincludedeconomicvariables,bothforthepurposeofpolicyanalysisvariables.Incontrast,centralbanksarethoughttomonitorandforthepurposeofassessingtheempiricalfitnessofandanalysealargenumberofdataseries,andtoconsiderthe1structuralmodels.Sims(1980)suggeststheuseofaVectorinformationcontainedintheseserieswhenmakingdecisions.Autoregression(VAR)toderivetheimpulseresponsesofkeyThusthereisapotentialmissinginformationproblemwithmacroeconomicvariablestomonetarypolicyshocks,traditionalVARs,andthe‘identifiedmonetaryshocks’frombasedonarecursiveidentificationscheme.ThisVARthesemodelscouldbesubjecttomeasurementerror.approachhaslongbeenafundamentaltoolofempiricalRecentresearchhascombinedtheVARapproachand2macroeconomics.factoranalysistoovercomethemissinginformationproblem.*Correspondingauthor.E-mail:dliu1@kent.edu1SeerecentstudiesinRomerandRomer(2004),Boivin(2006),BoivinandGiannoni(2006),SimsandZha(2006),andmanyothers.2SargentandSims(1977)firstproposedageneralformofdynamicfactormodelorindexmodeltoanalysetheUSbusinesscycle.VariousversionsofSargentandSims’modelhavebeenstudiedbyGeweke(1977),Singleton(1980),EngelandWatson(1981),StockandWatson(1989,1991),QuahandSargent(1993),andForniandReichlin(1996,1998).StockandWatson(1998,1999,2002)appliedfactoranalysisintheforecastingliterature.AppliedEconomicsISSN0003–6846print/ISSN1466–4283onlineß2013Taylor&Francis2511http://www.tandfonline.comhttp://dx.doi.org/10.1080/00036846.2012.669462 2512D.LiuandD.W.JansenThesepapersestimatea(relativelysmall)setoffactorsavailableatshorterfrequencies.Inmanycasesthetheoreticalsummarizingtheinformationinamuchlargersetofvariables,concepts,forinstance,realeconomicactivitymaynotbeandusethesefactorstoaugmentstandardVARs,theso-calledadequatelyrepresentedbyanysinglespecificseriesorevenanyFactorAugmentedVARmodel(FAVAR).See,e.g.Bernankesmallsetofspecificseries.Meanwhile,manyobservableseriesandBoivin(2003)andBernanke,BoivinandEliasz(BEE,arecontaminatedbymeasurementerrors.2005).Morespecifically,BEEextractseveralfactorsfromaTheSFVARmodeldoesnottakeastandonwhichspecificlargedatasetcomposedofseriesreflectingdifferentaspectofseriesisthebestmeasurefortheeconomicconceptsofrealtheeconomy(realproduction,labourmarket,price,monetaryactivityorthepricelevel.Insteadofpickingaparticularseriesaggregateandfinancialmarkets,etc.)andestimatedaVARtorepresentaconcept,aresearcheridentifiesasubsetofdatawiththesefactorsandthefederalfundsrate.ThisFAVARthatcontaininformationontheeconomicconceptinquestion,modelpreservestheadvantagesofthetraditionalVARwhileandtheSFVARmodelusesafactororfactorsderivedfromallowingextractionofadditionalinformationfromasignifi-thatsubsetofdataasthemeasureoftheconceptinquestion.cantlylargersetofdata.Thisnewapproachreceivedsignif-Allseriesinagivensubsetaretreatedaspotentiallycontainingicantattentionintheliterature.SeesomerecentapplicationsofinformationonthebehaviourofthetheoreticalconceptinthisFAVARmodelinBoivinetal.(2009),Helblingetal.question.Theideaisthatthenumerousindividualseriesreflect(2011),Lagana`andSgro(2011),MoenchandNg(2011),differentaspectsofsomeeconomicconcept,thattheyarenoisyamongothers.reflectionsofthatconcept,andthatwhatmattersaretheWegoastepfurtherandsuggesttwoalternativefactorunobservableunderlyingfactorsthatbettercorrespondtoVARmodelsbyimposingalimitedstructuralconstraintonwhatwemeanbytheeconomicconceptsinquestion.Theseestimationofthefactors.The‘structural’factormodelsthatestimatedunderlyingfactorscapturethecommonmovementweproposestilltakeadvantageofalargedatasetbutalsotheyamongtheseseriesandatthesametimemay‘averageaway’canhelpprovideabetterunderstandingoftheforcesthatareidiosyncraticmovements.drivingtheevolutionoftheeconomyandperhapsopentheWeusethreesetsoffactorsinourempiricalpresentation.doortousingaricherinformationsetwhenstudyingthe‘Realactivityfactors’arethefactorsdrawnfromasetofmonetarytransmissionmechanism.variablesthatcapturerealeconomicconditions.ThisincludesWefirstproposeaugmentingthetraditionalVARwithvariousmeasuresofemployment,unemploymentandoutput,structuralresidualfactors,andwecallthisaStructuralFactorbothaggregateand(somewhat)disaggregated.‘Inflation/priceAugmentedVAR(SFAVAR)model.ThetraditionalVARfactors’aredrawnfromvariousmeasuresofpricesbothtypicallyusesvariablessuchasindustrialproduction(IP),theaggregatedand(partially)disaggregated.Finally,unlikeBEE,consumerpriceindex(PI)andthefederalfundsrate(FFR).whoassumestheFFRasthethemeasureofmonetarypolicy,However,onesuspectsthatthereareotherimportantvariablesweestimate‘monetarypolicyfactors’torepresentthestanceofinawell-specifiedmodel.WeproposetoaugmentaVARwithmonetarypolicy.Inlieuofspecifyingoneormoreindividual‘realactivityresidualfactors,’‘inflation/priceresidualfactors,’series(suchasthefederalfundsrateornonborrowedreserves)and‘monetarypolicyresidualfactors’thatcontainimportantasaspecificmeasureofmonetarypolicy,wederiveafactorinformationwhichisnotcapturedbytheabovethreevariablessummarizingcommonbehaviourinasetofinterestrateandtypicallyincludedinaVAR.Weseeifuseoftheseextraormonetaryaggregatemeasures.‘hidden’residualstructuralfactorstoestimatetheeffectsofThisarticleisorganizedasfollows.InthenextsectionwemonetarypolicyshocksimprovesonatraditionalVAR.outlinetheSFAVARmodelandtheSFVARmodelusedtoThereareseveralpotentialadvantagesoftheSFAVARevaluatetheeffectsofmonetarypolicy.ThenwedescribethemodelcomparedtoBEE’sFAVARmodel.First,itpotentiallydatasetandtheidentificationschemesappliedtoidentifyincludesmoreinformationaboutthedynamicsoftheecon-themonetarypolicyshocksfortheSFAVARmodelandtheomy,asitallowsinteractionsbetweenthosevariablestypicallySFVARmodel.NextwereporttheestimationresultsandtheDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012includedinaVARandasetofadditionalfactorsthateffectsofamonetarypolicyshock.Wealsocomparesummarizetheinfluenceofalargenumberofothervariables.theresultsofbothmodelswiththetraditionalVARmodelSecond,thefactorsweproposehaveanaddedmodicumofandtheFAVARmodelproposedbyBEE.Finally,wepresentstructuralmeaning.asummaryandconclusion.Wealsoproposeamodelthatispotentiallymoregeneral,theSFVARmodel.TraditionalmacroeconomicVARsincludeasetofvariablesusedtorepresentvariousconceptssuchasthepricelevel,realeconomicactivityormonetarypolicy.OftenII.TheModelsthevariableschosentomeasureeachoftheseconceptsissomewhatarbitrary.Forexample,studiesmightuserealGrossOurfirstmodel,theSFAVARmodel,isanaturalextensionofDomesticProduct(GDP),industrialproduction,orthethetraditionalVARmodel.Forexpositorypurposesweunemploymentratetomeasurerealactivity.ThepricelevelincludethreevariablestypicallyusedtosummarizeimportantmightbemeasuredbytheCPI,theGDPdeflator,orsomeaspectsofthemacroeconomy.Thesearethegrowthinothermeasureofprice.OftenthechoiceistousethoseindustrialproductionorIP,theCPIinflationrateorCPI,andvariablesthathavebeenmostoftenusedinpreviousstudiestheFFR.Inaddition,theSFAVARmodelincludesthree(e.g.IP,CPI,FFR)ortousethosevariablesknowntoproducegroupsof‘residualfactors’tosummarizeinformationnotreasonabledynamicresponses(e.g.thecommoditypricecapturedinthethreetypicalsummaryvariables.Thereisaindex).Dataavailabilityisalsorelevant,ascertainmeasuresvectoroftheseresidualfactorstoaccompanyeachtypicalmayonlybeavailableatquarterlyfrequencieswhileothersaresummaryvariable. Theeffectsofmonetarypolicyusingstructuralfactoranalysis2513OursecondmodelistheSFVARmodel.Inthismodelweindustrialproduction,theinflation/priceresidualfactorsareclassifyvariablesfromalargedatasetintoasmallnumberoforthogonaltothecontemporaneousconsumerpriceindexcategoriesandanalyseamodelwithfactorsdrawnfromtheseinflationrate,andthemonetarypolicyresidualfactorsarecategories.Forourexpositionwelookatthreecategories–theorthogonaltothecontemporaneousfederalfundsrate.realsector,inflationandthemonetarysector.WethenuseWeobtainthestructuralresidualfactorsbycollectingallthetheestimatedfactorsfromthesesubsetstosummarizetherealactivityseriesexceptindustrialproductioninthevectorcommoninformationineachcategory,andestimateaVARRXðRÞt,allseriesrelatedtopricesorinflationexceptthemodelforthesefactors.Tobeclear,thisVARmodelincludesconsumerpriceindexinthevectorRXðIÞt,andalltheinterestthefactors,butnotanyindividualseries.NotethattherateseriesormonetaryaggregateseriesexceptthefederalFAVARmodelwouldincludethetypicalindividualseriesasinfundsrateinthevectorRXðMÞt.WethenestimateEquation2atraditionalVAR,andaugmentthesewiththefactorsasbyOrdinaryLeastSquares(OLS).additionalexplanatoryvariables.23232323RXðRÞtb1100IPtruðRÞt676767674RXðIÞt5¼40b2205
4CPIt5þ4ruðIÞt5TheSFAVARmodelRXðMÞt00b33FFRtruðMÞtFollowingthenotationofBEE(2005),letYtbeavectorofð2ÞobservablevariableswithdimensionM1.Forourexposi-tionthevariablesinYaregrowthinIP,theCPIinflationrateNotethatthecoefficientmatrixbisblockdiagonal.(CPI),andthechangeintheFFR.SincethesevariablesmayAfterwards,weestimatethestructuralresidualfactorsbythe3notcompletelycapturetheforcesthatdrivethedynamicprincipalcomponentsmethodappliedtotheresidualsasbehaviouroftheeconomy,weincorporatetheinformationshowninEquation3.fromalargesetofothervariablesasfollows.First,we232323ruðRÞtRR00RFðRÞt11partitionalargedatasetintothreesubsets,onerelatedtoreal676I767activity,onerelatedtoinflation,andonerelatedtomonetary4ruðIÞt5¼40R2205
4RFðIÞt5þutð3Þpolicy.Second,foreachsubsetsuchastherealactivitysubsetruðMÞt00RMRFðMÞt33ofdata,weregresseachvariableinthesubsetonourHeretheblockdiagonalloadingmatrixRandtheresidualrepresentativerealactivityvariable(i.e.eachvariableinthefactorsareunknown.ByimposingtheloadingmatrixisblockrealactivitysubsetisregressedonIP)andretaintheresiduals.diagonal,weassumethateachsetofresidualsisinfluencedThenweestimatefactorsfromtheseresidualsandlabeltheseonlybythecorrespondingsetoffactors.Therefore,onecanresidualfactors.Sowehave‘realactivityresidualfactors’,interpreteachsetoffactorsstructurally,dependingonthe‘inflation/priceresidualfactors’and‘monetarypolicyresidualcommoncharacteristicofcorrespondingresiduals.Asthefactors.’InprincipletheseresidualfactorswouldcoverthevectorofresidualsfromEquation2arecontemporaneouslyspaceoftheeconomythatisnotexplainedbythethreeorthogonaltoIP,CPIandFFR,respectively,soarethetraditionalvariables–IP,theCPIandtheFFR.estimatedstructuralresidualfactorsfromEquation3.OurapproachistoaugmentourtypicalVARwiththese‘hidden’residualstructuralfactorsandestimatetheeffectsofamonetarypolicyshockinsuchamodel.TheSFAVARmodelTheSFVARmodelisillustratedinEquation1.2323TheSFVARmodelrecognizesthattheexactchoiceofRFðRÞtRFðRÞt1variablestobeincludedinatraditionalVARissomewhat66IPt7766IPt177ad-hoc.Forexample,itisdifficulttoknowifindustrial676766RFðIÞt7766RFðIÞt177productionbetterrepresentsrealactivitycomparedtovari-A
6CPI7¼CðLÞ
6CPI7þ"tð1ÞablessuchastheunemploymentrateorthecapacityutilizationDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May20126t76t176767rate.IntheSFVARmodelwedonotassumethatthesmallset4RFðMÞt54RFðMÞt15oftypicallyincludedvariablesaretheonlyindicatorsoftheFFRtFFRt1economicconceptsthesevariablesareintendedtocapture.HerematrixAisthecontemporaneouscoefficientmatrix,CðLÞInstead,weformsetsofvariablesthatarerelatedtotheisaconformablelagpolynomialoffiniteorderdthatcapturesunderlyingeconomicconceptsofrealeconomicactivity,pricestheintertemporalrelationshipsamongtheseresidualfactorsandmonetarypolicy,andusethesefactorstoexploretheandvariables,and"tisthevectorofthestructuralshockswithrelationshipsamongtheseeconomicconcepts.meanzeroandavariance–covariancematrixequaltotheThereislittleconsensusaboutwhichvariableisthebestidentifymatrix.HereRF(R)denotesthevectorof‘realactivityindicatorofmonetarypolicy.Manyyearsagoresearchersresidualfactor(s)’;RF(I)denotesthevectorof‘inflation/pricetendedtousesomebroadmonetaryaggregatevariables(e.g.residualfactor(s)’;andRF(M)denotesthevectorof‘monetaryM1,M2orM3).FriedmanandSchwartz(1963)arguedthatpolicyresidualfactor(s)’.Theseresidualfactorssummarizetheratesofchangeinmoneyaregoodapproximationstoextrainformationthatcannotbethetypicalvariablesinamonetarypolicydisturbances.However,identifyingmonetaryVAR–hereIP,CPIandFFR.Byconstruction,therealpolicyshockswithinnovationsinmonetaryaggregateshasledactivityresidualfactorsareorthogonaltocontemporaneoustotheliquiditypuzzle–positiveinnovationsinmonetary3RefertoBai(2003)formoredetailsonprincipalcomponentsmethod.WeestimatedtheprincipalcomponentsusingEviews6basedonthecorrelationmatrixoftheseriesineachsubsetafterthedataistransformedtobestationary. 2514D.LiuandD.W.JansenaggregatesappeartobeassociatedwithincreasesininterestwhereFRarethefactorsaffectingtherealstateoftrates,whichareonlyexpectedinmonetarycontractions.4theeconomy,FIarethefactorsdrivingtheinflationrateortPartlytosolvetheliquiditypuzzle,someauthors(e.g.pricelevelsandFMarethefactorsexplainingthemonetaryt6McCallum,1983;Sims,1986,1992;BernankeandBlinder,policyoftheeconomy.Theloadingmatrixisblock1992)suggestusingthefederalfundsrate.Otherssuggestusingdiagonal.somenarrowmonetaryaggregatestosolvetheliquiditypuzzle.Forthisarticle,wefindonerealactivityfactor,oneForexample,Eichenbaum(1992)andChristianoandinflation/pricefactorandonemonetarypolicyfactor.ThenEichenbaum(1992)provideevidencethatinnovationstoweestimateaSFVARmodelasshowninEquation5nonborrowedreservesreflectexogenousshockstomonetary2323policy,andKim(2001)usesinnovationsintheratioofFRFRtt1nonborrowedreservestototalreservestorepresentmonetaryAF
