Regime Switching in the Dynamic Relationship between the Federal Funds Rate and Innovations in Nonborrowed Reserves

Boardof GovernorsoftheFederalReserveSystem InternationalFinanceDiscussionPapers Number536 January 1996 REGIMESWITCHINGIN THE DYNAMICRELATIONSHIPBETWEENTHE FEDERALFUNDS RATEANDINNOVATIONSIN NONBORROWEDRESERVES Chan Huh NOTE: InternationalFinanceDiscussionPapersare prelimimrymaterialscirculatedto stimulate discussionandcriticalcomment. Referencesinpublicationsto InternationalFinanceDiscussion Papers(otherthanan acknowledgmentthatthewriterhashadaccessto unpublishedmaterial)should beclearedwiththeauthoror authors.

ABSTRACT This paper examines the dynamic relationship between changesin the finds rateand nonborrowedreserveswithina reducedform framework that allows the relationship to have WOdistinct patterns over time. A regime switching model a la Hamilton (1989) is estimated. Onaverage, CPI inflation has been significantly higher in the regime characterizedby large and volatile changes in funds rate. Innovations in money growth are associatedwitha strong anticipated inflation effect in this high inflation regime, and a moderate liquidity effect in the low inflation regime. Furthermore, an identical money innovation generates a much bigger increase in the interest rate during a transition period from the low to high inflation regime than during a steady high inflation period. This accords well with economic intuition since the transition period is when the anticipated inflation effect initially gets incorporated into the interest rate. The converse also holds. That is, the liquidity effect becomes stronger when the economy leaves a high inflation regime period and enters a low inflation regime period. . . .

REGIMESWITCHINGIN THE DYNAMICRELATIONSHIPBETWEENTHE FEDERALFUNDS RATEAND INNOVATIONSIN NONBORROWEDRESERVES ChanHuh] Introduction Many recent studies document a great deal of instability in the observed strength of the liquidity effect--i.e., the negative dynamic relationship between nominal interest rates and monetary aggregates (e.g., Thornton, 1988, Leeper and Gordon, 1992). Along with the particular monetary aggregate used, the sample period emerges as a crucial factor in determining the strength of the estimated liquidity effect. Even in studies with affirmative findings, there is evidence suggesting instability in the relationship seen in empirical models of conventiOnal, as well as new, varieties. As a result, some researchers pay close attention to the sample period. For example, this concern could be a key reason why some limit the sample of their study to a short, particular period, rather than usinga longersample(e.g., LeeperandGordon(1993)).2 1TheauthorisaneconomistintheDivisionofInternationalFinance,FederalReserveBoard,andthe FederalReserveBankofSanFrancisco.IwouldliketothankseminarparticipantsattheFederalReserve Bankof SanFrancisco,theBoardofGovernors,the Fall 1995SystemConferenceonMacroeconomics, andtheBankofKorea,aswellasJohnJudd,KenKas~ GlennRudebusch,TomSargent,MichaelBoldin, PhilipJefferson,andJonFaustforhelpfulcommentsandsuggestions.JudyKimprovidedableresearch assistance. Anyremainingerrorsaremyown. Theviewsexpressedherearethoseoftheauthoranddo notnecessarilyreflectthoseoftheFederalReserveBankof SanFranciscoortheBoardofGovernorsof the FederalReserveSystem. Pleaseaddresscorrespondenceto:ChanHuh,MailStop#23,Divisionof InternationalFinance,Boardof Governorsof the FederalReserveSystem,Washington,DC20551. Email:huhc@frb.gov,tel.:202-452-2296. 2 Mishkin (1981) finds instability in the coefficients of the model used in testing a negative relationshipbetween the unanticipatedparts of the short-terminterestrate and monetaryaggregates. Thornton’s(1988)resultsuggestsheteroskedasticity.EichenbaumandChristian (1992),andChristian (1994)offera similarobservationregardingthe “moneysupply”equationusedto netouttheanticipated componentof changeinthe monetaryaggregates. PaganandRobertson(1994)documentthe presence 1

This study,therefore,focuseson theobservationthatthe sampleperiodhasa critical influenceon estimatesof the liquidityeffect. Applyingthe stochasticregimechangingmodel developedby Hamilton(1989),I estimatea bivariateregressionequationof interestratesand “ reservesthat allowsforpotentialsystematicshiftsin the relationshipacrossdifferentperiods. Thispaperinvestigatesthe potentialinfluenceof suchregimeson measuresof the liquidity effect. Findingevidenceof a systematicandsignificantshifiin the relationshipwillofferan explanationof inconsistenciesseenin the empiricalliquidityeffectliterature. Shiftsin inflation momentum over time are conjectured to be an importantunderlying factorbehindpotential shifis in the interest rate-reserves relationship.3 The theoretical reasonfordeemingthe inflationtendencyimportantis straightfonvard. Fromthe Fisher effect,nominalinterestratespartlyreflectanticipatedinflation. Thus,the inflationary momentumshouldinfluencethe extentto whichthe anticipatedinflationcomponent dominatesmovementsin observed nominal interest rates in response to changes in some monetaryaggregates.4 The federaltids rate (FYFF)andnonborrowedreserves(NBR)are usedin this ofARCHintheresidualsoftheequationsoftheVARsystemusedtoexamineimpulseresponsesforthe liquidityeffect. 3Shifisininflationarymomentumcouldariseduetoseveralreasonsthatarenotmutuallyexclusive. Theyare; (i) changesinthe inflationarytendencyofmonetarypolicy,(ii) inflationaryimpulsescoming fromsupplyshocks,and(iii) changesinmarketparticipants’viewsof the inflationtrend. 4See,Fuerst(1992),Christian andEichenbaum(1992),Coleman,Gilles,andLabadie(1992,1994) forexamplesofa flexiblepricegeneralequilibriummodelingapproachtothe liquidityeffect. Theirsis acash-in-advanceframeworkwithsegmented(financialandgoods)markets. A liquiditypremiumarises . becausemoneyis valueddifferentlyinthe financialmarketthan inthe goodsmarket. LeRoy(1984)offers a modelwith a money-in-the-utilityfunctionspecification,in whichthe existenceof a liquidityeffect criticallydependson the serialcorrelationpropertiesof the exogenous moneyinjections. A changeinthecurrentmoneysupplywillhavedifferenteffectsdependingonwhat “ isexpectedto followinsubsequentperiods. . 2

