Using Measures of Expectations to Identify the Effects of a Monetary Policy Shock

Boardof Governorsof the FederalResemeSystem InternationalFinanceDiscussionPapers Number537 January1996 USINGMEASURESOF EXPECTATIONSTO IDENTIFYTHE EFFECTSOF A MONETARYPOLICYSHOCK AlIanD. Brunner NOTE: InternationalFinanceDiscussionPapersare preliminarymaterialscirculatedto stimulate discussionandcriticalcomment. Referencesinpublicationsto InternationalFinanceDiscussion Papers(otherthananacknowledgementthatthewriterhadaccessto unpublishedmaterial)shouldbe clearedwiththe authoror authors.

ABSTRACT Thispaperconsidersanalternativeeconometricapproachto the VARmethodologyfor identifyingandestimatingtheeffectsof monetarypolicyshocks. Thealternativeapproachincorporatesavailablemeasuresof marketparticipants’expectationsof economicvariablesinorderto calculateeconomicinnovationsto thosevariables. In general,expectationsmeasuresshouldprovide importantadditionalinformationrelativeto a standardVARanalysis,sincemarketparticipants presumablyusea muchricherinformationsetthanthatassumedinatypicalVAR model. The resultinginnovationsareeasilyincorporatedin aVAR-likefimework. Theempiricalresultsarequitesurprising. First,whenexpectationsare incorporated,the varianceof all innovationsisreducedsubstantially. Second,innovationsto the federalfundsrate derivedusingthealternativeapproachareonlysomewhatcorrelatedwiththeirVARcounterparts, whileinnovationsto othereconomicvariablesare essentiallyuncorrelated. Still,monetarypolicy shoch derivedusingthetwoapproachesare a(sosomewhatcorrelated,sinceinnovationsto pricesand economicactivityexplainonlya smallfractionof innovationsto thefderal fundsrate. Asa consequence,theimpulseresponsesof economicvariablesto thetwo setsof monetarypolicyshocks haveremarkablysimilarproperties.

UsingMeasures of Expectations to Identi& the Effects of a Monetary PolicyShock AllanD. Brunnerl I. Introduction Vectorautoregressiv(eVAR)models,popularizedby Sims(1980),havebeenusedwidelyand extensivelyby economiststo studythedynamicbehaviorof economicvariables. Theappealof VAR modelsislikelydueto severalattractivefeaturesrelativeto other econometric modeling approaches. These features include a minimum number of identi~ing restrictions, fewexogenousvariables,andan easeof implementation.Still,theuseof aVARmodelrequiresa fewstrongassumptionsaboutthe availabilityof informationto economicagents,someof whicharealsocommonto othermoreoveridentifiedeconometricmodels. Thispaperconsidersan alternativeapproachthataddresssome possibleshoticomingsof theVARapproach,whilemaintainingmanyof itsappealingfeatures. Theestimationof a structuralVARm~el generally requires two steps. First, a vector of economic variables, ~, is regressed on several lags of itself. The set of lagged variables (dated t-1 and earlier) is assumed to be a good proxy for the information set that is available to economic agents just prior to the determination of Xt. As a consequence, VAR residuals are interpreted as economic innovations, new informationaboutXtthatbecomesavailableattimet. In thesecondstepof estimation,the innovationsaredecomposedintoorthogonalshoch usingoneof severalmethods. Theseshocksare ofiengivena structuralor behavioralinterpretation. Thispaperisconcernedprimarilywithtwo implicitassumptionsthatare madeinthe firststep 1 Theauthorisan economistinthe InternationalFinanceDivision,Boardof Governorsof the FederalReserveSystem. Theauthorwouldliketo thankNeil Ericsson,BillHelkie,DaleHenderson, andworkshopparticipantsattheBoardof Governorsfor usefil commentsonearlierversionsof this paper. He isalsogratefulto LarryChristian, CharlieEvans,ChristianGilles,VincentReinha.rt,and GlennRudebuschfor helpfil discussionsandto AthanasiosOrphanidesandJamesWalshfor providing the MMSdata. Thispaperrepresentstheviewsof theauthorandshouldnotbe interpretedas reflectingthe viewsof the Boardof Governorsof theFederalReserveSystemor othermemberof its staff. Theauthorisresponsibleforanyerrors.

oftheVARmethodologythat may notaccordwellwithreality. First,sincemanyeconomicdatafora ptiicular periodare notreleaseduntilsubsequentperiods,the informationsetthat istypicallyusedby VARmodelscontainsinformationthat isnotyetavailableto someeconomicagents. Second,thereis an assumptionthattheappropriateinformationsetcontainsonly laggedvaluesof ~. In actuality,the comectinformationsetlikelycontainslagsof manyothereconomicvariablesnotcontainedin~. In thispaper,the firstproblemisaddressedby simplydroppingfromthe informationsetthose datathatarenotactuallyavailableto economicagents. Thesecondproblemismitigatedby incorporatingmarketparticipants’expectationsof economicvariables. Theseexpectationsmeasuresshould bring importantadditionalinformationintotheanalysis,sincemarketparticipantspresumablyusea muchricherinformationset(relativeto a standardVARmodel)to maketheir forecasts. Importantly, theexpectationsmeasuresserveas anefficientandconvenientwayto expandthe impliedinformation setbeyondthatusedby a typicalVARmodel. In orderto illustratethealternativeeconometricmethodology,thispaperconsidersthetaskof identi&ingmonetarypolicyshocksandestimatingtheireffectsonvariousmacroeconomicvariables. Indeed,therehasbeena greatdealof recentinterestinthistopic. Forexample,Christian and Eichenbaum(1992)and Leeperand Gordon(1992)examinedthe “liquidi~effects”of monetarypolicy shocks,the immediatereactionof economicvariablesto unexpectedchangesinthe stanceof monetary policy. Morerecently,Bemankeand Blinder(1992),Strongin(1992),Gordonand Leeper(1995), Christian, Eichenbaum,and Evans(1994)andBrunner(1994)haveexploredalternativewaysof identi~ing monetarypolicyshocksandtracingouttheireffectsonthemacroeconomy. Importantly, muchof thisresearchwasconductedusingvector-autoregressive(VAR)models. Theempiricalresultsare quitesurprising. Firs~whenexpectationsare incorporated,the varianceofall innovationsisreducedsubstantially. Second,innovationsto the federalfinds rate usingthetwomethodologies-- usinga VARmodelandusingmarketexpectations-- areonly 2