64FI75¼CFðLÞ
64FI75þ"Fð5Þtt1tpolicyshocks.EveniftheseapproachessucceedineliminatingMMFtFt1theliquiditypuzzle,thereisstillthepricepuzzle,thefindingthatpositiveinnovationsininterestratesandnegativeinno-whereAFisthecontemporaneouscoefficientmatrix,CFðLÞisavationsinnarrowaggregatesortheirratioareassociatedwithconformablelagpolynomialoffiniteorderdFthatdescribes5increasesinthepricelevel.theintertemporalrelationshipamongthesefactors,and"FistInpracticeitseemsclearthattheFedhasadoptedthethevectorofthestructuralshockswithmeanzeroandidentityfederalfundsrateasitspolicyinstrument.However,behindmatrixasthevariance–covariancematrix.changesinthefederalfundsratearechangesinmonetaryaggregatesastheFedconductsopenmarketoperations.Intheend,itisdifficultandperhapsnotevenappropriatetochooseasinglevariabletosummarizemonetarypolicy.Sims(1992)himselfacknowledgesthatthetraditionalVARanalysisreliesIII.TheDataandEstimationheavilyonpostulatingthatinnovationsinaparticularvariablerepresentmonetarydisturbances.ThedataIntheSFVARmodelwemeasuremonetarypolicyasthefactor(s)whichareestimatedfromalargesetofinterestrates,Thedatasetconsistsof308monthlyUSmacroeconomictimemonetaryaggregatesandoutstandingcreditseries,andweseries.TheperiodstartsinJanuary1972andendsinDecembertreattheinnovationstothemonetarypolicyfactorsasshocks72003,sowehave383observationsforeachvariable.tomonetarypolicy.TheoriginaldataseriesaretakenfromtheHaverUSECONForourexpositionweassumethattherearethreevectorsofdataset.Alltheseseriesarethentransformedtobevariables:thevectorofrealactivityvariables,XðRÞthat8tstationary.Weclassify172realactivityvariables,80inflationincludesIPandotherrealactivityvariables,thevectoroforpricevariables,and56monetaryvariables.Thelistoftheinflation/pricevariables,XðIÞtthatincludesCPIandotherseriesandtheirtransformationislistedintheAppendixpricevariables,andthevectorofmonetarypolicyvariables,(availablefromtheauthorsuponrequest).XðMÞtthatincludesFFRandothermonetarypolicyvariables.TherealactivitygroupconsistsofvariablesrelatedtoWethenestimatetheunderlyingfactorsfromthethreegroupsindustrialproduction,capacityutilization,manufacturers’ofobservableseriesusingprincipalcomponentsmethod.Weinventories,retailinventories,retailsales,realpersonalcon-furtherassumethatvariablesineachgroupareonlyinfluencedsumption,personalincome,newhousingstarts,employmentbythestateoftheeconomythroughthecorrespondingandaverageworkinghours.Theinflationorpricegroupisunderlyingfactors.So,wehave,composedofvariablesrelatedtotheconsumerpriceindex,theDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May201223232323producerpriceindex,thepersonalconsumptionexpenditureXðRÞtR00FReRttdeflatorandaveragehourlyearnings.Thelastgroupof6XðIÞ760I076FI76eI74t5¼45
4t5þ4t5ð4ÞvariablesiscloselyrelatedtomonetarypolicyanditincludesXðMÞt00MFMeMmonetaryaggregatevariables,avarietyofinterestrates,creditttoutstanding,etc.4SeeReichenstein(1987)andLeeperandGordon(1992).5Someauthorshavetriedtosolvetheprizepuzzlebyaddingvariablessuchascommoditypriceindexes.SeeSims(1992),Christianoetal.(1992),BernankeandMihov(1998)andrelatedstudies.6Inthisarticle,weconsiderthesethreecategoriesoffactorsrepresentingthereal,nominalandmonetarypolicyconditionsoftheeconomy.Furtherdividingthesefactorsintomoredetailedcategorieswilleventuallyviolatethespiritofthisexercise,whichistousefactoranalysistoreducedimensionality.Forsomesmallopeneconomies,webelievethereareextraexternalfactorsthatshouldbeconsidered,butgiventhattheUSisalargeopeneconomy,weassumethattheseexternalfactorsarerelativelylessimportant.Giventheongoingdebateaboutassetprices,wealsoconsiderthecasewhenthereisanextrasetof‘assetpricefactors’whichareestimatedfromalargenumberofassetpriceseries.TheestimatedimpulseresponsesafteramonetarypolicyshockfromtheSFVARmodelwithfourgroupsofstructuralfactorsare,qualitatively,almostidenticaltotheonespresentedhereusingonlythethreegroupsoffactors.7Inthisarticle,welookatthewholesampleperiodinsteadofsplittingitintosmallsubsamplesaccordingtotheFed’schairmaninposition.Webelievethatsincewearelookingattheeffectsofmonetarypolicyshocks,manuallysplittingthewholesamplewillloseonemajorsourceoftheexogenouspolicyshocks,changesofregimes,whichwillharmourpurposesofidentifyingandexaminingthemonetarypolicyshocks.8ThetheoreticalworkforfactoranalysisusingprincipalcomponentsislimitedtotheI(0)frameworkatthistime.SeeStockandWatson(1998)forreference. Theeffectsofmonetarypolicyusingstructuralfactoranalysis2515Estimationandidentification:theSFAVARmodelthecorrespondingvariable.Therefore,wecanwritetheidentificationmatrixAasWeestimateEquation2usingOLS.Wethenobtainresidual23vectorsthatareorthogonaltoIP,CPIandFFR,respectively.a1100000Finally,weestimatethecommonfactorsfromtheseresidual660a22000077vectorsusingthemethodofprincipalcomponents,asshownin66aaa0007763132337Equation3.AsdiscussedinStockandWatson(1998),A¼67ð7Þ6a41a420a44007principalcomponentscanconsistentlyrecoverthespace67spannedbythose‘surface’serieswhenthenumberofseries4a51a52a53a54a5505islargeenougheveninthecaseofhavingsmallamountsofa61a62a63a640a66datacontamination.Wefindthatthereisonlyonecommon19Sincevt¼A
"tthevariance–covariancematrixisgivenasstructuralfactorforeachresidualvector.ThenweusethesethreestructuralresidualfactorstoaugmentthetraditionalQ¼A1ðA1Þ0ð8Þthree-variableVARandestimateareduced-formSFAVARwhereQcanbeestimateddirectlyfromthereduced-formmodelasshowninEquation6.2323SFAVARmodel.RFðRÞtRFðRÞt1WegoastepfurtheranduseFisher’sz-statistictotest66IPt7766IPt177whethercorrelationsinEquation7aresignificantlydifferent6767fromzero66RFðIÞt7766RFðIÞt1776CPI7¼ðLÞ