study. Thereis a longlist of papersthat focuson thesetwovariables(forexample,Strongin (1989),Christian andEichenbaum(1992),Christian, EichenbaumandEvans(1994),and Hamilton(1994)). Here,however,I relaxthe usual singleregimeassumptionofthe existing literatureand insteadestimatereducedformequationsof interestratesandreservesakinto Mishkin(1982),addingthe stochasticregimeshifting feature.5Then,I ex~ine whetherthere is a noticeablechangein extant findings of the empirical liquidity effect literature.b The modelis estimatedusingfirst difference monthly data for the 1963-1993 sample period. The‘unanticipated’growthrateofNBR,as derivedin Mishkin(1982),is used as the money measureand it will be referredas unbr. Resultsindicatethatthe regimeswitchingmodelfitsthe databetterthana single regimemodel. The twodisjointsampleperiods,eachbestdescribedbythe two regime specificmodels,differin termsof averagechangein the interestrateandmoneygrowth,as well as the volatilityof the ratechanges. Moreimportantly,the historicalCPI inflationrate has beensignificantlyhigherduringperiodsdominatedby a largeraveragechangeandmore volatileregime. Basedonthis,thetworegimeswill be referredto as the high or low inflationregimes. The 1970sandearly’80sshowa greaterconcentrationof high inflation regimes. ‘Thus,thismodelmightberegardedasatwo-stateversionofthe singleequationmodelof Mishkin (1982). Therehas beenprogressin empiricalliquidityeffect literaturesinceearly 1980as shown,for example,inPaganandRobertson(1995). However,thepossibilityofasystematicchangeinregimesas modelled in this paper has not been considered. Since this work is in the spirit of a preliminary investigationon the importanceof regimeswitching,a singleequationframeworkis adopted. ‘Jefferson(1994)appliesasimilarregimeswitchingframeworktoissuesofmonetarypolicy.However, his focus is on assessing variousqualitativeindexesof policy stance. For general applicationssee Hamilton(1989, 1994), Filardo(1994),Boldin(1992),Kim(1994),andAmmerandBrunner(1994). 3

Interestrate responsesto an innovationin moneygrowthin the two regimesclearly diverge. Thelowinflationregimeis associatedwitha moresignificantnegativeshort-run comovementbetweenthe interestrateand unbr (i.e.,liquidityeffect). In response to an innovation in reserve growth, cumulative changes in the interest rate remain negative for ten months in the low inflation regime. In other words, in a regime of low inflation, the interest rate will remain below the level it was at before the initial period for at least ten months following a positive unbr shock. Incontrast,in a regimeof highinflationthe overallimpactof a reserveinnovation will be counteredquicklyandwillthusbe moreshort-lived. Forthe sameinnovation,the interestraterisessharplyabovethe initiallevelwithinfourmonthsof the initialperiod. This appearsto illustratean overwhelminganticipatedinflationeffect,in contrastto the modest liquidity effect seen in low inflation periods. An examination of dynamic properties of the estimated modelaroundregime switching periods indeed yields economically sensible results. It showsthe interestraterising by a largeamountas the economyentersa high inflation(regime)periodafierbeingin a low inflationperiodfor awhile. Thatis,the net increasein the rate followingan innovationin moneyduringsucha transitionperiodis muchbiggerthanthat seenfora persistentlyhigh inflationsampleperiod. Thisis intuitivebecausethetransitionperiodis whenthereis an increasein inflationarymomentumas the resultof botha higherinflationexpectationand inflationriskpremiagettinginitiallyincorporatedintointerestrates. The converseholds,i.e., the interestrate fallsby a largeamountas the economyentersintoa lowinflation(regime)

periodafterbeingin a highinflationperiodforawhile.7This observationfurthersuggeststhat it is reasonableto associateidentifiedregimeperiodswith highand lowinflation. Suchdisparatedynamicresponsesof the interestrate acrossthe two regimescould explainwhystudiesusingdifferentsampleperiodsfindpositive,as wellas negative, comovementpatternsbetweenmoneyandinterestrates.A relativelylargeconcentrationof observationsfroma particularregimecouldinfluencethe characteristicsof the liquidity effect. Forexample,PaganandRobertson(1994)documentsucha disparityin impulse responsesof the fundsrateto a nonborrowedreserveshockfor differentsampleperiods. Theyfoundthat the sizeof the bouncebackin the tids rate followingan initialnegative responseto be muchlargerforthe samplefrom 1974to 1993,comparedto that of the 1959 to 1993sample. In the shortersample,the sizeof the bouncebackwasevenlargerthanthe initialfall in the rate. Characteristicsof the shortersamplemightreflectthoseof high inflationregimeobservations,whichmakeup a largerproportionof the fill sampleinthe post-1974period. Finally,the goalof the exercisesin thispaperis to documentregimeswitchesin data rather than to examine why and how the regimes switch. However, this paper’s finding naturally raises a second set of questions. In that regard, any suggestion given here is speculative. For instance, one cannot interpret each regime as unambiguously capturing the 7Considerhvo distincthistories.In the first, a low inflationregime prevailsbeforeand afierthe reserve innovation. In the secondhistory,the economyremains in a high inflationregimeupto the innovationdatet,thenswitchestoandremainsina lowinflationregimethereafter. Itturnsoutthatthe magnitudeofthecumulativefallintheinterestrateofhistorytwo ismuchlargerthanthatofhistoryone. Thisdifferencecanbethoughtofasanaddedbenefit(deflationarybonus)whentheregimeswitchesfrom ahighto lowinflationtype. Conversely,thereseemsto bean inflationpenalty. Thatis,theinterestrate increaseassociatedwiththe lowto highinflationregimeswitchis biggerthanthatassociatedwiththe scenariowherea highinflationregimepersiststhroughout. 5