somewhatcorrelated. Thecorrelationbetweenthemo is .56-- enoughsothattheVARapproach cannotberejectedoutof hand,butnotsolargethattheapproachisvalidated. Innovationsto other economicvariables(pricesand indicatorsof economicactivity)are essentiallyuncorrelated. Still, monetarypolicyshoch derivedusingthetwo approachesare alsosomewhatcorrelated,since innovationsto pricesandeconomicactivityexplainonlya smallfractionof innovationsto thefederal finds rate. Asa consequence,the impulseresponsesof economicvariablesto thetwo setsof monetarypolicyshockhaveremarkablysimilar properties. The remainderof thepaperproceedsasfollows. Section11demonstrateshowthe VAR methodologycanbe replacedwithan alternativeapproachthatincorporatesmeasuresof expectations, SectionIII examineswhetherselectedmeasuresof marketexpectationsare, infact,accuratepredictionsof actualeconomicoutcomes. It alsocompareseconomicinnovationscalculatedwithboththe VARandalternativeapproaches. Similarly,sectionIV computes structural shocksusingboth methods,and itexaminestheireffectson severaleconomic variables, Section V provides some concluding remarks. II. UsingMeasuresof Expectations Thissectionhastwo objectives. Thefirstobjectiveisto reviewthetraditionalVARapproach, popularizedby Sims(1980),andto describesomepotentialprobIemswiththatmodelingstrategy. Thesecondobjectiveisto outlineanalternativeapproachthataddressesthepossibleshortcomingsof the VARapproach. The main advantage of the alternative approach is that it incorporates measures of market participants’ expectations in the estimation of economic innovations, while maintaining many of the appealing features of the VAR modeling strategy. This approach is illustrated by outlining the necessary steps to identi& monetary policy shocksandto traceouttheireffectson selectedeconomic variables. Thisparticularapplicationispursuedfirther insubsequentsectionsof thepaper.

TheVARApproach Supposethatan economistisinterestedinstudyingthedynamicbehaviorof an nxl vectorof economicvariables,y. Onemodelingstrategyisto estimatea structuralVAR(p)modelof ~: AOX, = p +A(L)Xt.l +~t (1) wherep isan nxl vector,A(L)= Al + A2L+ ... + APLP1,Ai isan nxnmatrix,L isthe lagoperator, and ~t isa nxl vectorof structural(orthogonal)shocks. Theestimationof a structuralVARmodelgenerallyrequirestwo steps. Thefirststepisto estimatethereduced-formrepresentationof ~, where~ isregressedon p lagsof itselfi x, = p’ +B(L)Xl-l +ut (2) wherep’ isan nxl vector,B(L)= B1+ B2L+ ... + BPL~l, Biis~ nxnmatri~ and LItisa nxl vector containingthereduced-fore VARinnovations. Notethat,by assumption,Utcontainsall new informationabout~ thatbecomesavailableduringperiodt, andthe onlynew informationthat is obtainedduringperiodt isaboutvariablesdatedattimet. In thesecondstep,the VARinnovations(ul)are usedto estimateA. andto recoverthe structuralshocks(qt). Equatingequations(1) and(2) impliesthe followingrelationshipbetweenthe reduced-forminnovationsandthe stmcturalshocks: A. u, = Tlt (3) 1norderfor AOandql to beidentified,AOmustcontainat leastn(n-1)/2zero-restrictions. Sims (1980)assumedthatAOwaslower-triangularinorderto ofiogonalize the innovations. Withthis assumption,A. andtheqs can beestimatedwithOLS,simplybyregressingeachinnovationonother appropriateinnovations. In contras~Sims(1986)andBemanke(1986)consideredalternative 4

decompositions,wheresufficientzero-restrictionswereimposedonAObasedon economictheory. rn thiscase,moresophisticatedestimationmethods,suchas instrumentalvariabIesor maximum likelihoodare required.2 once A. andtheqs havebeenestimated,theremainingstructuralparametersarecalculatedby *O-lBi(i=l,...p). Thes~ctural observingthatequations(1) and (2) alsoimplyAi= modelcanthen be usedto studythetime-seriespropertiesof thedataina numberof ways. Ofieneconomistsare interestedin examiningimpulseresponsefinctions, whichcapturethedynamicresponsesof ~ tothe setof structuralshocks(q). The impulseresponsefunctionscanbe obtainedby invertingtheVAR, yieldingthevector-moving-average(VMA)representation: x, = IA. -A(L)]-l p + IA. -A(L)]-l q, (4) = P’/ + C(L)q, where p“ is an nxl vector, C(L) = C. + CIL+ ..., andCiisan nxnmatrix. The impulseresponseof * anyelementof ~ to a particularstructuralshockcorrespondsto theappropriateelementsof C(L). In addition,the VMArepresentationcanalsobe usedto decompose the forecast emors or the variance of ~ into components attributable to individual elements of qt. There are a numberof attractivefeaturesof theVARmethodologythathaveledto its popularity. First, the identificationof thestructuralVARmodelinequation(1) isachievedwitha minimum number of identifyingrestrictions. Indeed,restrictionsareoftenplacedonlyonAo,leaving A(L) unrestricted. In contrast,otherstructuralapproachesofieninvolvelargenumbersof restrictions on A(L)thatareofiennottestedandthatmayor maynotbeguidedbyeconomictheory. Sincethe parametersof a VARmodelare relativelyunconstrained,someeconomistsconsidera VARmodelto 2 SeeBlanchardandQuah({989)for analternativeidentificationschemethat placesrestrictions on the 1ong-runeffectsof qt. 5

bea relativelyatheoreticalapproach,allowingfor a (possibly)richersetof dynamicsthana moreoveridentifiedmodelwouldallow. Second,thereareofienno exogenousvariablesintheVARmodelotherthanconstants, seasonaldummies,anddeterministictimetrends. Asa consequence,theemphasisisplacedonthe effectsof structuraldisturbanceswithinthe contextof a filly-articulatedsystemof endogenous variables,ratherthanontheeffectsof certaineconomicvariables(endogenousor exogenous)onother variables. Finally,sinceeachstructuralequationinthe VARmodelistreatedsymmetricallywith respectto explanatoryvariables,the VARmethodologyiseasilyandquicklyimplemented,ofienwith onlya few linesof computercode. PotentialProblemswithVARS Theestimationof AOandq~in equation(3) dependscriticallyon estimatesof the VAR innovations(u~),the “first-stage”regressionsshowninequation(2). Thereare at leasttwo reasons whytheVARinnovationsinequations(2) maybe poorproxiesforthetrue innovationsto ~. First, thereis goodreasonto believethatthe informationset impliedbya typicalVARcontainsinformation that isnotyetavailableto economicagents. For example,theVARmethodologyassumesthatall laggedvaluesof Xlare publiclyobsemableat theendof periodt-1. Unfortunately,mosteconomic datafor a particularperiodare notavailableuntilsubsequentperiodsandmay be subjectto revisions for months,weeks,or evenyearsafiertheirinitiairelease. Asa consequence,if somevariablesonthe right-handsideof theregressioninequation(2) are notactuallyobservableat timet-I, the innovations will be improperlyestimated. Similar)y,theVARmethodologyassumesthatthesetof informationavailableto economic agentsat timet-1 containsonlylagsof ~. In aIl likelihood,theappropriateinformationset ismuch richerthantheoneimpliedbya typicalVARmodel. If thereexistsadditionalinformationattimet-1 thathelpspredict~ andthatisomittedfromthe regressioninequation(2), the resultingestimated 6