6CPI7þvtð6Þpffiffiffiffiffiffiffiffiffiffiffi6t76t171j1þði,jÞj6767z½ði,jÞ¼n3lnð9Þ4RFðMÞt54RFðMÞt152j1ði,jÞjFFEDtFFEDt1HerenisthenumberofobservationsusedtoestimatetheHereðLÞ¼A1
CðLÞandvt¼A1
"t.BothðLÞandthecorrelations,(i,j)istheunconditionalpopulationcorrelationvariance–covariancematrixoftheresidualvectorvt,calledQ,betweenseriesiandseriesj.Ifr(i,j)istheunconditionalcanbeestimateddirectly.However,ifwewanttoderivethesamplecorrelationbetweenseriesiandj,thenz[(i,j)]impulseresponsefunctionsofstructuralshocks,weneedtogoz[r(i,j)]hasastandardnormaldistribution,providedthatbacktoEquation1whichtakesthecontemporaneousseriesiandjarenormallydistributed.Thenullhypothesisofrelationshipsamongthesevariablesandresidualfactorsintothetestisthatthecorrelationbetweenthetwoseriesiszero.consideration.SincetherearemoreparametersinEquation1BytestingthosecorrelationswederiveanextrarestrictionthaninEquation6,weneedtoimposerestrictionsontheonA,thata31iszero.ThenthefinalidentificationschemeismatrixA.2a00000311Wenowdescribetheassumptionsmadewithregardto60a00007identification.Webeginwithatypicalrecursiveordering.622767First,weassumethattheinnovationstothefederalfundsrate660a32a330007767
vt¼"tð10Þarethemonetarypolicyshocks,asinmuchoftheprevious6a41a420a4400767literature.Second,weassumethatthefederalfundsrateand4a51a52a53a54a5505theothermonetaryvariablesthataresummarizedbyaa61a62a63a640a66monetarypolicyresidualfactorreacttorealeconomicactivityandinflation/priceconditionswithinamonth.Third,weEquation10representsatypicalrecursiveidentificationassumethattheCPIinflationandotherpricerelatedvariablesprocessmodifiedtoincorporateinformationknownaboutthecontainedintheinflationresidualfactorrespondtorealresidualfactorsandtheadditionalzerorestrictionfromusingeconomicconditionwithinthemonth,butrespondtomon-theFishertest.AnalternativeweexploreistouseanDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012etarypolicyafteramonth.Fourth,forindustrialproductionidentificationmethodbasedonDirectedAcyclicGraphsandotherrealeconomicconditionswhicharedrivenbythe(DAGs)asproposedbySpirtesetal.(1993)andSwansonrealactivityresidualfactor,weassumethattheyareexogenousandGranger(1997).BesslerandYang(2003)andHaighandcontemporaneously.Asaresult,theorderorpreferenceoftheBessler(2004)aretwoexamplesofapplyingtheDAG11threevariablesandtheremainingthreestructuralfactorsisasmethodologytoidentifystructuraldisturbances.Forthisfollows:therealactivityresidualfactor,industrialproduction,approachwestartwithanundirectedgraphwithlinesbetweentheinflation/priceresidualfactor,theCPIinflationrate,theeveryvariableintheset.Herewehavesixvariables.These10monetarypolicyresidualfactorandthefederalfundsrate.linesareremovedsequentiallybasedonzerocorrelationorThisistheorderingshowninEquation6.Thenwemodifythiszeroconditionalcorrelation.Thatis,wetestthecorrelationsorderingtoincorporatetheideathat,byconstruction,eachbetweeneachtwovariablesorfactorsintheSFAVARinorderstructuralresidualfactoriscontemporaneouslyorthogonaltotoderivestructuralrestrictionsfortheelementsofmatrixA.9HereweincludeonlyonefactorfromeachgroupofseriesintheSFAVARmodelandSFVARmodel.Weexaminedthevalidityofthisassumptionbyestimatingmodelswithone,two,three,four,five,andsixresidualfactorsforeachpartitionofthelargedataset.FortheSFAVARmodel,thelargestloglikelihood,andsmallestSICandAIC,occurwhenthereisasingleresidualfactorforeachpartition.10Theorderbetweeneach‘observable’variableandthecorrespondingresidualfactorcanbeswitched.Forinstance,wecanputindustrialproductionfirstandtherealactivityresidualfactorsecond.ThatwillonlycausetheswitchofthefirstrowofmatrixAwiththesecondrowofmatrixAinEquation7.Theidentifiedinnovationsandtheimpulseresponsefunctionswillnotbeaffected.11SeemorerecentDAGapplicationsinYangetal.(2006)andWangetal.(2007). 2516D.LiuandD.W.JansenVerybriefly,theDAGmethodworkstoassigncausalityaswhereistheblockdiagonalloadingmatrixfollows.Theconditioningvariableonremovedlinesbetween23R00twoseriesiscalledthesepsetofthevariableswhoselineis6I7removed.Edgesaredirectedbyconsideringtriplessuchas¼4005ð13ÞX–Y–ZsuchthatXandYareadjacentbutnotXandZ.The00MlinesbetweenX,YandZaredirectedasX!YZ(meaningXcausesYandZcausesY)ifYisnotinthesepsetofXandZ.InEquation12,XðRÞtisthevectorcomposedof172seriesIfX!Y,YandZareadjacent,XandZarenotadjacent,andrelatedtorealactivity,XðIÞtisthevectorof80price/inflationthereisnoarrowheadatY,thenorientY–ZasseriesandXðMÞtisthevectorof56monetarypolicyindicatorseries.WefindthatthereisonestructuralfactorfromeachY!Zstructuralvector12–therealactivityfactorFR,theinflation/tpricefactorFIandthemonetarypolicyfactorFM.WethenApplyingtheDAGprocedure,weendupwiththefollowingttgraphdescribingtherelationshipamongoursixvariablesestimateareduced-formSFVARmodelasshowninTheaboveDAGimpliesthefollowingidentificationmatrix.Equation14.ComparedtoEquation10above,thisidentificationmatrixhas2323FRFRamuchlessrecursivestructure.Ithasmorecontemporaneoustt16FI7FðLÞ
6FI7impactsontherealresidualfactorandonIP,andfewer4t5¼4t15þtð14ÞcontemporaneousimpactsontheinflationresidualfactorandFMFMtt1onCPI.HereFðLÞ¼ðAFÞ1
CFðLÞ,¼ðAFÞ1
"F,andthevar-23tta1100a14a15a16iance-covariancematrixof,QF,canbeestimateddirectly.660a22a230a25a2677Foridentificationweagainfollowtwoapproaches.First,67followingmuchoftheliteratureintraditionalVARmodels,we600a3300076677
vt¼"tð11Þidentifythesystembymeansofarecursiveordering,a6a4100a4400767Choleskydecomposition.Werecursivelyorderthethree4a51a5200a5505structuralfactorswiththerealactivityfactorfirstandthea61a62a63a640a66monetarypolicyfactorlast.WecanspecifytheidentificationschemeasInapplicationtheidentificationschemeinEquation11generatedasingularHessianmatrixinourstructuralVARFFA