monetarypolicystance,i.e.,shifisin the reservesupplycurve. However,shifis in inflation momentumovertimedo appearto be an importantunderlyingfactorbehindshifisin the interestrate-reservesrelationship. Furtherstudy,witha moreelaborateidentificationscheme, mightyieldinformativeresults. SectionsII and III offera descriptionof the modelandestimationresults. Dynamic responsesof the interestrateto an innovationin moneygrowthforeachregimeareexamined in SectionIV. SectionV offersa briefdiscussionof the findingsandSectionVI concludes. II. Model Specification The followingmodelrepresentsan extensionof the univariatemodelof Hamilton (1989), (1) where et -N(O, u(St)). Herer denoteschangesin interestrateand unbr denotesunanticipatedgrowthin money. St is the regimeindex,indicatingwhatregimeis in placeinperiodt. Boththe averagelevelof ~(i.e.,~~)~d its interaction with its own lags and monetary aggregates depend on the regime in placeat anygivenperiodt (i.e.,P(S,)’S).Theerrortermsareassumedto be fromtwo normaldistributionswithzeromeans,andthe varianceof eachdistributionis regime dependent(i.e.,~(s)’s). Thus,heteroskedasticityis a propertyof themodel. The cument regime S, is assumed to be unobservable, but agents can draw probabilistic inferences. That 6

is, agentscancalculateP(S1) giventhe historiesof the observablevariablesr and unbr. Two types of regimes are posited, type H and type L. Switches between the two are assumed to be governed by the following two-state Markov process with constant transition probabilities; prob(S, =L ISt-l =L) =p, prob(Sl =H IS1-l=L) =1-p, prob(S~ =H IS,-l =H) =q, and Prob(S, =L IS,-l =H) =1-q. Thisregimeswitchingpropertyisthe mainimovation of the modelinthis paper. The moneyvariable(unbr) usedin the estimationis the unanticipatedchangein moneyderivedalongthe lineof Mishkin(1982). That is, unbrt=Anbrt - Anbrte where Anbrte=E( AnbrtIxt_~) and x,-~=(A ip,-i, AcPi,-i,Art_i,Anbrt.i ~i=1,2,3,....). To be specific, the anticipated monthly growth in NBR for each period is obtained by 7

regressingit on the informationsetconsistingof six laggedvaluesof the growthrateof industrialproduction,CPIinflation,changesin the fundsrate,andthe growthrateof NBR.8 Figure 1intuitivelydescribesthe reservemarketsituationthatis envisionedb}’the currenttwo regimemodel.9 Supposethat the nonborrowedreservesupplyis inelasticbut can shifibetweentwo levels,H and L. Also supposethattherearetwodistinctdemandsforthe reservesof H and L. Overtime,we will observemarketclearingpairsof nonborrowed resemesandthe tids ratesas boththe supplyand demandare buffetedby respectiveshocks. Furthermore,the observeddata willlikelyformtwo distinctclusters. Supposethe two followingconditionsare met. First,eachregimeis sufficientlypersistentsothatwe willhave a numberof observations,contiguousin time.thatare generatedundersimilarcircumstances. At the sametimea shifibetweenthe two regimesoccursfrequentlyenoughso that we will havea reasonablenumberof observationsforeachregimeperiod. Oncetheseconditionsare met.the dichotomyschemeadoptedherewill fit the databetter. *Strictiyspeaking,thisprocedureinvolvestheassumptionthatthecontemporaneousmoneydemand factorsarenotimportant.Nonetheless,thefocusofthepaperistoexamineadivergenceinthebivariate dynamicpatterns,ortheliquidityeffect. Thus,forexpositionalpurposesthisassumptionisretained. The currentmodelwillhaveabetterchanceofcapturingthegeneraltendenciesoftheinteractionbetweenthe fundsrateandthereserveattwodistinctintersectionpointsifsuchshifisoccurreasonablyfrequently. i 9Weare ignoringthe borrowedcomponentintotalreservesfor reasonsof brevity. 8

111.Estimation Results Twoversionsof (1) areestimatedusingthe numericalmaximumlikelihoodmethod describedin Hamilton(1994). Thefirstspecificationassumesthat thereis a distinctshifiin theaveragerate of changein r acrossthe tworegimes, i.e., P,(H) > p,(L). However, no such restriction of a distinct shifi is imposed on unbr. The second specification, shown below, imposes that both the timing of the regime shifi and the magnitude of average rates of changes in each regime be identical for r and unbr. 4 3 r, =V,(St) +~ ~!(st) [r, _j - V(St-j)] +~ ~~(st) (unbrt-i - ~(sr-i)] + Et(st) . j=1 j=0 Themodelsare estimatedusingfirstdifference monthlydataon FYFF,andurzbr, whereboth seriesare measuredby theirmonthlyaverages.]o Estimationresultsaregivenin Tables1and2 for modelsI (thefirstspecification)andII (the secondspecification). Standarderrorsof estimatedcoefficientsaregivenin parentheses. Beforegoingfurther.weneedto addressthe questionof whetheror not the two regimespecificationversusa singleregimealternativeis mostappropriate.Thisis doneby ‘“Thesampleperiodisfrom 1963:1to 1993:12andtheseriesweretransformedas follows. First,~ = 1og(1+~100)*100, thenr,= (R-K.,)*1O. Fornonbomowedresenes (’NBR),nbrt=log(NBVB&- ,)*100. The innovations(unbr’s)inNBR are derived by regressing nbr, onthevariables shownin (2). Theregressionwasrunrecursivelywiththestartingdateof 1959:6. Thisensuresthattheestimationof (1) for periodt doesnot involveany informationbeyondperiodt. Thisprocedurecouldgiveriseto a generatedregressorproblemandhencethestandarderrorsoftheestimatedcoefficientscouldunderstate the true extent of uncertainty. However,results do not change perceptiblywhen equation(1) was estimatedusingtheactualchangesinnonborrowedreservesinsteadoftheunanticipatedmoneyofequation (2)(Huh(1995)). 9