innovations are not true innovations and are inappropriate for identifying structural shocks to ~. Importantly, either of these two problemscanbeovercomewithpropermodificationsto the structuralVARinequation(1). In the first case,thestructuralmodelcouldbe constructedsothat onlyinformationthat isactuallyavaiiabieisusedas anexplanatoryvariable. In the secondcase,~ couldbeexpandedto includeanynecessaryadditionalexplanatoryvariabies. Unfortunately, increasingthedimensionsof ~ isofien undesirableor simplyinfeasible. SinceevensmallVAR modeistypicallyrequiretheestimationof a largenumberof parameters,addingmorevariabiesto the VARsystemwouidonlyfurtherexacerbateanyproblemswithfewdegrees-of-freedom. An AlternativeAo~roach Thispaperconsidersan alternativeeconometricapproachto theVARmethodologythat attemptsto gaugethe importanceof the shortcomingsdescribedabove. First,the probiemof assuming too muchinagents’informationset isaddressedby reconstructing~ sothatonly informationthatis actuallyknownattimet-1 isusedto caicuiateinnovations. Second,theprobIemof excluding informationthatagentsdo haveavailabieisaddressedby includingavailablemeasuresof market expectations in the estimation of economic innovations, These measures seine as a convenient and eficient wayto includeail reievantinformationnecessaryto calculateinnovations. In orderto illustratethealternativeapproach,considerthetaskof identi~ing monetarypolicy shocksandof tracingouttheireffectson variouseconomicvariablesof interest(~). Supposethatthe FederalReserve’spolicyinstrumentisthe federalfundsrate-- oneof thevariablesin ~ -- andthat the Fed’sreactionfunction-- analogousto oneof the structuralequationsinequation(1) -- canbe writtenas foliows: (5) FFRt = @+y [ X;J X;J.* 1’+ **+n;p l where ~ is a constant, y is a nx1vector, Xl ~is a vector of variables describing period t and observable 9 7

attime t, X2,tisa vectorof variablesdescribingperiodt andobservableattimet+], andqml denotes a monetarypolicyshock. Notethatwiththisspecification,the federalfinds raterespondscontempo- ~eousiy to newinformationaboutX1,~and X2,t-1.Finally,ycontainssomezeroelementsfor identificationpurposes,analogousto thezero-restrictionson Ao. As withtheVARmethodology,thefirst stepisto calculateinnovationsto the federalfunds rate, X1,tand Xz,t-1: (6) x + ~3(L)[ X;P,-l X;4-Z]’ + 63E[X2,t-I I~-l 1+U:2 2J-1 = a3 where~i(Li)samatrix polynomial,E[. I~t-l]representsan observablemeasureof marketparticipants’ expectationsof a particularvariable,and~t-lisan unobsenable informationsetthat is impliedbythe observedexpectationsmeasure. Therearea few interestingaspectsof equation(6) thatare worth discussing. First, itcouldbethecasethatusingonlylagsof Xl,tand X2,~.1are requiredto calculate innovationsto the federalfundsrate,to Xl,tandto X2,t-1.Thatis,the inclusionof the expectations measuresaddsno additionalexplanatorypowerto theregressionsinequation(6). Thispossibility correspondsto thetestablehypothesisthat~iisequalto zero. On theotherhand,itcouldbethecase thatmarketparticipants’forecastsof thesevariablesare unbiasedandeficient. That is, includingthe expectationsmeasuresintheregressionsinequation(6) actuaIlyprecludeusinglagsof othervariables, if marketparticipantsuseall wefi2 informationto maketheir forecasts. Thispossibilitycorresponds to thetestablehypothesesthat&iisequalto one(a testof unbiasedness)andthat ~i(L)areequalto zero(a testof efficiency). I

Inthe secondstepof thealternativeapproach,innovationsto the federalfundsrateare regressedon innovationsto allnecessa~ variablesinthe Fed’s reaction function: U F t FR = yl U:l + y2u; MP (7) + Vt Analogousto equation(3) for the VARapproach,the regressioninequation(7) yieldsa setof structuralmonetarypolicyshocks. Finally,analogousto the inversionprocessin equation(4), >-- theoriginalvariablesof interest-- canberegressedoncontemporaneousand laggedvaluesofthe structuralshocks: (8) where p(L) is a matrix polynomial. The estimate of p(L), along with estimates for the structural shocks,can beusedto calculateimpulseresponsetinctions, forecast error decompositions, and variancedecompositionsinthe usuaiways. -* Of course,thisalternativeapproachisnotwithoutsomepotentialpitfalls,somewhichit shares withthetraditionalVARapproach. First,aswith a conventionalVARmodelor any otherstructural model,theeconometricianmustspeci~ whicheconomicvariablesintheFed’sreactionfinction containnewly-availableinformation(Xlt and X2~.1above). Any importantvariablethat isomitted fromtheanalysiswil[biastheestimatesof the structuralshocks. In addition,as illustratedinthe aboveexample,theremustbeavailableandreliablemeasuresof marketparticipants’expectationsfor thefederal-funds rate and for each relevant variable intheFed’sreactionfinction. Finally,aswitha conventionalVARmodelor anyotherstructuralmodel,therecouldbesimultaneitybetweenthe federalfundsrateandvariablesthatare inthe Fed’sreactionfinction. In thatcase,onemustfind additionalinnovationsto useasinstrumentsto estimatey in equation(7). This requiresstill more assumptionsaboutwhichinnovationsto useas instrumentsandadditionalexpectationsmeasuresin 9

orderto derivethe requiredinstruments. . 111.EconomicInnovations Theprevioussection of thepaper described an alternative econometric approach to identi&ing monetary policy shocks and calculating their effects on economic variables. This section proceeds with thefirst stepof thatapproach-- thederivationoftheeconomicinnovationsusingavailable measuresof expectations,aswellas lagsof traditionalmacroeconomicvariables. Theseinnovations arecontrastedwiththosederivedfrom a traditionalVARmodel,andtheyare usedinthe nextsection to calculate monetary policyshocks,aswell as impulseresponsefunctionsfor severalvariableswith respectto a monetarypolicyshock. A Benchmark VAR In order to contrast results from the alternative approach with those from a traditional VAR, a benchmark VAR modelisrequired. Therehasbeena greatdealof recentdebateconcerningthe appropriatemonetarypolicy instrumentandtheappropriatesetof economicindicatorsto includeinthe FederalReserve’sreactionfinction -- see,forexample,Bemankeand Blinder(1992),Strongin(1992), Gordonand Leeper(1995),Christian, Eichenbaum,andEvans(1994),andBrunner(1994). Althoughthe recentconsensusappearsto bethatthe federalfinds ratebestrepresentsthe Fed’s operationalinstrument,thereis littleagreementona reasonablesetof economicindicatorsto include inthe Fed’sreactionfunction. The following setof economicvariables,however,isrepresentativeof variablesusedinthat literature,andtheywillseineasa benchmarkfor subsequentanalysis: x, = [ Y, CPIt PCOM, FFR, NBR, ~~, Mlt ] (9) whereY is somemeasureof economicactivity,CPI istheconsumerpriceinde~ PCOMisa price indexof sensitivecommodities,FFR isthefederalfinds rate,NBR isnon-borrowedreserves,TOTR 10