t¼"tð15Þlikelihood.Apparentlywehavetoomuchbi-directional,orundirected,causalstructure.ThuswemodifiedEquation11bywithaddingtheassumptionofacausalorderingonthecontempo-23aF00raneousrelationshipofmonetarypolicyandourrealvariables.11IntheDAGwefoundthatFFRandbothIPandtherealAF¼64aFaF075ð16Þ2122residualfactorwereconnectedbutthatcausalitycouldnotbeaFaFaF313233directed.ForestimationpurposesweimposetheassumptionthatthecausalityisfromtherealvariablestoFFRandnotinThisrecursiveidentificationschemeseemsreasonablegiventheotherdirection.Thatis,weimposea(16)¼a(26)¼0.theshortfrequencyofthedata.Theeconomy’srealactivityisOnereasonforincludingbothidentificationschemes,thecontemporaneouslyexogenouswithrespecttoboththemon-firstbasedonamodifiedrecursiveorderingandthesecondetarypolicyfactorandtheinflation/pricefactor,anditusuallybasedontheDAGmethodology,isthatidentificationistakeslongerthanamonthfortherealactivitytoadjusttoalwaysatleastpotentiallycontentious,andwewanttoprovideeitherchangesinmonetarypolicyorchangesinthecostofDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012someevidencethatourresultsarerobusttotheuseoftwoliving.However,monetarypolicy,whichisdesignedtowidelydifferentmethodsforcomingupwithidentifyinginterveneandinfluenceboththerealactivityandthepriceassumptions.level,shouldbeendogenouscontemporaneously,sothatitreactsquicklytotherealandnominalconditionsoftheeconomy.Estimation:theSFVARmodelWealsouseaDAG-basedidentificationscheme.TheDAGmethodologybasicallyidentifiesboththemonetaryfactorandFortheSFVARmodelweestimatethestructuralfactorsfromtherealfactorasexogenous,whilebothofthesefactorshavethe308timeseries.Byassumingablockdiagonalloadingcontemporaneousimpactsonthepricefactor.Thuswehavematrix,weestimatethecommonfactorsbyprincipalcompo-Equation17nentsasshownbelow.232323XðRÞFRaF00tt116XðIÞ76I7AF¼64aFaFaF75ð17Þ4t5¼
4Ft5þetð12Þ212223XðMÞFM00aFtt3312FortheSFVARmodelweestimatedone,two,three,four,fiveandsixfactorsforeachpartitionofourlargedataset,andagainwefoundthelargestlog-likelihoodandsmallestAkaikeInformationCriterion(AIC)andSchwarzInformationCriterion(SIC)occurredwhenourmodelhasonefactorfromeachpartition. Theeffectsofmonetarypolicyusingstructuralfactoranalysis2517IPCPIFederalFundsRate.0010.0008.8.0005.0006.6.0000.0004.4-.0005.0002.2-.0010.0000.0-.0015-.0002-.0020-.0004-.2510152025303540455101520253035404551015202530354045Fig.1.Theimpulseresponsestoafederalfundsratemonetarypolicyshockfromathree-variableVARNotes:ThethreevariablesareIP,theCPIandtheFFR.Thefirsttwovariablesareinfirstdifferencesoflogarithmsforstationarity.Thesolidlineistheimpulseresponseofeachvariable,andthedashedlinesaretheupperandlowerboundsofthetwo-SDconfidenceinterval.AgainweseethattheidentificationrestrictionsgeneratedbyFigure2reportstheimpulseresponsesfromthe14theDAGmethodologycandiffermarkedlyfromthoseFAVARmodelwithfivefactors.OnecanobservethatthetraditionallyimposedonVARmodels.ThesedifferencespricepuzzleisreducedconsiderablycomparedtotheVARhavebeenreportedinbyotherauthorsinotherapplications,modelbutitstillexists.Itseemsthatthefactorsdoandtheissuedeservesfurtherconsiderationasatopicinitscapturemoreinformationabouttheeconomy.Itis,however,ownregard.Forourpurposeshereitisimportantthatwehardtogiveanystructuralinterpretationtothesefactors,andinvestigatetherobustnessofourfindingstothesetwodifferentthismayimpedeourunderstandingofthestructureoftheidentificationschemes.economy.Figure3showstheimpulseresponsesgeneratedfromtheSFAVARmodelwiththreefactorsandthreevariables,andwithourmodifiedrecursiveidentificationassumptions.AgainIV.EmpiricalResultsontheEffectsofwetreattheinnovationstothefederalfundsrateasmonetaryMonetaryPolicypolicyshocksinthismodel.Thethreeresidualfactorscapturetheextrainformationabouttherealactivity,theIPandWecompareresultsfromourestimatedSFAVARandmonetaryconditionsthatarenotcontainedinindustrialSFVARmodelswithresultsfrombothaconventionalVARproduction,theCPI,andtheFFR,respectively.modelandfromourversionofBEE’s(2005)FAVARmodel.TocheckthattheinformationcapturedbythesethreeFirst,welookattheimpulseresponsestoafederalfundsresidualfactorsisimportant,weapplyamodelspecificationratemonetarypolicyshockfromtheconventionalthree-test.TheunrestrictedmodelisvariableVAR(IP,CPIandFFR),asshowninFig.1.We232323observeastrongexampleoftheso-calledpricepuzzle–pricesIPtIPt1RFðRÞt1676767goupsignificantlyafteracontractionarymonetarypolicy4CPIt5¼11ðLÞ
4CPIt15þ12ðLÞ
4RFðIÞt15þv1tshock.AccordingtoSims(1992),thiscouldbetheresultsthatFFRtFFRt1RFðMÞt1Downloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012thedatainthestandardVARmaynotadequatelycapturetheð18Þsignalsoffutureinflationandwhatappearstobeamonetarypolicyshockcouldbejustaresponsetofutureinflation.So,Wetestthenullhypothesisthat12ðLÞ¼0,orthatthetheresultscouldbeseriouslycontaminatedbecauseofinfor-residualfactorscanbeeliminatedfromthemodel.ThemationmissedintheVAR.likelihoodratioteststatisticstronglyrejectsthisnullhypoth-15BEE(2005)suggestsaFAVARmodel.Theirmodeltreatsesis.Thissuggeststhattheinformationcontainedinthethefederalfundsrateasanobservedfactor,andtheyestimateresidualfactorsisimportantandshouldnotbeneglectedinadditionalfactorsfromatotalof120timeseries.Werepeatspecifyingourmodel.theirexerciseusingourdataset,whichhas188additionalWealsoapplythelikelihoodratiotesttotestiftheinclusionvariablesandisupdatedtoDecember2003.13ofthethreetraditionalvariables(IP,CPIinflationandFFR)is13Weestimatethefactorsfortheirmodelusingprincipalcomponents.BEE(2005)alsouseaGibbssamplingproceduretosimultaneouslyestimatethefactorsandthedynamicbehaviouroftheeconomy.Regardingthelatter,theyreportthatthelikelihood-basedestimationmethodsuffersfromtheadditionalstructuralrestrictionsitimposesandproducesfactorsthatdonotsuccessfullycaptureinformationaboutreal-activityandprices.14BEE(2005)alsoestimateathree-factorFAVARmodel.Theyfindthatthismodelandthefive-factormodelreachbasicallythesameconclusions.Theyalsoreportthatfurtherincreasingthenumberoffactorsdoesnotchangethequalitativenatureoftheirresults.15Thelikelihoodratioteststatisticisequalto2timesthedifferencebetweenthelog-likelihoodoftherestrictedmodelandthatofthe2unrestrictedmodel.Ithasadistributionwiththedegreeoffreedomthatequalstothenumberofrestrictions.Inthistest,theteststatisticis337.396,whilethecriticalvalueat5%withthedegreeoffreedomthatequalsto36is51.Thenumberoflagsis12. 2518D.LiuandD.W.JansenIPCPIFederalFundsRate.0006.0003.6.0004.0002.4.0002.0001.0000.2-.0002.0000-.0004.0-.0001-.0006-.2-.0002-.0008-.0010-.0003-.4048121620242832364044480481216202428323640444851015202530354045Fig.2.TheimpulseresponsestoafederalfundsratemonetarypolicyshockfromtheFAVARmodelwithfive-factorsNote:TheimpulseresponsesinthefigurearegeneratedfromtheFAVARmodelwithfive-factorsasgivenbyBernankeetal.(2005).importantforexplainingtheresidualfactors.Forthispurposeandtherealeconomicactivityresidualfactorisdirectlyrelatedtheunrestrictedmodelistounemploymentandnegativelyrelatedtocapacity232323utilization.RFðRÞtIPt1RFðRÞt1WhenweexaminetheresponsesoftheCPI,wenoticethat6767674RFðIÞt5¼21ðLÞ
