Opportunistic and Deliberate Disinflation under Imperfect Credibility

Opportunistic and Deliberate Disinflation Under Imperfect Credibility Antulio N. Bomfim and Glenn D. Rudebusch (cid:3) December 1997 Abstract Onestrategyfordisinflationprescribesadeliberatepathtowardslowinflation. Acontrasting opportunistic approach eschews deliberate action and insteadwaitsforunforeseenshockstoreduceinflation. Thispapercompares theabilityofthesetwoapproachestoachievedisinflation—andatwhatcost. Weanalyzetheseissues usingtheFederalReserve'sFRB/USmodel, which allowsalternativeassumptionstobemadeaboutexpectationsheldbyagents intheeconomy;hence, thecredibility ofthecentralbankcanbeconsidered inassessing thecostofdeliberate andopportunistic disinflations. JELClassification: E52 Keywords: monetarypolicy,inflationexpectations,policyrules,inflationtargets (cid:3) FederalReserveBoardandFederalReserveBank ofSan Francisco,respectively. We thank Steve Sumner for excellent research assistance. Helpful comments were provided by seminar participantsatthe1997NBERSummerInstitute,theIIES,andtheSwedishRiksbank,aswellas byourmanycolleaguesintheFederalReserveSystem. Theopinionsexpressedinthispaperare notnecessarilysharedbyanyoneelseintheFederalReserveSystem.

1 Introduction Centralbanksindifferentcountrieshaveadopteddifferentstrategiesforachieving price stability. One approach is to take a deliberate path to an ultimate goal of low inflation. In the past decade, this approach has often been followed using explicit inflation targets (Leiderman and Svensson 1995 and Haldane 1995). For example, in early 1990, New Zealand's central bank announced interim inflation target ranges of 3 to 5 percent by the end of 1990 and 1.5 to 3.5 percent by the end of 1991, as well as an ultimate inflation target range of 0 to 2 percent by the end of 1992. Similarly, in February 1991, with Canadian core inflation of about 4 percent, the Bank of Canada (1991) announced a deliberate disinflation with a target of 3 percent by the end of 1992 and an ultimate target of 2 percent by the endof1995. In contrast to a deliberate approach, an opportunisticstrategy for disinflation hasrecentlygatheredattention.1 Anopportunisticdisinflationpolicyalsoassumes anultimatetargetoflowinflation;however,exceptwheninflationistoohigh,the opportunistic policymaker's interim inflation target is simply the current rate of inflation. Thus, the opportunistic strategy typically eschews deliberate action to reduce inflation, and instead waits for unforeseen shocks to reduce inflation. An opportunisticstrategyfordisinflationwasdescribedbyaparticipantattheFOMC meeting in December 1989: “Now, sooner or later, we will have a recession. I don't think anybody around the table wants a recession or is seeking one, but sooner or later we will have one. If in that recession we took advantage of the anti-inflation[impetus]andwegotinflationdownfrom4-1/2percentto3percent, and then in the next expansion we were able to keep inflation from accelerating, sooner or later there will be another recession out there. And so, . . . we could 1Forexample,seeOrphanidesandWilcox(1996),Rudebusch(1996),Meyer(1997),andOrphanides et al. (1997). Like our paper, the last of these studies also investigates opportunism withsimulationsofaneconometricmodelwithexplicitexpectations.However,theauthorsdonot considercredibilityanduseadefinitionofopportunismthatisakinto“inflationzonetargeting.” 1