istotal reserves, and Ml is the M1monetary aggregate.3 It is also assumed that stmctural shockscan be identifiedwitha triangulardecompositionbasedonthe orderinginequation(9) andthat monetary policy shocks are associated with structural shocks to the federal finds rate. This benchmark VAR model corresponds to one of the monthly models studied by Christian, Eichenbaum, and Evans (1994). As they discuss, this identification scheme is somewhat defensible when using monthly data, as willbethecaseinthispaper.4 Withtheseassumptions,the Fed isassumed to respond to: i) contemporaneous changes in output, consumer prices,andcommodityprices,ii) laggedvaluesof allvariables,and iii)a monetary policyshock: (lo) That is, using equation (3), innovationsinthe federalfinds rateareassumedto respondcontemporaneouslyto innovationsinoutput,consumerpricesand commodityprices: U F t FR = y, Uty + y2u;p’ + y3U;coM MP (11) + nt As in equation (2), all VAR innovations are derived by regressing each variable in ~ on several lags of ~: x, = p’ + B(L)x,-l + Ut (2) Asdiscussedin theprevioussection,thereareat leasttwoworrisomeaspectsof thedecompositionof the federalfundsrate inequation(11). First,neitherthe CPInormostbroadmeasuresof s Withtheexceptionof thefederalfundsrate,allvariablesareexpressed~ loglevels. 4 Theprimarypurposeof thispaperisto illustratean alternativeestimationstrategythat incorporatesexpectationsmeasures. It isnotto arguethemeritsof anyparticularsetof economic variablesor anyparticularidentificationscheme. 11

economicactivityfor a givenperiodarepubliclyobservableduringthatperiod. Thismeansthatthe innovationsusedasregressorsinequation(11)havebeenderivedusinginformationthat isnotyet availableto the Fedortoothermarketparticipants.Second,all innovationshavebeenderivedby assuminga limitedinformationsetfor the FederalReserve. Evenif the Fedrespondsonlyto innovationsinY, CPI, and PCOM,itsexpectationosfthosevariablesarelikelybasedonamuch richerinformationsetthanjustlagsof~. Accordinglyt,hereisacompellingcasetobemadefor: i)excludingY~-landCP1t.lfromthelistofregressorswhencalculatingthe innovationsto FF~ and PCOMt,ii)derivinginnovationsto Y~-1andCPIt-l rather than Yt and CPItfor useinequation(11), andiii) derivingall innovationswithan assumedricherinformationsetfor the Fedby incorporating availablemeasuresof expectations. Thisisthe focus of the nextsubsectionof the paper. DerivingInnovations AsshowninTable 1,thereare severalavailableoptionsfor measuringmarketparticipants’ expectationsof the federalfundsrate, economicactivity,andtheconsumerpriceindex. First,there areseveralavailablemarketreadingsontheexpectedfederalfundsrate. Bankscancontractto bonow or lendfederalfundsfor l-month intewalsattheterm-federal-fundsrate. Thus,if marketsare forward-looking,the 1-monthterm-federal-findsrateobsemedon the 1astdayof a month(TFF~.l) shouldbea goodpredictorof the month-averagefederalfundsratefor the followingmonth. Similarly, thereareotherfo~ard-looking interestrates,includingthe l-month Treasurybillsrate (TB~-l), the l-month CD rate(CD~-l), andthe l-month Eurodollarrate(ED~.l). Finally,if the Fedispursuinga finds-rate targetingstrategy,thenthefederalfinds rateshouldreflectall economic informationavailableto the Fed, andthe laggedfederalfinds rate(FF~.l) canalsosewe asa forecast of thecurrentfderal fundsrate. Thefederaltinds rate isplottedagainsteachmeasuresin Figure 1. Fortheremainingvariables,MoneyMarketSeNices (MMS) provides frequent forecasts for upcomingeconomicreleasesfor CPI inflationandfor severalmonthlyindicatorsof economicactivity 12

growth,includingthe unemploymentrate(UR), retailsales(RSLS),and industrialproduction(1P). Actualandforecastedvaluesfor eachof thesevariablesare shownin Figures 2 and 3. An important question concerns whether these measures of expectations are, in fact,eficient and unbiased estimators of future values of the variables. Table 2 examinesthisquestionfor the forward-looking interest rates. Thetablesummarizesregressionresultsbasedon: (6-1) E[FFR, I~t-l] +U:FR (12) where Xl ~= [ PCOMt FF~ NBRt TOTRt Mlt ~’andX2~= [ Y~ CP1~]’, andwhereEIo] 9 l represents a foward-looking interest rate. In particular,thetablepresentssignificancelevelsfor four Wald tests and the R2 for each regression. The WaIdtestscorrespondsto the followinghypotheses:i) thatthereisnota time-invariantriskpremium(a=O), ii)thattheforward-lookinginterestrate isan efficientestimator(~s=O),iii)thattheforward-lookinginterestrate isan unbiasedestimator(5=1),and iv)thattheforward-lookinginterestisbothefficientandunbiased. An R2of zero wouldalsobea generalindicatorthatadditionalinformation(otherthanthe foward-looking interestrate)providesno additionalpredictivepower. TheresultsaregeneralIydisappointing.Althoughtheterm federalfinds rate,theCDrate,and theEurodollarrateappearto beunbiasedestimatorsof the federalfundsrate,noneofthe forward- Iookinginterestratesare efficientestimators. Otherthantheobviousexplanation-- thatbanksmake systematicforecasterrors-- theseresultscouldbe interpretedintwo ways. First,theadditional informationcouldbecapturingatime-varyingriskpremium. Thisargumentismostplausibleforthe Treasurybillrate,whichshowsevidenceof a time-invariantrisk premium(a notequalto zero). A second explanation might be that banks exhibit some habitat persistence, preferring not to always arbitrage away any predictable differences between current marketratesandexpectedfiture federal fundsrates. Still,the R2Sintheseregressions seem somewhat large to be associated with a time- 13

varyingriskpremiumor habitatpersistence. In anycase,whilethe marketinterestratesprovide additionalusefii information(5=0 isrejectedinallcases),theydo notbythemselvesprovide completeinformationfor forecastingthe federalfundsrate. Theabilityof marketp~icipants to makeaccuratepredictionsof economicactivity-- as measuredby MMSforecasts-- are evaiuatedinTable3 usingthefollowingregression: (13) where2*correspondsto thevariableslistedin thefirstcolumnofthe table. Theseresultsare somewhatmorepromisingthanthoseforthe federalfundsrate. First,only forecastsof retailsalesappearto be inefficient. Importantly,thisresultisconsistentwiththeprevious conjecturethatthe inefficiencyof the foward-looking interestratesisdueto the presenceof a timevaryingriskpremiumratherthan becausebanksmakesystematicforecasterrors. On theotherhand, MMSforecastsof two variables-- retailsalesandthe unemploymentrate-- are biased,tendingto followtheactualvaluesdownwhenthe variableisfallingandviceversa. Similarly,thejoint hypothesisof efficiencyandunbiasednesscanberejectedat conventionalsignificancelevelsfor retail salesandtheunemploymentrate. In summary,asbefore,whiletheMMSforecastsprovideadditional usefulinformationfor forecastingthesevariables,theydonotbythemselvesprovidecomplete information. Althoughtheseexpectationsmeasuresappearto includeimportantadditionalinformationona statisticalbasisfor forecastingtheseeconomicvariables,anotherimportantquestioniswhetherthese measuresareimportantinan economicsense. Thisquestionisexploredin Table4, whichpresents thevariancesandcross-correlationmatrixfor severalsetsof innovationsfor thevariablesdescribed above. Panel (i) liststhe variancesandthecross-comlationmatrixforthreesetsof innovationsto the federalfundsrate. ThefirstsetwasderivedusingthestandardVARmethodology,by regressingthe 14