usingthe likelihoodratiotest of the two specificationsas suggestedby Garcia(1992).’1This testoverwhelminglyrejectsthe singleregimenullhypothesis.lz D A negativecomovementpatternbetweenr and unbr, (i.e., the liquidity effect) holds in both regimes. For model I (Table 1) the coefficients on contemporaneous money growth are significantly negative for both regimes. A negative contemporaneous comovement is more pronounced in regime L (significant at 1 percent) than in regime H (significant at 5 percent) for model I. In model 11,the contemporaneous coefficient is significant only in regime L (at 1percent). A negativeeffectpersistsevenafieronemonthin regimeL, but not in regimeH (i.e., ~’mis significantat 10percent)for modelI. A furtherdiscussionof the dynamic responseof the interestrateto a changein moneywill be givenlater. Figure2 plotsthe inferredprobabilitythat regimeH was inplacein any givenmonth basedon informationupto eachperiod. Thisis basedon model1. Datageneratedfromthe otherspecification(modelII)doesnot differmuch. Regime H seemsto havebeendominant duringseveralperiods. Themostnoticeableisthe sample period from 1979 to 1982. The sampleperiodof 1973-75is alsoprominent. RegimeH has beenin threeadditionalperiods, 1969-70.1984-85,andearly 1987. To see if thereis a systematiclink betweeninflationand eachof the two regimes, Figure 3 showsannualCPI inflation(a 7 monthmovingaverageof annualizedmonthly ‘lThesingleregimemodelisnotidentifiedunderthenullhypothesisandconsequentlythelikelihood ratio has a non-standardChi-squaredistribution.For more discussionsee Garcia (1992) and Hansen (1993). . 12Thedifferenceinthelikelihoodfunctionvaluesis large. For ModelI, the likelihoodvaluefora singleregimeversionwas 714 compared with 594.7 from Table 1. This strongiy suggests that the four lag specification is a very poor one for single regime models. For example, the value falls to 670 from 710 when 12 lags are included. . 10

changesin CPI)alongwiththe infemedprobabilityof regimeH. Thereis a highdegreeof coherencebetweenthe actualhighinflationperiodsandregimeH periods. Withthe exceptionof the 1984-85interval,eachregimeH periodcoincideswitha risingor peaking CPIinflation. To be morespecific,regimespecificsamplesareconstructed basedon whetherP(S(t) = H), shownin Figure2, isgreater than0.5or not. The averageCPI inflationforperiods belonging to regime L (290outofthetotal 365months)was4.29percent. On the other hand,the averageforthe 75monthsbelongingto the typeH regimewas 8.31percent. The standarderrorsforeachperiodare2.2(typeL) and3.2(typeH). Averagegrowthin money dividedintotwo subsamplesexhibitsa similardivergencein characteristics. Averagegrowth innonbomowedreservesduringtheregimeH period is 2.8 times larger than in regime L. Withregardto the variabilitymeasuredin termsof standarderrorsof growthrates,it is 1.5 timesmorevolatilein regimeH thanin regimeL periods. Resultsalso indicatethata larger averagechangein the interestrateis associatedwith a significantly largervariability. Thatis, 02(H) > az(L). Theestimatesof the transitionprobabilities(p’sandq’s)suggestthatthe lowinflation regimehas beenabout 10percentmorepersistent.Overall,regimeL has beenmoreprevalent thanregimeH in the period between 1964-1993. The expected durations are 39 and 10 months for L and H regimes,respectively].3 13Becausethe modelis specifiedin terms of changesin the interestrate, it is conceivablethatthe modelmightidenti~ periodsduringwhichthe interestrateisraisedfrom 1to 2 percent as belonging to the high inflation regime! This wouldbeabsurdbasedonhistoricalexperiencewhichsuggeststhatsuch lowfundsrateswouldbecompatibleonlywithverylowinflation.However,itisalsohistoricallythecase thatthe fundsrate is not changedby a largeamountduringperiodsof low and stableinflation. For example,therangesofchangeinthefundsrate(measuredinbasispoints)duringregimeLandHperiods 11

IV. Dynamic Effect of Reserve Intervention on the Interest Rate 1.RegimeSpecificResponses A clearerdivergencebetweenthe two regimesemergeswhenweexaminetheir dynamicproperties. The quantitative experiment involves tracing effects of equal reserve interventions for each regime over time. We will use model I as the example. Due to the regime switching structure of the models, dynamic responses crucially depend on which regime is in place at period t, the period when the reserve imovation takes place. Furthermore,intracingtheseeffects,we haveto allowforthepossibilityof regimeswitching overtime. First,weassumethattheeconomyhas been in the same regime for five months (periodt-4 throughperiodt) withno innovationin the moneysupply(~nb~i= O,i =t-4,..t-l).14 Then,we subjectthe economyto a one-timeimovation in money(i.e.,unbrt>O)andtraceout pathsof interestrateresponses. SupposeregimeH is inplacein periodt. Thentherearetwo possiblevaluesforr in are respectively[-70,73]and [-265,305]. Theserangesdo notincfudeextremevaluesateitherends. Tworegimeperiodsareidentifiedinthesamewayasinthetext. Forthesampleperiodusedinthestudy, the hypotheticalcaseof seeinga largechangeinthe interestratewheninflationis lowandstabledoes not exist. Furthermore,the size of rate change is only part of the properties used for regime determination.Thus,thispotentialpitfallofthemodelspecificationdoesnotposea problemforthe currentanalysis. “T0 be moreprecise,the interestrate responsesalso dependuponthe relevantpasthistoryof the regimes. SupposethatweareinregimeH inperiodt whenthereisa surpriseincreaseinnonborrowed reserves. Theshapeof the interestrateresponsesto this shockin futureperiods(i.e., t+l. t+2,...)will dependonhowwearrivedinperiodt,orthepastrealizationsoftheregimes. Thatis,theresponseofthe . interestratewhenS(t-4)=H,S(t-3)=H,S(t-2)=H.andS(t-1)=HwillbedifferentfromthatwhenS(t-4)=H. S(t-3)=H,S(t-2)=L,and S(t-l)=L. Forsimplicity,this complicationwill notbeconsidered. . 12