bring inflation down from cycle to cycle . . . .” Indeed, the gradual ratcheting down of inflation over time is the hallmark of the opportunistic approach. As longasinflationisnottoohigh,theopportunisticpolicymakertakesnodeliberate action to reduce inflation further, but waits to exploit recessions and favorable supply shocks to lower inflation. When inflation gets pushed down by a shock, theinterim inflationtarget is re-set toequal thenewprevailinglowerrate, and, in thisfashion,pricestabilityiseventuallyachieved. Howshouldapolicymakerchoose,oneconomicterms,betweendeliberateand opportunisticstrategies for disinflation? Twokeyconcerns are thetimingand the cost of the disinflation. An opportunistic approach, which waits for shocks, will almost certainly take longer to reach price stability than a deliberate approach. However, an opportunisticstrategy may be able to achieve disinflation at a lower cost,forexample,bytakingadvantageofunforeseennegativepriceshocksrather than having to create excess slack in the economy. The answer to the choice between these two approaches to disinflation depends, in part, on the nature and thefrequencyoftheshocksthataffect theeconomy. Thecosts ofa disinflationare alsocommonlybelievedtodependonthecredibilityofthecentralbank'scommitmenttothenewlowerinflationtarget. Indeed, a major impetus behind the historical adoption of deliberate disinflation policies with explicit inflation targets was the view that by clearly communicating a low inflationgoal to the publicand by taking transparent actions to achieve that goal, the costs of disinflation could be lowered. As noted in the press release by the Bank of Canada (1991) at the initial announcement of its inflation targets: “The intentioninsettingoutexplicittargets. . . istoencourageCanadianstobasetheir economic decisions on this downward path for inflation so that the lower inflation will be more readily achieved. . . .” That is, if people believe that inflation willindeedfall,then inflationmaybereduced withasmallercost interms oflost output and employment. In contrast, during an opportunistic disinflation, a lack of credibility may be a concern. The continued use of the current inflation rate 2

as an interim target may foster questions about the importance of the professed ultimatetargetoflowinflation. Also,thefuturepathoftheinteriminflationtarget depends to a very large extent on the size and distributionof future shocks to the economy. Thus, the absence of transparent announcements and decisive action under opportunism could well reduce credibility and undermine disinflationary expectations. In this paper, we shall explore these issues. In the next section, we describe two simplepolicyrules that capture the essence of thedeliberate and opportunistic approaches to disinflation. In section 3, we define credibility and describe howcredibilitycan begainedand lostovertime. Section4 outlinestheempirical macroeconomic model of the U.S. economy that we use—the Federal Reserve's FRB/US model. Our discussion of this model focuses on its expectational structureandonthecostsofdisinflation. Section5presentsoursimulationresults,and section6concludes. 2 Alternative Approaches to Disinflation This section defines deliberate and opportunistic approaches to disinflation. For bothapproaches,theimpetusforthedisinflationcomesfromareductionintheultimateinflationtarget, (cid:25) (cid:3) t (cid:3) . Afteradoptionofanewlowerultimateinflationtarget, thedeliberatepolicymakerimmediatelybeginstotakeconsistentactions toreach that goal. We model this behavior by assuming that the deliberate policymaker followsasimplevariantoftheTaylor(1993)rule: i t = r (cid:3) + (cid:25)(cid:22) t + (cid:12) 1 ( (cid:25)(cid:22) t (cid:0) (cid:25) (cid:3) t (cid:3) ) + (cid:12) 2 y t (1) where i t is the nominal short-term policy interest rate (the federal funds rate), r (cid:3) is the equilibrium real short-term rate (which is assumed to be known), (cid:25)(cid:22) t is 3

the 4-quarter inflation rate, and y t is the real output gap.2 That is, the deliberate policymakerconsistentlystrivestoeliminateinflationdeviationsfromtheultimate target. Theopportunisticpolicymakerbehavessomewhatdifferently. Weassumethat theopportunisticpolicymakersetstheshort-terminterestrateaccordingto: i t = r (cid:3) + (cid:25)(cid:22) t + (cid:12) 1 ( (cid:25)(cid:22) t (cid:0) (cid:25) (cid:3) t ) + (cid:12) 2 y t (2) Equation (2) is identical to (1) in all respects, except that the ultimate inflation target does not explicitly appear on its right-hand side. Instead, the opportunistic policymaker sets the short rate according to the gap between current inflation and an interim inflation target, (cid:25) (cid:3) t . To capture the essence of the opportunistic approachtodisinflation,we assumethattheinterimtarget evolvesaccordingto: (cid:25) (cid:3) t = m i n ( (cid:25) (cid:3) t(cid:0) 1 ; (cid:25)(cid:22) t(cid:0) 1 ) (3) with (cid:25) (cid:3) t boundedfrom belowby (cid:25) (cid:3) t (cid:3) . Equations (2) and (3) implythat as long as inflation is stable ( (cid:25)(cid:22) t = (cid:25)(cid:22) t(cid:0) 1 ), the opportunisticpolicymaker takes no action to reduce it. However, the opportunistic policymaker will attempt to prevent prices from accelerating further. Also, if actual inflation happens to fall below the interim target—because of an unanticipated recession or favorable supply shock—then the opportunistic policymaker resets the interim target to the newly achieved lower inflation. This process continues until the disinflation is achieved and the interim and ultimate targets are equal. 2Ofcourse,therearemanypossiblerulesthatcouldbeconsistentwithadeliberateapproach todisinflation,see,forexample,RudebuschandSvensson(1997). 4