federalfundsrateon 12lagsof eachvariablein~. 5 Thesecondsetwasderivedina similar fashion,exceptthatthe first lagof URandCPIwereexcludedfromtheregression,sincetheyare not observablebythe Fedattimet-1. Sincesomeinformationisdeletedfrom theassumedinformation set,thevariance of these innovations is a bit larger, although they are highly comeIated with the standard VAR innovations. The third set Wascalculated by excluding the first lag of UR and CP1but inc]uding the term federal funds rate (TFF~-l) as a regressor. Interestingly, the variance of these innovations is substantially smaller than for the other two sets of innovations, although the innovations are still somewhat comelated with the other sets. Panels(ii) and(iii) providesimilarinformationfor innovationsto the unemploymentrateand to the consumerpriceindex. It shouldbenoted,however,thatthe standardVAR innovationsareto URtandCPIt,whilethe othertwo setsof innovationsareto U~-l andCPIt.l, sinceit isassumedin the alternativeapproach that the Fed responds contemporaneously to the Iatter innovations. There are several important features of these results. First, innovations derived usingthealternativeapproach areessentiallyuncomelatedwiththestandardVARinnovations. Second, as before, including expectationsmeasuressubstantiallyreducesthe varianceof the innovations. Still,the innovationsto U~-l andCP1t-l-- derivedwithandwiththeexpectationsmeasures-- are highlycorrelated(.76and .68,respectively). Themainresultsof this sectioncanbe summarizedas follows. First,availablemeasuresof marketparticipants’expectationsof economicvariablesare notbythemselvessufficientfor developing innovationsto thosevariables. That is,the expectationsmeasuresare sometimesbiasedand ineticient estimators. Still,theyprovidesignificantadditionalinformationrelativeto standardVARtechniques. In alI casesexamined, including the expectations measures reduced the innovation variance by at least s AII of theresultspresentedillTable 4 were calculated using the unemployment rate as the measure of economic activity and the term federal funds rate as the expectations measure for the funds rate. Similar results were obtained with other measures. 15

one-half. Finally,innovationsto the federalfinds ratederivedusingthealternativeapproachareonly somewhatcorrelatedwithstandardVARinnovations. Innovationsto othermacroeconomicvariables areessentiallyuncorrelatedwiththeirstandardVARcounterparts,primarilybecausethe former are innovationsto laggedvaluesof thesevariablesratherthan contemporaneousvalues, On balance,theseresultscouldhaveseriousimplicationsfor the identificationof monetary policyshocks-- whichrelyon correctlyestimatedinnovations-- aswellas for any conclusionsto be drawnabouttheeffectsof theseshockson othermacroeconomicvariables. Theseimplicationsarethe focusof the nextsectionof thepaper. IV. MonetaryPolicyShocks Theprevioussectioncalculatedandexaminedthetime-seriespropertiesof innovationsto the federalfinds rate,theCP1,andvariousindicatorsof economicactivity. Theseinnovationswere calculatedusinga standardVARapproachand usingan alternativeapproachwhichincorporated marketexpectations. Thissectionusestheseinnovationsto derivestructuralshocksthatwillbe interpretedasmonetarypolicyshocks. Theeffectsof theseshocksonvariousmacroeconomic variablesisalsoexamined. PolicvShocks Asdiscussedearlier,innovationsto thefederalfundsratecanbedecomposedusingthe relationshipshowninequation(1O). That is,theresidualsfroma regressionof federalfinds rate innovationson innovationsto economicactivity,theCPI, andPCOMcanbe interpretedas monetary policyshocks-- theexogenouscomponentof monetarypolicy. An importantquestionthat is addressediswhethermonetarypolicyshocksderivedwitha standardVARapproachhavesimilar time-seriespropertiesto thosederivedwiththealternativeapproach. Table5 presentsthedecompositionresults,usingthe innovationscomputedintheprevious 16

section. Alongwiththeparameterestimates(theys),thetableliststhe R2for eachregression. The firstthree rowsof thetablecorrespondto a regressionsusingstandardVARinnovations,where economic activity is measured by, respectively, the unemployment rate, retail sales, and industrial production. Thenextthreerowscorrespondto regressionsusingthe modifiedVAR approach,andthe lastthreeto regressionsthatuseinnovationsderivedusingmarketexpectations. The importantresultsinthetablecan besummarizedas follows. First,as indicatedinthefirst lineof each setof regressions,thefederalfundsraterespondscontemporaneouslyto newinformation aboutthe unemploymentrate. Thisistrueregardlessof howthe innovationsare calculated,although theeffectsare lessstrongfor thealternativeapproachthanfortheothertwo methods. (Thisresultis alsorobustto otherexpectationsmeasuresfor the federalfinds rateotherthanthe term federalfunds rate.) Bycontrast,the federalfundsratedoesnotrespondto newinformationaboutretailsalesor theCPI andonlyweaklyto innovationsin industrialproduction. Thiscouldbeattributabletothefact -b thatretailsalesandtheCPIare morevolatileseriesthantheunemploymentrate,andtheyarealso subjectto manymorerevisionsthantheunemploymentrate. TheFedalsoappearsto respond contemporaneouslyto PCOM,althoughthe estimatedresponseisnotrobustto how innovationsare calculated. On balance,theseresultsareconsistentwith Brunner(1994),who foundthatthe unemploymentrate isoneof the feweconomicindicatorsthatthe Fed hasrespondedto consistentlyin thepost-warera, whereastheFed hasnotrespondedvery stronglyto pricedevelopmentsandto other indicatorsof economicactivity in recentyears. It isalso interestingto observethatwhen additional information is usedto calculateeconomic innovations(thethird setof regressions),manyof the regressorsbecomelesssignificantor even insignificant. Thissuggeststhatpartof theirrole inthe firsttwo setsof regressionsisnotcausal. Rather,theyare servingascovariateswith informationthathasbeenomittedinthe standardand 17

modifiedVARapproaches. Finally,it is impotiantto notethatthe R2for allof theregressionsinTable5 arequitelow. In otherwords,althoughtheresponseof the federalfundsrateto someof theseeconomicindicatorsis statisticallysignificant,theseinnovationsaccountfor onlya smallfractionof thevarianceof federal fundsrate innovations.ThisresultisalsoconsistentwithBrunner(1994),whoconcludedthat between85and 100percentofthevarianceof innovationsto the federalfundsratecanbeattributed to monetarypolicyshocks. ASa consequence,thetime-seriespropertiesofthe monetarypolicy shocksthatare impliedbytheregressionsinTable5 are nearlythe sameasthepropertiesofthe innovationsto the federal fundsratethatare shownin Table4. ImpulseResponses The finaltaskof thispaperisto examinetheeffectsof monetarypolicyshocksonthe macroeconomy. FortheVARmodel,theseeffectscan becalculatedby invertingthe VARmodel,as shownin equation(4). Forthealternativeapproach,impulseresponsefinctions canbecalculatedby regressingW,,a variableof interest,on severallagsof the estimatedmonetarypolicyshocks: (14) Notethata few lagsof W~areincludedintheregression. It wasfoundthatthesefagswerenecessary to stabilizetheestimatesof Pzi,especiallywhenWtisa non-stationaryvariable.b It isalsoimportant to pointoutthatthisapproachforcomputingimpulseresponsefunctionsisreminiscentof Bamo’s (1977, 1978)approachforexaminingtheeffectsof unanticipatedmoney,althoughthe identificationof the regressors(theEs)isquitedifferent. 6 Thiswasthecaseformostvariablesexaminedinthispaper. 18