4CPIt15þ22ðLÞ
4RFðIÞt15þv2ttheprizepuzzleisreducedconsiderablycomparedtotheRFðMÞtFFRt1RFðMÞt1traditionalthree-variableVARbutnoteliminated.Wealsonotethatthereisnopricepuzzlefortheinflation/priceresidualð19Þfactor.16Thenullhypothesisthat21ðLÞ¼0isalsostronglyrejected.AsshowninTable3,thisinflation/priceresidualfactorisBothtestsjustifythemodelspecificationoftheSFAVARmorecorrelatedwithanothertwoimportantmeasuresofcostmodelthatincludesinformationbothfromthethreetradi-ofliving:theproducerpriceindex(PPI)forfinishedconsumertionalvariablesandthecorrespondingthreeresidualfactors.nondurablegoodslessfood,andthepersonalconsumptionTable1reportsthecontemporaneouscorrelationamongtheexpenditure(PCE)deflatorlessfoodandenergy.Thissuggestsresidualfactors.Theinflation/priceresidualfactorhaslittlethatasinglevariable(e.g.theCPI)maynotbesufficienttocorrelationwitheitheroftheothertworesidualfactors.Itmayadequatelycapturethepriceeffect.ItalsosuggeststhatCPIseemabitsurprisingtoseetherealactivityresidualfactorisinflationdoesnotquitecapturewhatwemeanby‘inflation’.morecorrelatedwiththemonetarypolicyresidualfactorthanInsteaditsuggeststhatweshouldlookatothermeasuresofwiththeinflation/priceresidualfactor.pricechangeinordertohaveamorecompletepictureoftheTheimpulseresponsefunctionsappearinFig.3.Afterapriceeffect.positiveshocktothefundsrate,industrialproductionFinally,wenotethatthemonetarypolicyresidualfactorisdecreasessignificantlyatlag5beforeeventuallyreturningtosignificantlypositivelycorrelatedwithmonetaryaggregatesitsoriginallevel.Thisisconsistentwiththeconventional(M1andM2)asshowninTable4,andthatisconsistentwithwisdomthatmonetarypolicytighteninghasanegativeimpactourobservationthatthemonetarypolicyresidualfactoronrealeconomicactivity.NotethattherealactivityresidualdeclinessignificantlyafteracontractionarymonetarypolicyDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012factorshowsareversepattern.Itincreasesafterapositiveshock.Noliquiditypuzzleisobserved.shocktothefundsrate.BecausethisistherealactivityresidualWealsoestimatedourSFAVARmodelwiththeDAG-factor,foundaftersubtractingthedirectimpactofchangesininspiredidentificationassumptions.Theresultingimpulsethefundsrateonindustrialproduction,thisprocyclicalimpactresponsefunctionsarenearlyidenticaltothosereportedinofmonetarypolicyislesssurprising.Fig.3.Inparticularthepricepuzzleremains,andofnearlyTable2providesmoreperspective.ItshowstheexplanatoryidenticalmagnitudeandcharacterasshowninFig.3.poweroftherealactivityresidualfactorforeachrealvariableTurningnowtoourSFVARmodel,weexaminethethreelisted.Therealactivityresidualfactorhasthebiggeststructuralfactorsestimatedbytheprincipalcomponents2explanatorypower(intermsofR)forthosecapacitymethod.InTable5,weseethattherealactivityfactorhasautilizationvariablesanditalsohashighexplanatorypowerlowcorrelationwiththemonetarypolicyfactor,consistentforunemploymentrate.Moreover,thisrealactivityresidualwiththeviewthatmoneyhaslittleimpactonrealactivityevenfactorisnegativelycorrelatedwithcapacityutilizationandintheshortrun.Wealsoobservethattheinflation/pricefactorpositivelycorrelatedwiththeunemploymentrate.Thisandthemonetarypolicyfactorarehighlycorrelated,some-explainstheprocyclicalresponseoftherealactivityresidualthingwewouldexpect.Tables6–8displaytheexplanatoryfactortoafederalfundsrateshock.Thefundsrateincreasepowerofeachstructuralfactor.Weseethattherealactivitywouldincreaseunemploymentandreducecapacityutilization,factorhasaquitelargeexplanatorypowerformanyimportant16Theteststatisticis513.298. Theeffectsofmonetarypolicyusingstructuralfactoranalysis2519RealActivityResidualFactorIP1.6.0012.00081.2.00040.8.0000-.00040.4-.00080.0-.0012-.0016-0.4-.0020-0.8-.00245101520253035404551015202530354045Inflation/PriceResidualFactorCPI1.0.0008.00060.5.0004.00020.0.0000-.0002-0.5-.0004-1.0-.00065101520253035404551015202530354045MonetaryPolicyResidualFactorFederalFundsRate0.8.80.4.40.0.0-0.4Downloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012-.4-0.8-1.2-.85101520253035404551015202530354045Fig.3.TheimpulseresponsestoafederalfundsratemonetarypolicyshockfromtheSFAVARmodelTable1.CorrelationmatrixofthestructuralresidualfactorsRealactivityInflation/priceMonetarypolicyresidualfactorresidualfactorresidualfactorRealactivityresidualfactor10.0860.350Inflation/priceresidualfactor0.08610.056Monetarypolicyresidualfactor0.3500.0561 2520D.LiuandD.W.JansenTable2.Explanatorypoweroftherealactivityresidualfactor2VariableCoefficientRCapacityutilization:industry0.5583*(0.0000)0.8456Capacityutilization:manufacturing0.6237*(0.0000)0.8482Capacityutilization:durablegoodsmanufacturing0.8155*(0.0000)0.8550Capacityutilization:nondurablegoodsmanufacturing0.3980*(0.0000)0.6003Manufactures’inventories0.0006*(0.0000)0.1577Manufactures’shipments0.0002(0.0974)0.0072Retailinventories0.0003*(0.0000)0.0750Retailsales0.0000(0.7261)0.0003Personalconsumption:durablegoods0.0006*(0.0137)0.0218Personalconsumption:nondurablegoods0.0001(0.1520)0.0054Personalconsumption:services0.0000(0.2840)0.0030Disposalpersonalincome0.0000(0.9288)0.0000Newprivatehousingauthorized0.0145*(0.0000)0.1262Manufactures’shipmentofmobilehomes0.0347*(0.0000)0.4148Housingstarts0.0163*(0.0000)0.1938Allemployees:totalnonfarm0.0002*(0.0000)0.2188Civilianemployment0.0001*(0.0000)0.0436Indexofhelpwantedinnewspapers0.0003(0.2579)0.0034Unemploymentrate0.1493*(0.0000)0.3905Averageweeklyhours:totalprivateindustries0.0690*(0.0000)0.2381Averageweeklyhours:manufacturing0.0536*(0.0000)0.2173Notes:Forthistableweregressedeachvariableinthefirstcolumnontherealactivityresidualfactor.Thesecondcolumnreportsthecoefficientonthefactorineachregression,andthenumbersinparenthesesarep-values.ThelastcolumnistheR-squareofeachregression.