periodt+l foreachof the possibleregimes,i.e., r~+[(S(t+l) = H IS(t) = H) and rl+,(S(t+l) = L IS(t)= H). Giventhat regime H is in periodt, the probabilitiesforeachof thetwo valuesareq and l-q, respectively. Sincethe regimecanshifiin eachperiod,thereare 2k distinctpathsalongwhichr responsecanevolvek periodshence. Foreachof thesepaths, we canassignprobabilitiesconditionalon the regimeof periodt. Furthermore,we can determinethe most likelypathby findingan outcomewiththe highestprobabilityof occurringin eachperiod. Forthe estimated values of p and q and for k less than 31, the most likely sequence of regimes over time is S(t)= S(t+l) = S(t+2)= .... = S(t+k)= H. This pathhasthe largestprobabilityof qkof all sequenceswiththe lengthk whenregimeH is in the initial period.15 Similarly, the most likely sequence of regimes over time is S(t) = S(t+l) = s(t+2) = .... = S(t+k)= L, when period t regime is L. This event has the largest conditional probability p ‘. Figure 4 shows the cumulative changes in r in response to a unbr shockforeachcase describedabove. The shockis assumed to be one-time, that is, growth in money is held to zero before and afier period t. Its size is 2 x o~(H), i.e., two times the standard error of growth in nonbon-owed reserves in the historical regime H sample period. The standard error is 2.11percent. Theresponsesof changesin the interestrate in thetwo regimesclearlydiverge. A IsThiscan be shown as fo[lows: Since both p and q are greater than 0.5, qk> q ‘-1(l-q). The former is the probability that regimeH remainsthroughoutk periodsstartingint. However,p isgreaterthan q accordingto the estimatesshownin Table3. Thus,it ispossiblethatthe probabilityassociatedwith the eventthat the regime is switchedfrom H to L early on and the economyremains in regimeL thereafterwouldbegreaterthanthatoftheeventof regimeHremainingin placethroughoutk periods. ThemostlylikelycandidateiswhentheswitchfromH to Loccursinperiodt+l andregimeLremains thereafter. Theassociatedprobabilityis(l-q) p ‘-l. It turnsoutthatqkisgreaterthan(l-q) pk” fork lessthan31, for theestimatedva[uesof p andq. . 13

negativeinterest rate response lasts less than three months in regime H, then gets reversed. The relative size of responses for each regime is misleading because they are not adjusted for estimation uncertainty. For example, confidence intervals constructed allowing for 1.5 times the standard error of each coefficient for the first two periods for regime H are [0.29, -10.06], . [8.46, -9.30] and for regime L, [-0.02, -1.41] and [-0.41, -3.14].16 That is. for regime H, the confidenceintervalforthe responseof r in the initialperiodincludeszero. Onthe other hand, similar confidence bands of r for regime L do not includezeroforat leasttwoperiods. ., Startingin the fourthmonthafierthe initialshock,the interestrate startsnslng sharplyabove the initiallevel. Thatis,the cumulativechangein theinterest rate turns positive. In contrast, the cumulativechangesin the interestrate remainnegativeforten monthsin regimeL. In otherwords,the interestrate willremainbelowthe levelit wasat beforethe initialperiodfor at leastten monthsfollowingthe unexpectedincreasein nonborrowedreserves. Theduration of the liquidityeffectis at leastthreetimes longerin the regimeL periodcomparedto regime H. Theoverallimpactof a reserveinnovationwillbe counteredquicklyandthuswillbe moreshort-livedin regimeH than in regimeL. The fomer appearsto illustratean overwhelminganticipatedinflationeffect.in contrastto themodestliquidityeffectseenin the lowinflationperiods. Thus,it is not surprisingthat studiesusingdifferentsampleperiods findbothpositiveandnegativecomovementpatternsbetweenmoneyand interestrates. Thisobsemationconfirmsa findingregardingthe impulseresponsepatternbetween ‘bTheupperand lowerboundsforregimeS arecalculatedas follows: upper(S)= (zinbr)x (~O~(S)+1.5xs.e.(~O~(S)))+ v(S), and lower(S)= (unbr) x (~O~(S)- 1.5x s.e.(~O~(S)))+ P(S). The choiceof the 5 confidencelevelcriteriaandtheemorbandconstructionare somewhatarbitrary. YO Thisanalysisismeantto be suggestive. . 14

the fundsrateandnonbonowedreservesby PaganandRobertson(1994). In responseto an innovationin reserves,the fundsrate initiallyfalls,but is shortlyfollowedby a bounceback. Theyfindthe sizeof this bouncebackto be muchlargerforthe samplefrom 1974to 1993, comparedto thatof the 1959to 1993sample. Remarkably,the sizeof the bouncebackis largerthanthe initialfall in the rateof the firstsample.” A highbouncebackis a distinctcharacteristicof regimeH. Accordingto Figure2, the post-1974samplehas a highconcentrationof observationsbelongingto the highinflation regimecomparedto the earlierperiod. Thus,as a whole,the lattersampleperiodwould exhibitmoreregimeH patternsthanthe 1959-1993sample. It is interestingto notethatthe reducedformequationcouldcapturepropertiesidentifiedby a morefullyspecified multivariatesystemof equationsoncethe potentialshifisin the regimesare allowed. 2. Dynamic Responses when Regimes Switch Thequantitativeanalysisso farfocuseson caseswhenoneregimepersists. Further examinationof dynamicresponsesof the interestratein caseswhenregimesswitchalso yieldsinterestingresults. Thoughthispaper’sanaiysisdoesnot explainwhy regimeswitches occur,it doesofferan insighton whathappenswhenthe regimeswitchestake place. We thenusethisto seewhetherthe estimatedmodelis economicallysensible. Supposethatthe economyhasbeenin a lowinflationregime,or regimeL forawhile. Furthermore,themonetaryauthorityhascontinuedto exploita favorable‘liquidityeffect’ . environmentby generatinga seriesof reserveinnovationsas describedabove. As a “Figures 4C, 4D, 8A, and 8B of Pagan and Robertson (1994). 15