Figure 4 presents impulse response functions for several macroeconomic variables, using monetarypolicyshockscalculatedusingbothmethodologies. The impulseresponsesto a VARshock (thesolidlines)werecalculatedusingshocksderivedfrom a VARmodelthat includedthe unemploymentrateasthe indicatorof economicactivity. Thatis,theseimpulseresponsesare basedon the monetarypolicyshockscalculatedinthe firstrow of Table5. Confidenceboundsfor the VAR impulseresponsefunctionsarealsoplotted(the long-dashedlines), Similarly,impulseresponsefinctions for the marketexpectationsmodel(the short-dashed lines)werecalculatedusingtheunemploymentrateasthe indicatorof economic activity and using expectations measures as discussed earlier. The regressions in equation (14) included three lags of the dependent variable (q=3)and24 Iagsofthe monetary policy shocks (~24). Inaddition, consistent with the previous analysis, the regressions for UR, CPI, and PCOM did not include the contemporaneous value of the monetary policy shock(e~p~). In otherwords,the assumptionisthattheseparticular variablesdo notrespondwithintheperiodto monetarypolicyshocks. Theresultsare quitesurprising. Althoughthetwo setsof monetarypolicyshocks-- derived usinga VARmodeland usingmarketexpectations-- areonlysomewhatcorrelated,they have remarkablysimilareffectson macroeconomicvariables. Asshownin panel(a), bothshockshavea persistent,positiveeffectontheunemploymentrate. Panel(b) illustratesthewell-known“price puzzle,”thecounter-intuitiveresultthatconsumerpricesincreasefor a fewmonthsfollowinga contractionarymonetarypolicyshock. Evident[y,themarketexpectationsmeasureof thepolicyshock suffersfromthe samedefectastheVARmeasure. Thatis,asdiscussedby Christian, Eichenbaum, andEvans(1994),there issomevariable-- likelysomemeasureof raw materialor laborcosts-- that affectscontemporaneouslyboththefederalfundsrateandtheCPI. As showninpanel(c), however, bothsetsof shockshavea smallnegative(but insignificant)effecton commodityprice inflation. Asshownin panel(e), bothsetsof shockshavea strongliquidityeffecton NBR,consistent 19

with the effectsdocumentedby LeeperandGordon(1992),Christian, Eichenbaum,andEvans (1994),andBrunner(1994). Theeffectsofa monetarypolicyshockarealsoseen(eventually)in TOTRandMl, shownin panels(f) and(g), respectively. V. Conclusion Thispaperhasconsideredanalternativeeconometricapproachto theVARmethodologyfor identi~ing andestimatingtheeffectsof monetarypolicyshocks. Thealternativeapproachincorporatesavailablemeasuresof marketparticipants’expectationsof economicvariablesinorderto calcuIateeconomicinnovationsto thosevariables. In generaI,measuresof expectationsshouldprovide impotiantadditionalinformationrelativeto a standardVARanalysis,sincemarketparticipantsusea muchricherinformationsetto maketheirforecaststhanthe informationsetthat isassumedina typicalVARmodel. Theresultinginnovationsareeasilyincorporatedina VAR-likefimework, simiiarto the approachtakenby Bamo(1977, 1978)to examinetheeffectsof unanticipatedmoneyon economicvariables. Theempiricalresultsare quitesurprising. First,whenexpectationsare incorporated,the varianceof all innovationsisreducedsubstantially.In allcasesexamined,thevarianceswerereduced by at leastone-half. Second,innovationsto the fedemlfinds rate usingthetwo methodologies-usinga VARmodeland usingmarketexpectations-- areonlysomewhatcorrelated. innovationsto othereconomicvariablesareessentiallyuncorrelated. Still,monetarypolicyshocb derivedusingthe twoapproachesarealsosomewhatcorrelated,sinceinnovationsto pricesandeconomicactivity explainonlya smallfmctionof innovationsto thefedemlfinds rote. Asa consequence,the impulse responsesof economicvariablesto thetwosetsof monetarypolicyshockshaveremarkablysimilar properties. 20

REFERENCES Bemanke, Ben(1986),“AlternativeExplanationsof the Money-IncomeCorrelation,”in KarlBrunner andAlIanMeltzer,eds.Carnegie-Rochester Conferenceon Public Policy, Real Business Cycles, Real ExchangeRates, and Actual Policies, 25:49-100. Bemanke, Ben and Alan Blinder (1992), “The Federal Funds Rate and the Channels of Monetary Policy Transmission,” American Economic Review, 82:901-921. Barre,Robeti B. (1977). “Unanticipated Money Growth and Unemployment in the United States,” American Economic Review, 67(2):101-15. Barre,Robert B. (1978). “Unanticipated Money, Output and the Price Level in the United States,” Journa!of Political Economy, 86(4):549-80. Blanchard,Olivier,and DannyQuah(1989),“TheDynamicEffectsof AggregateDemandand Supply Disturbances,”American Economic Review, 79:655-673. Brunner,AlIanD. (1994),“TheFederalFundsRateandtheImplementationof MonetaryPolicy: Estimatingthe FederalReserve’sReactionFunction,”InternationalFinanceDiscussionPapers, No. 466,Boardof Governorsof the FederalReseweSystem,Washington,D.C. Christian, LawrenceJ. andMtiin Eichenbaum(1992),“LiquidityEffects,MonetaryPolicyandthe BusinessCycle,” American EconomicReview, 82:346-53. Christian, LawrenceJ., MartinEichenbaum.~nd CharlesL. Evans(1994),“Identificationandthe Effectsof MonetaryPolicyShocks,” FederalReserveBankof ChicagoWorkingPaper94-7. Gordon, David B. and Eric M. Leeper (1993), “The Dynamic Impacts of Monetary Policy: An Exercise in Tentative Identification,” Federal Reserve Bank of Atlanta Working Paper Series, Working Paper 93-5. Leeper,EricM.andDavidB. Gordon(1992). “InSearchof the LiquidityEffect,” Journalof MonetaryEconomics, 29:341-69. Sims,ChristopherA. (1980). “MacroeconomicsandReality,”Econometric, 48:1-48. Sims,Christopher(1986),“AreForecastingModelsUsablefor PolicyAnalysis?” Quar/erZyReview, FederalReserveBankof Minneapolis,Winter:xxx-xx. Strongin, Steve (1992), “TheIdentificationof MonetaryPolicyDisturbances:ExaminingtheLiquidity Effect,” FederalResemeBankof ChicagoWorkingPaper92-27. 21