*Denotessignificanceatthe5%level.Table3.Explanatorypoweroftheinflation/priceresidualfactor2VariableCoefficientRPPI:finishedgoods0.0005*(0.0000)0.1083PPI:finishedconsumergoods0.0007*(0.0000)0.1770PPI:finishedconsumerdurablegoods0.0002*(0.0017)0.0255PPI:finishedconsumernondurablegoodslessfoods0.0013*(0.0000)0.2599Averagehourlyearning:totalprivateindustries0.0002*(0.0059)0.0197Averagehourlyearning:goods-producingindustries0.0003*(0.0000)0.1464Averagehourlyearning:manufacturing0.0003*(0.0000)0.1273Averagehourlyearning:durablegoodsmanufacturing0.0003*(0.0000)0.1004Averagehourlyearning:nondurablegoodsmanufacturing0.0003*(0.0000)0.1077Averagehourlyearning:privateservice-providingindustries0.0002*(0.0000)0.1112PCE0.0000(0.2273)0.0038PCE:lessfoodandenergy0.0003*(0.000)0.2104Downloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012PCE:durablegoods0.0003*(0.0000)0.1331PCE:nondurablegoods0.0004*(0.0000)0.1477PCE:services0.0003*(0.0000)0.1835Notes:Forthistableweregressedeachvariableinthefirstcolumnontheinflation/priceresidualfactor.Thesecondcolumnreportsthecoefficientonthefactorineachregression,andthenumbersinparenthesesarep-values.ThelastcolumnistheR-squareofeachregression.*Denotessignificanceatthe5%level.realactivityvariablessuchasindustrialproduction,capacityFinally,inTable8weseethatthemonetarypolicyfactorisutilization,housingstartsandemployment.Further,thisrealhighlypositivelycorrelatedwithshort-runinterestratessuchactivityfactorispositivelycorrelatedwithalloftheserealasthefederalfundsrateandtheTreasurybillrates,andisactivityvariablesexcepttheunemploymentrate.negativelycorrelatedwithhighpoweredmoney,themonetaryTheinflation/pricefactorispositivelycorrelatedwiththebaseandnonborrowedreserves.CPI,thepersonalconsumptionexpendituredeflator(PCE)Figure4displaystheimpulseresponsesofthethreefactorsandtheproducerpriceindex(PPI).Again,thisisanexpectedwhenweestimatetheSFVARmodelwithourrecursiveresultandsupportstheideathattheinflation/pricefactoridentificationscheme.Acontractionarymonetarypolicyactuallycapturestheunderlyingconceptofinflation.shock–anincreaseinshort-runinterestratesand/ora Theeffectsofmonetarypolicyusingstructuralfactoranalysis2521Table4.Explanatorypowerofthemonetarypolicyresidualfactor2VariableCoefficientR3-Monthtreasurybillrate0.1098*(0.0054)0.02016-Monthtreasurybillrate0.1390*(0.0003)0.0334Nonborrowedreserve0.0000(0.9115)0.0000Monetarybase0.0001(0.0980)0.0072M10.0003*(0.0007)0.0296M20.0001*(0.0075)0.0186M30.0000(0.3747)0.0021Nonrevolvingconsumercreditoutstanding0.0001(0.1259)0.0061Consumercreditoutstanding0.0002*(0.0008)0.0291Notes:Forthistableweregressedeachvariableinthefirstcolumnonthemonetarypolicyresidualfactor.Thesecondcolumnreportsthecoefficientonthefactorineachregression,andthenumbersinparenthesesarep-values.ThelastcolumnistheR-squareofeachregression.*Denotessignificanceatthe5%level.Table5.CorrelationmatrixofthestructuralfactorsRealactivityfactorInflation/pricefactorMonetarypolicyfactorRealactivityfactor10.1210.010Inflation/pricefactor0.12110.568Monetarypolicyfactor0.0100.5681Table6.Explanatorypoweroftherealactivityfactor2VariableCoefficientRIndustrialproduction0.0007*(0.0000)0.4255IP:durableconsumergoods0.0009*(0.0000)0.0876IP:nondurableconsumergoods0.0003*(0.0000)0.0491IP:manufacturing0.0008*(0.0000)0.4189Capacityutilization:industry0.4387*(0.0000)0.6109Capacityutilization:manufacturing0.5000*(0.0000)0.6375Capacityutilization:durablegoodsmanufacturing0.6275*(0.0000)0.5923Capacityutilization:nondurablegoodsmanufacturing0.3581*(0.0000)0.5685Manufactures’inventories0.0002*(0.0016)0.0259Manufactures’shipments0.0010*(0.0000)0.1677Retailinventories0.0004*(0.0000)0.1109Retailsales0.0004*(0.0004)0.0322Downloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012Personalconsumption:durablegoods0.0004(0.1058)0.0069Personalconsumption:nondurablegoods0.0001*(0.0449)0.0105Personalconsumption:services0.0000(0.2092)0.0041Disposalpersonalincome0.0002*(0.0109)0.0169NewPrivatehousingauthorized0.0208*(0.0000)0.3023Manufactures’shipmentofmobilehomes0.0338*(0.0000)0.4589Housingstarts0.0212*(0.0000)0.3822Allemployees:totalnonfarm0.0003*(0.0000)0.6678Civilianemployment0.0002*(0.0000)0.1935Indexofhelpwantedinnewspapers0.0019*(0.0000)0.1321Unemploymentrate0.1014*(0.0000)0.2110Averageweeklyhours:totalprivateindustries0.0576*(0.0000)0.1943Averageweeklyhours:manufacturing0.0628*(0.0000)0.3487Notes:Inthistable,weregressedeachvariableinthefirstcolumnontherealactivityfactor.Thesecondcolumnshowsthecoefficientbeforethefactorineachregressionandthenumbersintheparenthesesarethep-values.ThelastcolumnistheR-squareofeachregression.*Denotessignificanceatthe5%level. 2522D.LiuandD.W.JansenTable7.Explanatorypoweroftheinflation/pricefactor2VariableCoefficientRCPI:allitems0.0005*(0.0000)0.8681CPI:commodities0.0007*(0.0000)0.7303CPI:durables0.0005*(0.0000)0.4667CPI:nondurables0.0007*(0.0000)0.5607CPI:services0.0004*(0.0000)0.5469CPI:gasoline0.0031*(0.0000)0.2782PPI:finishedgoods0.0008*(0.0000)0.5444PPI:finishedconsumergoods0.0008*(0.0000)0.4638PPI:finishedconsumerdurablegoods0.0005*(0.0000)0.2500PPI:finishedconsumernondurablegoodslessfoods0.0013*(0.0000)0.4679Averagehourlyearning:totalprivateindustries0.0003*(0.0000)0.4172Averagehourlyearning:goods-producingindustries0.0004*(0.0000)0.3466Averagehourlyearning:manufacturing0.0004*(0.0000)0.3231Averagehourlyearning:durablegoodsmanufacturing0.0004*(0.0000)0.2610Averagehourlyearning:nondurablegoodsmanufacturing0.0004*(0.0000)0.2811Averagehourlyearning:privateservice-providingindustries0.0003*(0.0000)0.3571PCE0.0004*(0.0000)0.8450PCELessfoodandenergy0.0003*(0.0000)0.5535PCE:durablegoods0.0004*(0.0000)0.4604PCE:nondurablegoods0.0007*(0.0000)0.6701PCE:services0.0003*(0.0000)0.4483Notes:Forthistableweregressedeachvariableinthefirstcolumnontheinflation/priceresidualfactor.Thesecondcolumnreportsthecoefficientonthefactorineachregression,andthenumbersinparenthesesarep-values.ThelastcolumnistheR-squareofeachregression.*Denotessignificanceatthe5%level.Table8.Explanatorypowerofthemonetarypolicyfactor2VariableCoefficientRFederalfundsrate0.7314*(0.0000)0.93563-Monthtreasurybillrate0.6217*(0.0000)0.96216-Monthtreasurybillrate0.6151*(0.0000)0.9769Non-borrowedreserves0.0001(0.6654)0.0005Monetarybase0.0001(0.2702)0.0032M10.0000(0.8323)0.0001M20.0001*(0.0047)0.0208M30.0003*(0.0000)0.0003Nonrevolvingconsumercreditoutstanding0.0001(0.0838)0.0078Consumercreditoutstanding0.0002*(0.0034)0.0223Notes:Forthistableweregressedeachvariableinthefirstcolumnonthemonetarypolicyresidualfactor.Thesecondcolumnreportsthecoefficientonthefactorineachregression,andthenumbersinparenthesesareDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012p-values.ThelastcolumnistheR-squareofeachregression.