consequence,a shififroma lowinflationto a high inflationregimetakesplacein periodt+l and remainsthereafter. However,thereservesupplyimovation is assumedto takeplacein periodt as before. Thisscenariois representedby the sequence{S(t-4)= S(t-3)= .. = S(t)= L, S(t+l) = s(t+2) = ....=H}, andwillbe referredto as the switch(LIH). Figure5 comparesthe resultingcumulativechangesin the fundsrateto thosecases whentheregimeremainsin H and L throughout for the same unt)r~. The switch (LIH) is associatedwiththe largestincreaseinthe finds rate outof the threecases. It evensurpasses the increasein the regimeH case. Sixmonths after the shock (i.e., in period t+7), the cumulative increase in the interest rate in the switch (LIH)caseis aboutthreetimes larger than that in the regimeH case. That is,the rise in the interestrateinthe periodfollowinga transitionfromregimeL to H is evenlargerthan the increasein the ratewhenregimeH remainsinplacethroughout.Thisextraincreasein the rate canbe thoughtof as an inflation penalty,or an addedcostof enteringa high inflationregime. Symmetrically,we canconsiderthe caseof switch(1-?IL).Supposethe economyhas been in a high inflationregime.or regimeH, forawhilebutthe monetaryauthorityhas successfilly conveyedits intentionto restraininflationin the fiture. As a consequence,a shifi froma high to lowinflationregimetakesplace in periodt+l andremainsthereafter. This scenariois representedby the sequence{S(t-4)= S(t-3)= .. = S(t)= H, S(t+l) = S(t+2) = ....= L}. Figure 6 compares the resulting cumulative changes in the fids rateto thosecases when the regime remains in H andL throughout. Theswitch(HIL)is associatedwiththe largestdecreasein therateout of thethreecases.evensurpassingthe fallin the regimeL l 16

case. Sixmonths after the shock (i.e., in period t+7), the cumulative decrease in the interest rate associated with the switch (HIL)case is about20 timesthatof the regimeH case. That is, the magnitude of a fall in the interest rate in the period immediately following a transition from regime H to L is evenlargerthanthat of a decreaseinthe ratein the regimeL period. Thiscanbe thoughtof as a deflationbonus,or an addedbenefitof enteringthe lowinflation regime. Thesedynamicpropertiesof the estimatedmodelare indeedeconomicallysensible. An identicalimovation in moneygeneratesa risinginterestrate soonerduringhigh inflationaryperiodsthanduringlowinflationperiods. Furthermore,theprecedinganalysis indicatesthat interestrate hasto riseby a largeamountasthe economyentersintoa high inflation(regime)periodafierbeingin a lowinflationperiodforawhile. Thatis, thenet increasein the ratefollowinganinnovationin moneyduringsucha transitionperiodis much largerthanthe increasein the ratecausedby the samemoneyinnovationwhenhighinflation has beeninplacethroughout. Thisis intuitivebecausebotha higherinflationexpectation and inflationriskpremiawillbe incorporatedintointerestratesforthe firsttime duringsuch a transitionperiod. Theconverseholds. Thatis, the interestratefallsby a largeamount withthe onsetof a low inflationperiodafiera stretchof highinflation. ‘80necould interpretthis result in the followingway, Supposethe economyhas been in a low inflation regime for awhile. Agents would accumulatea large real balance as the low inflation environmentis favorablefor holdingmoney. Supposethe economyunexpectedlyenters into a high inflationregime,which is expectedto persistfor a while. Then,everyonewill try to reducetheirreal balanceholdings.Thiswill bepossibleonlywhenthere isa largerun-upinpricelevels,perhapsmore thanwhatwouldbethecaseiftheeconomyhadbeeninaninflationaryregimeforthewholetime. The deflationarycasecanbeexplainedbythereverseofthisscenario. Thatis,therewill bea rushto build uprealbalanceswhentheeconomymovesintoa lowinflationregimefromahighinflationone,causing pricelevelsto fail. .

V. Discussion Twoalternateinterpretationsseemmostplausible--eitherthe observedshifi relationshipsmainlyrepresentthoseinthe monetarypolicystance,or theyrepresentshifisin whatfinancialmarkets’perceivedas theprevailinginflationregime. Supposemovementsin the interestrate andnonborrowedreservesmostlyrepresentthe Fed’sactions. In thiscase, the tworegimescan be readilyunderstoodas capturingthe inflationarytendencyof monetary policy. Thatis, the stanceof monetarypolicyis a keydeterminantof a higheraverage inflationrateassociatedwithregimeH. Active intervention either to generate surprise changes in the bds rate, or to counter reserve demand shocks, could account for the high variability of regime H. Accordingly, the converse wilI be true for regime L. Thatis,botha less inflationarymonetarypolicystanceandlessactiveinterventionto counterthereserve demandshocksdescribetheperiodsbelongingto regimeL. However,there seemsto be seeminglyobviousmismatchesif wetake this interpretation. Forexample,Figure2 indicatesthatthe periodfromearly 1979to theendof 1982wasgovernedby regimeH. Accordingto historicalevidence,substantialtighteningof monetarypolicyseemedto havestartedmuchsoonerthan,say, 1982. Allowingsomelag time in patternrecognitioncouldexplainsucha mismatch. The estimatedtimingof regimes is basedon a verylimitedinformationset. namely,historiesof the interestrate changesand resemeimovations. Thus,forexample,the modeldoes notknowthatan increaseinthe volatilityof the interestrateduringthe 1979-1982periodwasmainlydue to a suspensionof interestrate smoothingpursuedbythe Fedthroughoutthe 1970s. Therefore,interpreting periodsof regimesH and L to be capturingthe inflationarytendencyof monetarypolicy 18