Table 1. Available Monthly Measures of Market Participants’ Expectations of Selected Economic Variables EconomicVariable Source(s)of Expectations Uq.1 MoneyMarketServicesSurvey RSLSt-l MoneyMarketSewicesSurvey IPt., MoneyMarketServicesSurvey cPIt., MoneyMarketServicesSurvey 22

Table 2. Are “Forward-Looking” Interest Rates Efficient and Unbiased Estimators of the Future Federal Funds Rate? (based on 179 monthly observations from 1980to 1994) significanceLevels Market InterestRate a=O ps = o 5 = ] ps = 0,6 = 1 R2 TFF~-l .85 <.01 .36 <.0] .41 TBq-1 .07 <.(]) <.01 <.01 .78 cDq.1 .36 <.01 .84 <,01 .41 ED%.] .74 <,()] .31 <.01 .43 FFR1-l .58 <.()] <.01 <.01 .45 23

Table3. Are MMSForecastsEfficientandUnbiased Estimatorsof FutureEconomicActivity? (basedon 179monthlyobservationsfrom 1980to 1994) (13) SignificanceLevels Economic Variable(Zt) a=O ps = o 8 = 1 ps = 0,5 = 1 R2 u~.1 .43 .05 .01 .05 .14 ‘/oARSLS~-l .90 <.(1) .01 <.01 .26 ‘/oAlPt-l .24 .13 .06 .13 .18 ‘/oACP1[-l .82 .61 .89 .62 .00 24

Table 4. Are VAR Innovations Correlated with Innovations Derived Using Market Expectations? (based on 179 monthly observations from 1980to 1994) i) Federal Funds Rate Comelationwith: Sourceof Innovation Variance (1) (2) (3) 1) Standard VAR a .411 1.00 2) ModifiedVAR b .503 .95 1.00 3) ModifiedVAR plusTFF~-l c .155 .56 .55 1.00 aDerivedusing 12lagsof ~URtCP1tPCOMtFF~ NB~ TOT%Mlt). bDerived as above, excluding u~.l and Cprt-]” c Derived as above, including expectations measure. ii) UnemploymentRate Correlationwith: Sourceof Variance (1) (2) (3) Innovation 1) StandardVARa .024 1.00 2) ModifiedVARb .023 .05 1.00 3) ModifiedVARplus MMSForecastc .013 -.04 .76 1.00 ‘ Derivedfor UK using 12lagsof {U~ CPItPCOM1 FF~ NB~ TOT~ Mlt}. bDerivedfor U~-l using 12lagsof {U~-{CP1t.l PCOM~FF~ NB~ TOT~ Ml~}. cDerivedasabove,includingexpectationsmeasure. 25

Table4. (cont.) Are VARInnovationsCorrelatedwith InnovationsDerivedUsingMarketExpectations? (basedon 179monthlyobservationsfrom 1980to 1994) iii) Consumer Price Index Correlationwith: Sourceof Variance (1) (2) (3) Innovation 1) StandardVARa .033 1.00 2) ModifiedVARb .034 .14 1.00 3) ModifiedVARplus .016 -.04 .68 1.00 MMSForecastc a Derived for CPIt using 12 lags of {U% CPIt PCOMt FF~ NB~ TOT~ Mlt}. b Derived for CpIt-l ~~ing 12 lagsof {U~-1 cplt-~ PCOMt FF~ NB~ TOT% Mlt}. c Derived as above, including expectations measure. 26

Table 5. Decomposition of FFR Innovations (based on 179monthly observations from 1980to 1994) FFR CPI PCOM MP lit = ylu:+ y2ut + Y3ut + ~t (lo) ParameterEstimates Sourceof Innovation Y] Y2 Y3 R2 1) Standard VAR a Y=UR -.51*** -.18 .91** .06 Y=RSLS .00 -.14 .72** .02 Y=IP .12* -.11 .64** .04 2) Modified VAR b Y=UR -.84”’” .02 1.07”” .10 Y=RSLS .01 .12 .80”” .02 Y=IP .10* .12 .84** .04 3) ModifiedVARplus Expectationsc Y=UR -.43* -.03 .10 .01 Y=RSLS .05 -.03 -.05 .00 Y=IP .00 -.10 .02 .00 aDerived using 12 lagsof Xt = {YtCPIt PCOM1FF~ NB~ TOT%Mlt) . bSee “b~rtable notes in Figure 4. ~*~erived as above, including TFF~-l or MMSexpectationsmeasure. Significant at the IVOlevel. * Significant at the 5V0level. l Significant at the IOVOlevel. l 27

Figure1. The Federal FundsRate and Fomard-LookingInterest Rates 22.5 a)FFR(t) and TFFR(t-1) 20.0 l i 17.5 I i 15.0 I 12.5 10.0 7.5 5.0 2.5 , 1980 1982 1984 1986 1988 1990 1992 1994 25.0 b) FFR(t) and EDR(t-1) 1 22.5 20.0 17.5 15.0 12.5 10.0 7.5 ! 5.0 2.5 1 1 I 1980 1982 1984 1986 1988 1990 22.5 c) FFR(t) and TBR(t-1) I ) 20.0 17.5 15.0 12.5 \ 10.0 1 7.5 \ \ 5.0 -J 1, 2.5 , , 1980 1982 1984 1986 1988 1990

Figure1 (cent). The Federal Funds Rate and Fotward-LOOking Interest Rates 22.5 d)FFR(t) and CDR(t-1) I 20.0 . 17.5 15.0 12.5 10.0 7.5 1 ““-w 5.0 f 2.5 1980 T , 1982 T 1984 t , 1986 , I 1988 , 1990 ,,* 1992 1994 e) FFR(t) and FFR(t-1) 22.5 I 20.0 ( ~ 1 17.5 I, I , 15.0 12.5 I / I I 10.0 7.5 J 5,0 2.5 I r 1980 1982 29

i Figure2. Actualand MMS Forecastsof Economic Growth . a)UNR and Forecasted UNR 11 A 1 l 10 9 8 /, 3 \ b \ 7 i {- f’~ )< ]p ~ ! \ \’ 6 t \ i \ 5 1980 , 1982 , 1984 z 1986 , 1988 , 1990 , , 1992 , , 1994 b) RSLS and Forecasted RSLS 6 4 2 0 “2 -4 -6 1980 8 I 1982 1 1 1984 1 1 1986‘ I 1 1988 1 1 1990 I # 1992 1 1 1994 3 c) [Pand Forecasted 1P i 2 1 . 0 . -1 . “2 . -3 30

i Figure3. Actual and MMS Forecastsof CPI Inflation 1.50 1.25 1.00 0.75 0.50 0.25 0.00 -0.25 -0.50 31