3 Monetary Policy Credibility Intheprevioussection,weintroducedtheinterimandultimateinflationtargetsin therulesformonetarypolicy. Here,wedefinemonetarypolicycredibilitythrough the relationship between the ultimate inflation target and inflation expectations. Wealsoconsidertheachievementandthemaintenanceofcredibility. Our definitionof central bank credibilityis straightforward. At the beginning of each period, the central bank announces an ultimate inflation target. The private sector must evaluate the future reliability of this target. Agents must judge the central bank's credibility of intent—that is, whether the target represents the true goal of the central bank—and its credibility of action—that is, whether the central bank has the ability to meet the target even if it wants to (say, in the face of fiscal constraints). We measure overall credibility by the extent to which the pronouncement of a target is believed by the private sector in the formation of theirlong-runinflationexpectations.3 Specifically, weassumethat long-runinflationexpectationsat timet,denoted (cid:25) e 1 tj , are a weighted average of the current target and last period's (four-quarter) inflationrate: (cid:25) e 1 tj = (cid:21) t (cid:25) (cid:3) t (cid:3) + ( 1 (cid:0) (cid:21) t ) (cid:25)(cid:22) t(cid:0) 1 : (4) Theparameter (cid:21) t (with 1 (cid:21) (cid:21) t (cid:21) 0 )indexesthecredibilityof thecentral bank. If (cid:21) t = 1 , there is perfect credibility, and private sector's long-run inflation expectations are equal to the announced long-run goal of the policymaker. If (cid:21) t = 0 , thereisnocredibility,andtheinflationtargetisignoredintheformationofexpectations. Intermediatevaluesof (cid:21) t representthepartialcredibilityoftheannounced 3Thisdefinitionofcredibilitydiffersfrommuchofthetheoreticalliterature,whichstressesincentivecompatibilityinagame-theoreticsetting.Inanempiricalcontext,wefocusontheoutcome ofsuchcompatibilityasthealignmentofexpectationsandtargets. Ourmeasureofcredibilityis preciselytheoneemployedbyKing(1995)whoanalyzesthedifferencebetweenlong-runinflationexpectations(derivedfromnominalandrealyieldcurves)andinflationtargets.Itisalsoclose totheexpectationaldefinitionsinJohnson(1997a,1997b)andCroushoreandKoot(1994),which employshort-runinflationexpectationsfromsurveys. 5

inflationtarget. Withrepresentativeagents, (cid:21) t may represent thesubjectiveprobabilitythatan agent attaches tothefutureachievementofthetarget. Withheterogeneousagents, (cid:21) t couldbeconsideredthefractionofthepopulationthatbelieves thetarget willbeachieved. Credibility as indexed by (cid:21) t is unlikely to be exogenous. The weight that agentsplaceontheannouncedtargetplausiblyreactstodevelopmentsintheeconomy. For example, targets that are egregiously missed on a consistent basis are likelytobedown-weightedintheformationofexpectations. Therearemanypossible channels through which economic developments could affect the evolution ofcredibility. Weconsiderthreedifferentmechanismsforendogenouscredibility. In our first mechanism,credibility is establishedby outcome. If past inflation matches the inflation target, then the target is given more weight by the private sector in the formation of expectations of future inflation. In this formulation, credibilityevolvesaccordingto (cid:21) t = 1 (cid:0) (cid:11) j (cid:25)(cid:22) t(cid:0) 1 (cid:0) (cid:25) (cid:3) t (cid:3) j : (5) That is, credibility is reduced in a linear fashion as (the absolute value of) the deviationofpastinflationfrom thetarget increases (withthebound (cid:21) t (cid:21) 0 ). Oursecondmechanismallowscredibilitytobeestablishedbythebehaviorof the central bank. Here agents are more forward-looking than in the first formulation. Agentsdonotjustconsiderinflationovertheimmediatepast,buttheyassess thestanceofmonetarypolicyandforecastinflationoneyearahead( (cid:25) e +t 4 tj (cid:0) 1 ). As thenear-termforecastforinflationisclosertothetarget,then,irrespectiveofpast inflation,credibilityis higher. Specifically,ourformulationis (cid:21) t = 1 (cid:0) (cid:11) j (cid:25) e +t 4 tj (cid:0) 1 (cid:0) (cid:25) (cid:3) t (cid:3) j : (6) Thus,ifthecentralbankcantakeactionsthatcanfocusnear-terminflationexpectationsonitsgoal,itslong-runcredibilitywillincreaseeventhoughpastinflation 6