warrantscaution. An alternativeinterpretationis thatthetwo regimesmightbe capturingwhat financial marketsperceivethe prevailinginflationregimeto be. Forexample,the yieldon 30-year Treasurybondsroseonlygraduallyuntilmid-1979,despitethe factthatrelativelyhigh inflationprevailedthroughoutthe precedingthreeyears. Theimplicitpricedeflatorrarely wentbelow7 percentduringthat period. Thisobservationnotwithstanding,the publicmight nothavebeensureabouthow longthe spellwasgoingto last (Goodfriend(1993)). This couldexplainwhyFigure2 doesnot identi~ the late 1970sas a highinflationregimeperiod. Onthe otherhand,therewasa rapidrun-upin the longratein rnid-1983dueto a serious‘inflationscare’’.9 Thisset offthe run-upin the fids rateto August1984. Therise inthe model’sestimateof the probabilityof high inflationregimebeingin placein 1984 couldbe partlyexplainedby this chainof events. Observationsso far suggestthat we needmorestructureto understandthe natureof the regimesandtheirshifts. In particular,specifyingthe marketfor federaltids more explicitlyshouldbe usefil if we are goingto attributethe observedchangesto those of the monetarypolicystanceper se (Coleman,GillesandLabadie(1994)andHamilton(1994)). Also,an identificationschemeproposedin Leeperand Gordon(1995)that structurally distinguishesreservesupplyanddemandshocksmightyieldinformativeresults. However,the factremainsthatregimeH periodshavea significantlyhigheraverage inflationrate comparedto regimeL periods. Thissuggestsa weakeror narrowersecond ‘9Goodfriend(1983)definesthe‘inflationscare’asasignificantriseinlong-ratesintheabsenceofan aggressivefundsratetightening,thusmainlyreflectingrisingexpectedlong-runinflation. . 19

interpretatiOn. The two regimes represent two distinct environments, largely affected by the prevailing inflation trend. V. Conclusion Thispaperexaminedthe potentialinfluenceof monetarypolicyregimechangesonthe liquidityeffectinthe contextof a bivariatereducedformrelationship. Thestochasticregime switchingmodelis ableto capturesomestatisticallyandeconomicallysignificantpatternsthat are distinctacrossthe twopositedregimes. Mostsignificantis the identificationof each regimewithhighand lowinflationperiods. It’salso shownthatthe divergencein the dynamicmoney-interestraterelationship acrosslowand highinflationperiodscanbe quitesignificant. Examinationsof dynamic propertiesof the estimatedmodelindeedyieldeconomicallysensibleresults. In general, a high inflation regime is associated with a stronger anticipated inflation effect. Furthermore, results indicate that the interest rate has to rise by a large amount as the economy enters into a high inflation (regime) period afier being in a low inflation period for awhile. That is, the net increase in the rate following an innovation in money during such a transition period is muchlargerthanthe increasein the rate causedby the samemoneyinnovationwhenhigh inflationhasbeenin placethroughout. This is intuitivebecauseboth a higherinflation expectationand inflationrisk premiawillbe incorporatedintointerestratesforthe firsttime duringsucha transitionperiod. Theconversealsoholds.Giventhesefindings,the potential regimeshiftwarrantsmoreattentionin fiture empiricalinvestigationsof the liquidityeffect. However,the reducedformnatureofthe analysisputsa limiton answering&her 20

structuralquestions. Incorporatingmorestructurein the modelspecification,parallelto the recentdevelopmentinthe conventionalliquidityeffectliterature,mightbe necessaryfor strongeridentification. 21

References 3 Ammer,J., and A.D.Brunner,(1994),“U.S.MonetaryPolicyandBusinessCyclePrediction Usinga Switching-RegimeModel,”manuscript. Boldin(1992),“Using SwitchingModelsto StudyBusinessCycleAsymmetries:1.Overview of MethodologyandApplication,”FederalReserveBankof New YorkResearchPaperNo. 9211. Christian, L.J. (1994),“Comment”on ‘AModelof the FederalFundsMarket,’by Coleman. GillesandLabadie.manuscript. Christian, L.J., and M. Eichenbaum(1992),“Identificationand the LiquidityEffectof a MonetaryPolicyShock,”in A. Cukierman,,Z. Hercowitz,and L. Leideman, eds.,Business Cycles, Growth and Political Economy, Cambridge,MA. MITPress,pp. 335-370. and C. Evans (1994),“TheEffectof MonetaryPolicyShocks: Evidencefrom’the Flow’ofFunds,”NBERWorkingPaper4699. Coleman,W.J., C. Gilles,and P. Labadie(1994),“AModelof the FederalFundsMarket,” manuscript. , and (1992),“TheLiquidityPremiumin AverageInterest Rates,”Journ;l of Monetary Economics, 30, pp.449-465. Filardo,A. J., (1994),“BusinessCyclePhasesandTheir TransitionDynamics.”JournaZ of Business and Economic Statistics 12, pp.299-308. Fuerst, T.S., (1992), “Liquidity, Loanable Funds, and Real Activity,” Journal of Monetary Economics 29, pp.3-24. Garcia.R.,(1992), “Asymptotic Null Distribution of the Likelihood Ratio Testin Markov SwitchingModels,”workingpaper,Universityof Montreal. Goodfriend,M., (1993),“InterestRatePolicyandthe InflationScareProblem:1979-1992,” Economic Quarter@F,ederal ReserveBankof Richmondvol. 79. Hamilton,J.D., (1994),“TheDailyMarketforFedFunds,”Universityof Califomi< San Diegoworkingpaper. , (1994), TimeSeries AnaZysis,Princeton,NJ. PrincetonUniversityPress. 22

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Table 1. Results without Common Mean: Model I 4 3 rt s ~r(St) +~ P~(St)trt-j - P~(s~-j)l+~ b~(s~)‘nbrt-i +ct(sf) j=1 i=0 Variable Coefficients(S= L) Coefficients(S= H) P, 0.343(0.33) 2.248(1.35)** p“m(s J -0.211(0.09)*** -1.426(0.69)** p ‘m(SJ -0.137(0.10)* -0.105(1.31) p 2m(SJ 0.031(0.10) 0.175(0.55) p ‘m(SJ -0.046(0.13) 0.005(0.19) 02 4.198(0.41) 74.249(12.88) P 0.975(0.01) q 0.906(0.04) Loglikelihood -594.71 ***,**,~d * reswctivelydenotecasessignificantat 1,5 and 10percentlevel. 24