Figure4. Responsestoa Monetay PolicyShock ( VAR= EXP=–-- ) 0.100 a)ResponseofUR l ——-~~—- 0.075 -\\ -Yr ~- / 0.050 \\ -O\ ----- ----- / I \ --- ---- 0.025 0.000 A- /’w ~ \ . \ -0.025 -L /L \ I \ -0.050 I \ -0.075 0 , r I I 5 1 T v 1 1 , 0 r 1 , 15 , , 20 , , 2 T 5 , 30 ‘ 35 0.1 b)ResponseofCPI Yr”\—~— -— -0.0 \ —~ 1 \\ -0.1 \ \ -\ -0.2 ------- \ -0.3 1 \ -0.4 -0.5 ! , ? -0.6 0 v 1 5 , 1 w 1 1 1 8 0 1 , t 1 1 v 5 1 8 m 2 1 0 1 1 , u 25 t v , 1 3 , 0 , 1 1 I 3 1 5 0.050 c)ResponseofPCOM & ————— ~. — >“4 / 0.025 / ““’ “;\ / \_/ \ -0.000 \ \ -a -”---- -- -0.025 \ \ \ #@ -# --- ~—— &#45;&#45;&#45; \ “0.050 \ /“’- / 1 ~~ L— /\ / -0.075 —\ / I \/ 1I 4.100 0 , 1 1 1 1 5 , * 1 v , 1 , 0 , 1 , 1 , 5‘ 1 mv 2 , 0 ‘ 1 1 9 2 1 5 m8 1 , 3 , 0 9 , 8 1 3 , 5 32

Figure4 (cent). Responsesto a MonetaryPolicy Shock 0.80 d)ResponseofFFR / 0.64 --i * 1A/’/ 9 \\ 0.48 I \\’ 0.32 0.16 \ 0.00 \/~-—- ——~. 1 I ,,,,, \3,\,J,fl,’\,~,, Y ,, />1 _-~ \ -0.16 -H \ -0.32 \/ —\~———~ o 5 10 15 , , , , 1 , I I 1 1 I , 1 1 , 20 25 30 35 0.32 e)ResponseofNBR 0.16 /~\ / /—-—\ \ / \———- 0.00 / \ \/’ -0.16 ) --- -- -------- -------- -- ----------- 0 \/ -0.32 .~ \/ / \/ -0.48 / -, -0.64 / 1~” \ / \ —— —- / -0.80 \ —1—~ / -0.96 \ / \/ I -1.12 01 I 1 , 1 5I , 1 I 1 1 1 0 1 s , 1 1 1 5 I 1 1 1 2 I 0 1 I 8 1 2 1 5 a 1 m1 3 4 0 s I r 1 3 I 5 \ 0.1 \ f)ResponseofTOTR I -0.0 -0.1 -0.2 1 ~“ L- -0.3 0 \ \ -0.4 --- _ ----- _- --- ---------- A \ -0.5 \/ L ~– -0.6 i \— \ ~—- “0.7 ~—— —1 \4~— -008 0I 1 I 1 I 51 1 u 8 r 110 a , I I 1 1 5 1 I I 1 2 1 0 1 s 1 1 2 I 5 8 1 I 1 3 I 0 1 1 0 n 3 v 5

Figure4 (cent). Responsesto a Moneta~ PolicyShock -0.0 g)ResponseofMl J -0.1 ——l - -0.2 \ . --- ~- =--------------------- \ -0.3 \ \ L -0.4 \F \ \ -0.5 Lb \ -0.6 o , , 5 r , , 10 , , , 1 r 5 L , “- , I 2 I 0 1 — T I —— 2 , 5 — , — 1 1 r 30 — 1 —— , 1 35 34

International Finance Discussion Papers IFDP e - uthor[S) 96 537 Using Measures of Expectations to 1denti& the AlIanD. Brunner Effects of a Monetary Policy Shock 536 Regime Switching in the Dynamic Relationship Chan Huh between the Federal Funds Rate and Innovations in Nonborrowed Reserves 535 TheRisksandImplicationsof ExternalFinancial Edwin M. Truman Shocks: LessonsfromMexico 534 CurrencyCrashesin EmergingMarkets: An Jeffrey A. Frankel Empirical Treatment Andrew K. Rose 533 Regional Patterns in the Law of One Price: CharlesEngel The Roles of Geography vs. Currencies JohnH. Rogers J995 532 Aggregate Productivity and the Productivity SusantoBasu of Aggregates John G. Femald 531 A Century of Trade Elasticities for Canada, Japan, Jaime Marquez and the United States 530 Modelling Inflation in Australia Gordonde Brouwer Neil R. Ericsson 529 Hyperinflation and Stabilisation: Cagan MarcusMiller Revisited LeiZhang 528 On the Inverseof the CovarianceMatrixin Guy V.G. Stevens PortfolioAnalysis 527 InternationalComparisonsof the Levelsof Unit Peter Hooper LaborCostsin Manufacturing ElizabethVrankovich 526 Uncertainty,InstrumentChoice,andthe Uniqueness DaleW. Henderson ofNash Equilibrium: Macroeconomicand Ning S.Zhu MacroeconomicExamples Pleaseaddress requests forcopiesto InternationalFinanceDiscussionPapers,Divisionof InternationalFinance,Stop24,Boardof Governorsof the FederalReserveSystem, Washington,DC 20551. 35

International Finance Discussion Papers IFDP ti J995 525 TargetingInflationinthe 1990s: RecentChallenges RichardT. Freeman JonathanL. Willis 524 EconomicDevelopmentand Intergenerational MuratF. Iyigun EconomicMobility 523 HumanCapitalAccumulation,Fertilityand MuratF. Iyigun Growth: A Re-Analysis 522 ExcessReturnsand Riskat the LongEndof the AllanD. Brunner TreasuryMarket: An EGARCH-MApproach DavidP. Simon 521 TheMoneyTransmissionMechanismin Mexico MartinaCopelman AlejandroM. Werner 520 Whenis Moneta~~PolicyEffective? JohnAmmer Al[anD. Brunner 519 CentralBankIndependence,Inflationand PrakashLoungani Growth in TransitionEconomies Nathan Sheets 518 AlternativeApproachesto RealExchangeRates HaliJ. Edison and RealInterestRates: ThreeUp and ThreeDown WilliamR. Melick 517 Productmarketcompetitionand the impactof VivekGhosal priceuncertaintyon investment: someevidence PrakashLoungani from U.S. manufacturingindustries 516 BlockDistributedMethodsfor Solving Jon Faust Multi-countryEconometricModels RalphTryon 515 Supply-sidesourcesof inflation: evidence PrakashLoungani fromOECDcountries PhillipSwagel 514 CapitalFlighthorn the CountriesinTransition: NathanSheets SomeTheoryand EmpiricaIEvidence 5!3 BankLendingand EconomicActivityinJapan: AlIanD. Brunner Did “FinancialFactors”Contributeto the Recent StevenB. Kamin Downturn? 512 EvidenceonNominalWageRigidityFroma Panel VivekGhosal of U.S. ManufacturingIndustries PrakashLoungani 36