*Denotessignificanceatthe5%level.RealActivityFactorInflation/PriceFactorMonetaryPolicyFactor0.4.80.80.0.4-0.40.4.0-0.80.0-.4-1.2-0.4-1.6-.8510152025303540455101520253035404551015202530354045Fig.4.TheimpulseresponsestoamonetarypolicyfactorshockfromtheSFVARmodel Theeffectsofmonetarypolicyusingstructuralfactoranalysis2523IPCPIFederalFundsRate.0002.0004.7.0003.6.0000.0002.5-.0002.0001.4.0000.3-.0004-.0001.2-.0006-.0002.1-.0003.0-.0008-.0004-.1-.0010-.0005-.2048121620242832364044480481216202428323640444804812162024283236404448CapacityUtilization:IndustryCapacityUtilization:ManufacturingMonetaryBase.1.2.00002.1.00001.0.0-.1.00000-.1-.2-.2-.00001-.3-.3-.00002-.4-.4-.00003-.5-.5-.00004-.6-.6-.7-.00005048121620242832364044480481216202428323640444804812162024283236404448Manufactures'InventoriesPersonalConsumption:Non-durableGoodsDisposalPersonalIncome.00005.00004.00004.00000.00000.00000-.00005-.00004-.00004-.00010-.00008-.00015-.00008-.00012-.00020-.00012-.00025-.00016-.00030-.00016-.00020048121620242832364044480481216202428323640444804812162024283236404448Fig.5.TheimpulseresponsesofvariousvariablestoamonetarypolicyfactorshockfromtheSFVARmodeldecreaseinmonetaryaggregates–causestheinflation/priceWefindnoliquiditypuzzle.Therealactivityvariablesdeclinefactortoincreaseinsignificantlyrightaftertheshockandthenaftertheshock,excepttheunemploymentrate,whichrises.Downloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012declinegradually.ThepatterndoesnotshowstatisticallyThepricepuzzletotallydisappears,andtheresponseofthesignificantevidenceofthepricepuzzlewhichhastroubledaggregatepriceindexesshowsevidenceofstickyprices.previousVARresearch.Further,thisresultisconsistentwithWeplottheidentifiedmonetarypolicyshocksseriesfromtheideathatpricesaresticky.thethree-variableVARmodel,BEE’sfive-factorFAVARInresponsetoacontractionarymonetaryshock,therealmodel,andourthree-factorSFVARmodelinFig.6.Theseactivityfactorrisesimmediatelybutnotsignificantly,thenseriesgenerallyshowsimilarpatterns.Forinstance,1973–1974dropssignificantlyandpersistsforaboutayearbeforeandthelate1970’s–early1980’sareperiodsofgreaterreturningtoitspreviouslevel.Thisisconsistentwiththevolatilityinallthreeseries.However,ifweexaminethevaluesideaoflong-runmonetaryneutrality,andalsowiththegeneraloftheseseriesmorecloselyweobservebigdifferences.Theagreementthatrealactivitytemporarilydeclinesaftera1973–1974oilcrisisofficiallystartedinOctober1973,butthecontractionarymonetarypolicyshock.crisiswasexpectedmonthsearlier,asshownbythelargeTheSFVARmodelalsoallowsustoderivethedynamicincreaseintheFFR,about2%pointsorfrom8.49%to10.4%behaviourofeachofthe308variablesinthedatasetafteranyinJuly1973.Asexpected,allseriesshowsignificantcontrac-kindofshock.InFig.5,weplottheimpulseresponsesoftionaryshocksinthatmonth,withmagnitudesof3.07,2.55variouskeyvariablestoamonetarypolicyfactorshock.Theseand1.28,respectively.Itseemsthatthepolicyshocksfromtheresponsefunctionsareallconsistentwithwhatwewouldfirsttwomodelsaresomewhatextremegiventhattheactualexpect.ThefederalfundsraterisesandmonetaryaggregateschangeintheFFRwaslessthan2percentagepoints.Thedeclineafterthecontractionarymonetarypolicyfactorshock.VARandFAVARmodelsseemtooverestimatethepolicy 2524D.LiuandD.W.JansenHousingStartsAllEmployees:TotalNonfarmUnemploymentRate.005.0001.16.000.0000.12-.005-.0001.08-.010-.015-.0002.04-.020-.0003.00-.025-.030-.0004-.04048121620242832364044480481216202428323640444804812162024283236404448M1PCEPPI.000004.0003.0006.0002.0004.000000.0001.0002-.000004.0000.0000-.0001-.000008-.0002-.0002-.000012-.0003-.0004-.000016-.0004-.0006048121620242832364044480481216202428323640444804812162024283236404448Fig.5.Continued.shock.SimilarextremevaluesareobservedinNovember1979,First,similartotheFAVARmodel,theSFVARandwhentheactualFFRdecreasedbyabout0.6percentageSFAVARmodelsincorporatemoreinformationthanthepoints.Herethethree-varaibleVARmodelandtheFAVARtraditionalVARmodel.TheSFVARandSFAVARmodelsmodelgenerateshocksaslargeas2.46and2.48percentageprovidealimitedstructuralinterpretationforthefactors.Thepoints,respectively,whileourSFVAR’sshockis0.1.Givenresultingimpulseresponsesareconsistentwithconventionaltheaboveobservations,webelieveourSFVARmaymoretheoriesandwithpriorempiricalresults,andthepricepuzzleaccuratelycapturetheexogenousmovementsinmonetaryandtheliquiditypuzzleareattenuated(inthecaseofthepolicy.SFAVARmodel)oreliminated(inthecaseoftheSFVAR19Wealsoexaminethecorrelationsamongthreeshockseries.model).TheresultsareconsistentwithSims’(1992)missingWefoundtheshocksfromthree-variableVARmodelandinformationexplanationsforthepuzzlesobservedusingtheBEE’sFAVARmodelarehighlycorrelated,withacorrelationtraditionalVAR.coefficientof0.788;whilepartiallyexplainwhybothshocksgeneratesimilarimpulseresponses.OurSFVARmodelisDownloadedby[K.U.Leuven-Tijdschriften]at08:3809May2012correlatedwiththethree-variableVAR,butthecorrelationV.Conclusions17coefficientislower,0.555.WealsoestimatedtheSFVARmodelwithourDAG-Inthisarticle,weusethemethodofstructuralfactoranalysisinspiredidentificationassumptions.Thisprovidednearlytoevaluatetheeffectsofmonetarypolicyinadatarichidenticalqualitativeandevenquantitativeresultstothoseenvironment.ThisallowsustoemploytheinformationfromashowninFig.4.AswasthecasewiththeSFAVARmodel,theverylargedataset,andatthesametimewecanstillinterpretlargedifferencesincausalstructuredidnottranslateintotheunderlyingfactorsestimatedbyprincipalcomponentsdifferencesintheimpulseresponsefunctions.structurally.WethinkthereareclearadvantagesinusingtheSFVARToevaluatetheeffectsofmonetarypolicy,weproposetwomodel,andperhapsadvantagesinusingtheSFAVARmodel,structuralfactormodels.OneistheSFAVARmodel,where18relativetothetraditionalVARandBEE’sFAVARmodel.shockstothefederalfundsratearetreatedasinnovationsto17WealsoobserveamorevolatilenatureoftheshockseriesgeneratedfromSFVARcomparedwiththeothertwoseries.18InLiuandJansen(2007),similarSFVARmodelswereappliedtoforecastsomekeymacroeconomicvariables.TheyfoundtheSFVARmodeloutperformsothermodelsincludingtraditionalVARandBEE’sFAVARmodelinmostcases,especiallyatlongerforecastinghorizons.19Itisworthnotingthattheaimofthispartofthearticleistoproposeappropriatewaystoexaminetheeffectsofmonetarypolicyshocksinadatarichenvironment,insteadofjusttoeliminatethepuzzles.Thereareofcourseotherwaysoffixingthepuzzles,suchasbyincludingacommoditypriceindexinaconventionalVAR. 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