Table2. Resu16witi CommonMean:ModelII i Variable Coefficients(S = L) Coefficients(S = H) P,= v. 0.259 (0.18) * 14.25 (3.14) *** p ‘m(s,) -0.229 (0.09) *** -0.004 (0.10) ~ ‘m(s ,) -0.115 (0.10) 0.539 (0.36) p 2m(s J 0.023 (0.09) -0.310 (0,48) B‘In(s t) 0.042 (0.08) 0.658 (0.35) ** 02 4.40 (0.46) 75.75 (14.84) P 0.983 (0.01) q 0.925 (0.03) Log likelihood -595.04 ***9**7~d * respectively denote cases significant at 1,5 and 10percentlevel. 25

Figure 1: Supply and Demand for Nonborrowed Reserves, ~o Regime World d FYFF Y % x x Y v Demand(H) x x supply (H) Supply(L) 26 .

Figure 2: Inferred Probability, Prob[S(t)=H It,t-l,...] 1.0 I PROB — . 0.8 0.6 0.4 . 0.2 u 0.0 I I r I I I I 1 64 69 74 79 84 89 Figure 3: CPI Inflation and Inferred Probability (right scale) 3.5 1.0 PROB ---- 3.0 0.8 2.5 2.0 0.6 1.5 1.0 0.4 . 0.5 . 0.2 0.0 -0.5 0.0 64 70 76 82 88 27

i \ n \ \ \ \ \ \ z . \ \ \ \ \ \ 0 \ \ \ \ \ \ u) \ \ \ \ \ \ a \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ I < I I \ I x I w I I I I 8 0 , 28

Figure5: CumulativeEffectofOne-timeReserveInnovationonFYFF;S(t)=H RegimeSwitchingCase:S(t)=L, S(t+l)= ... = H 200 150 100 50 0 -50 Jan Feb Mar Apr May Jun Jul Figure6: CumulativeEffectofOne-timeReservehnovation onFYFF;S(t)=L RegimeSwitchingCase:S(t)=H,S(t+l)= ... = L 150 100 50 0 -50 -1oo . -150 -200 -250 Jan Feb Mar Apr May Jun Jul 59

International Finance Discussion Papers IFDP m uthor(~ 1996 536 Regime Switching in the Dynamic Relationship Chan Huh betweenthe FederalFundsRateandInnovationsin NonborrowedReserves 535 TheRisksand Implicationsof ExternalFinancial Edwin M. Truman Shocks: LessonsfromMexico 534 CurrencyCrashesin EmergingMarkets: An Jeffrey A. Frankel EmpiricalTreatment Andrew K. Rose 533 RegionalPatternsinthe Lawof OnePrice: Charles Engel TheRolesof Geographyvs.Currencies JohnH. Rogers 532 AggregateProductivityandthe Productivity SusantoBasu of Aggregates JohnG. Femald 531 A Centuryof TradeElasticitiesforCanada,Japan, JaimeMarquez andthe UnitedStates 530 ModeliingInflationinAustralia GordondeBrouwer Neil R. Ericsson 529 Hyperinflationand Stabilisation:Cagan MarcusMiller Revisited LeiZhang 528 On the Inverseof theCovarianceMatrixin GuyV.G. Stevens PortfolioAnalysis 527 InternationalComparisonsofthe Levelsof Unit PeterHooper LaborCostsinManufacturing ElizabethVrankovich 526 Uncertainty,InstrumentChoice,andtheUniqueness DaleW.Henderson of Nash Equilibrium: Macroeconomicand Ning S.Zhu MacroeconomicExamples 525 TargetingInflationinthe 1990s: RecentChallenges RichardT.Freeman JonathanL. Willis Pleaseaddressrequestsforcopiesto InternationalFinanceDiscussionPapers,Divisionof InternationalFina~ce,Stop24;BoardofGovernorsof theFederalRese~e System, Washington,DC 20551. 30

International Finance Discussion Papers IFDP * Titl~ Author(s) 1995 524 Economic Development and Intergenerational MuratF. Iyigun Economic Mobility 523 HumanCapitalAccumulation,Fertilityand Murat F. Iyigun Growth: A Re-Analysis 522 ExcessReturnsandRiskattheLong End of the AllanD. Brunner Treasury Market: An EGARCH-M Approach DavidP. Simon 521 The MoneyTransmissionMechanisminMexico MartinaCopelman AlejandroM.Werner 520 Whenis MonetaryPolicyEffective? JohnAmmer AllanD. Brunner 519 CentralBankIndependence,Inflationand PrakashLoungani GrowthinTransitionEconomies NathanSheets 518 AlternativeApproachesto RealExchangeRates HaliJ. Edison andRealInterestRates: ThreeUpandThreeDown WilliamR. Melick 517 Productmarketcompetitionandtheimpactof VivekGhosal priceuncertaintyon investment: someevidence PrakashLoungani fromU.S.manufacturingindustries 516 BlockDistributedMethodsfor Solving Jon Faust Multi-countryEconometricModels RalphTryon 515 Supply-sidesourcesof inflation: evidence PrakashLoungani fromOECD countries PhillipSwagel 514 Capital Flight from the Countries in Transition: NathanSheets Some TheoryandEmpiricalEvidence 513 BankLendingand EconomicActivityin Japan: AllanD.Brunner Did “FinancialFactors”Contributeto the Recent StevenB. Kamin Downturn? 512 EvidenceonNominalWageRigidityFroma Panel VivekGhosal of U.S.ManufacturingIndustries PrakashLoungani 511 DoTaxesMatterforLong-RunGrowth?: Harberger’s EnriqueG. Mendoza SupemeutralityConjecture GianMariaMilesi-Ferretti PatrickAsea 31