hasnot matchedthetarget. It should be noted that these mechanisms for the establishment of credibility by outcome and by behavior are broadly similar to those used in the theoretical literature on acquiring credibility (or reputation) in repeated games (as surveyed in Rogoff 1989 and Blackburn and Christensen 1989). However, that literature has typicallyemployed“trigger” mechanismsthat assumedaquickandcomplete collapse of credibility after even a minor failure by the policymaker to meet the target. Equations(5) and (6), whileinthe samespirit,can displaymore plausible macrodynamics because variation in (cid:11) allows more flexibility in modeling how much and how quickly agents revise their inflation expectations in response to missedtargets.4 Finally, in our third channel, credibility may be enhanced merely by the announcementoftransparentgoalsforinflation. Informinglong-runinflationexpectations, the public may place a higher weight on inflation targets that are clearly and unambiguously stated. Indeed, as noted in the introduction, the recent adoption of deliberate disinflation paths with explicit inflation targets by various central banks was motivated in part by the belief that some credibility could be established by announcement. Such a perspective is not that surprising at central banks where policymakers that are less than circumspect often find that their offthe-cuff comments can move financial markets (and sometimes there is intended “jaw-boning” as well). Still, there is much to be skeptical about regarding credibility by announcement. Presumably, agents do not just listen to policymakers' wordsbutalsojudgetheirunderlyingpreferencesandincentives. Targetsareeasy to announce but may be hard to deliver. The empirical evidence on credibility by announcement is decidedly mixed, but there is some evidence that past policy announcements of deliberate disinflations had some small effect on inflation 4Whileweviewourmechanismsforendogenouscredibilityasplausible,thereareothercandidatesintheempiricalliterature. Forexample,FuhrerandHooker(1993)andHuhandLansing (1997)consideraBayesianlearningmechanismthatisperhapsmorerigorousinformulation,but wouldbedifficulttoimplementwithournonlinearpolicyrule. 7

expectations (e.g., Johnson 1997a, 1997b and Amano, et al. 1997). We shall consider this possibilityin some of our simulations by slightlyboostingcredibilityimmediatelyafter theannouncementofadeliberatedisinflationslightlyabove whata forward-lookingspecificationwouldsuggest. 4 The Model The FRB/US model that we employ in our analysis is a large-scale macroeconometricmodeloftheU.S.economywithanexplicitexpectationalstructure,which wasdevelopedattheFederalReserveBoardforanalysisandforecasting. Itslongrun structure is akin to a neoclassical growth model. In the long run, economic growth is solely a function of population and technology growth, and inflation is determined by the long-run inflation target implicit in the specification of monetary policy. In the short run, however, because of adjustment costs and other dynamicfrictions,householdsand firms are oftenaway from theirlong-runequilibrium paths, and monetary policy can have significant short-run effects on real activity. Below,wehighlighttwoaspectsofthespecificationthataremostrelevant forouranalysis: thecostsofadjustmentandtheformationofexpectations.5 4.1 Evolution of Key Macro Variables TwodistinctmodelingapproacheswereusedintheconstructionofFRB/US.Nonfinancial variables are assumed to evolve according to a generalized adjustment costframework. Financialmarketsaregovernedbystandardarbitrageequilibrium conditions. Non-FinancialMarkets. Firmssetpricesandmakefactorallocationdecisionsun- 5SeeBomfim,Tetlow,vonzurMuehlenandWilliams(1997),BraytonandTinsley(1996),and Brayton,Mauskopf,Reifschneider,TinsleyandWilliams(1997)formoredetaileddescriptionsof theFRB/USmodel. 8

der imperfect competition. Households make consumption decisions in the context of a life-cycle framework. We shall use the firms' price setting problem to illustratethegeneralmodelingapproachusedinallkeynon-financialequationsof FRB/US.6 In doing so we shall pay special attention to the role played by expectationsinthemodel'sdynamics. Non-financial variables are modeled according to two basic tenets. First, all economic agents are assumed to be forward looking, with their expectations of future conditions explicitly modeled in all key behavioral equations. Second, decision making in all non-financial markets is subject to non-trivial adjustment costs or frictions that prevent agents from instantaneous reaching their long-run or“target”factorallocationsandprices. Inpractice,thisapproachisimplemented by assuming that agents follow a two-state decision making process. In the first stage, target values for all decision variables are determined; these are the values that would prevail in the absence of adjustment costs. For instance, given imperfect competitionandaCobb-Douglasproductionfunction,targetprices ( p (cid:3) t )area functionofmarginalcostsofproduction( c t )andacyclicalmark-up. Inthesecond stageofthedecisionmakingprocess,agentsseektoclosethegapbetweenactual and target values of their decision variables subject to adjustment costs. Again using price setting as an illustration, the second-stage decision problem reduces tosolvingthecost minimizationproblem: min C t = E t(cid:0) 1 1 X =i 0 (cid:12) i [ b 0 ( p +t i (cid:0) p (cid:3) +t i ) 2 + X k m = 1 b k ( p +t i (cid:0) p +t i(cid:0) k ) 2 ] (7) where p t denotes the actual price level and p (cid:3) t its target value. Equation (7) generalizes the adjustment cost assumption to go beyond the level-adjustment cost specification commonly used in standard linear quadratic models—e.g. Sargent (1978) and Rotemberg (1982). For instance, for m=2, equation (7) says that it is 6ThedetailsofthemodelingapproacharedescribedbyTinsley(1993). 9

costly not just to change the price level, but also its rate of change.7 The solution to the above minimization problem leads to the following decision rule for inflation: (cid:1) p t = a 0 + a 1 ( p t(cid:0) 1 (cid:0) p (cid:3) t(cid:0) 1 ) + X j 2 = 1 (cid:26) j (cid:1) p t(cid:0) j + 1 X = j 0 (cid:13) c ;j (cid:1) c +t j + 1 X = j 0 (cid:13) u ;j u +t j + e p ;t (8) where the cyclicality of the mark-up is captured by the term involvingthe unemploymentrate( u t ),and e p ;t is apriceshock. Inthecontextofthemodel'spricesettingbehavior,equation(8)hasastraightforwardeconomicinterpretation: Itcanbethoughtofasaforward-lookingPhillips curve where today's inflation depends not only on past and expected inflationary developments,butalsoonanticipatedconditionsinthelabormarket.8 Inabroader context, (8) allows for the explicit decomposition of macroeconomic dynamics into“adjustmentcosts”andexpectationalfactors. Inparticular,thelaggeddependentvariableappearsontheright-hand-sideof(8)solelytoreflectthenatureofthe generalized adjustment costs. Thus, if we only had level-adjustment costs—i.e. producerscanadjusttherateat whichtheychangetheirprices costlessly—thenit canbeshownthat (cid:26) j = 0 forall j . Incontrasttothisexplicitattempttodecompose dynamicsbetweenexpectationsandadjustmentcosts,traditionalspecificationsof thePhillipscurveuselaggedvaluesofinflationtocapture both“inflationinertia” andtheusefulnessofpastinflationinpredictingitsfuturevalues. Equations like (8) permeate all aspects of key non-financial sectors of the model. For households, the two-stage decision problem of consumers involves, first, specifying “target” consumption as a function of lifetime income, and, second,solvinganoptimizationproblemsimilarto(7). Again,theresultisadecision 7Thus,thoughthemodeldoesnotexplicitlyspecifythestructureofthedynamicfrictionspreventingfullyflexibleprices,theabovespecificationcapturesthenotionthatchangingtheinflation rateiscostly(e.g.FuhrerandMoore,1995). 8Theestimatedcoefficientsaresuchthatexpectationsofhighunemploymentleadtoadecelerationinpriceincreases. 10

rule where consumption growth is a function not only of the gap between actual and target consumption, but also of past values of consumption growth and expectedchangesinconsumptionfundamentals. Firms' factorallocationandinventoryaccumulationdecisionsarealsoderivedwithinthisframework.9 Financial Markets. The main financial equations involve three long-term interest rates—for the 5- and 10-year government bonds and the 30-year corporate bond—and the stock market. Adjustment costs are assumed to be small enough to be negligibleso that there is no distinctionbetween target and actual values of financial variables. Long-term interest rates are determined according to the expectations theory of the term structure. Following Shiller (1979), the yield on a long-term bond of maturity m is given by the expected future path of short-term interest rates ( i t ) plusatermpremium( (cid:30) m ;t ): i m ;t = m X j (cid:0) = 1 0 (cid:28) j i +t j tj + (cid:30) m ;t (9) The model's equation for stock market also follows standard specifications. It is based on the familiar notion that stock prices reflect the present discounted valueofexpecteddividends. 4.2 Expectation Formation As discussed above, expectations play a potentially important role in the evolution of both financial and non-financial variables in FRB/US. The version of the model used for the experiments described in this paper assumes that agents base their expectations on a simplified reduced-form representation of the economy. Thus, rather than explicitly using all 300+ equations and identities that make up 9BraytonandTinsley(1996)providedetailsofindividualequations 11

the model, agents rely on small-scale vector-autoregressions to form their expectations. Such expectations are within the spirit of our disinflation exercise. As stressed by Taylor (1993), fully rational expectations may be unrealistic during the transition period after a new policy has been put in place. Certainly, the assumption that agents may be not fully aware of the policy generating process motivatesouranalysisofcredibility. The VAR forecasting systemsvary from sector to sector—for example,while the price setting decision leads firms to forecast the unemployment rate, householdsarerequiredtogenerateexplicitincomeforecastswhendecidinghowmuch to consume. Nevertheless, all small-scale forecasting models include a restricted VAR in three core macroeconomic variables: inflation ( (cid:25) t ), short-term interest rates( i t ),andanoutputgap( y t ).10 Thesubsystemformedbythesethreevariables canbewrittenas: (cid:1) i t = (cid:18) 1 ( (cid:25) t(cid:0) 1 (cid:0) (cid:25) e 1 tj (cid:0) 1 ) + (cid:18) 2 ( i t(cid:0) 1 (cid:0) i e 1 tj (cid:0) 1 ) + (cid:18) 3 y t(cid:0) 1 + A 1 ( L ) x t(cid:0) 1 (10) (cid:1) (cid:25) t = (cid:18) 4 ( (cid:25) t(cid:0) 1 (cid:0) (cid:25) e 1 tj (cid:0) 1 ) + (cid:18) 5 ( i t(cid:0) 1 (cid:0) i e 1 tj (cid:0) 1 ) + (cid:18) 6 y t(cid:0) 1 + A 2 ( L ) x t(cid:0) 1 (11) (cid:1) y t = (cid:18) 7 ( (cid:25) t(cid:0) 1 (cid:0) (cid:25) e 1 tj (cid:0) 1 ) + (cid:18) 8 ( i t(cid:0) 1 (cid:0) i e 1 tj (cid:0) 1 ) + (cid:18) 9 y t(cid:0) 1 + A 3 ( L ) x t(cid:0) 1 (12) where A i ( L ) are polynomials in the lag operator L , and x t (cid:17) [ (cid:1) i t ; (cid:1) (cid:25) t ; (cid:1) y t ] 0 . (cid:25) e 1 tj (cid:0) 1 is the private sector's expected long-run inflation rate, and i e 1 tj (cid:0) 1 is analogously defined (as r (cid:3) + (cid:25) e 1 tj (cid:0) 1 ).11 The estimated coefficients of the core VAR 10Effectively, the inclusion of these three variables endows all agents in the economy with knowledgeofitsthreeessentialmacroeconomicrelationships:aPhillipscurve,amonetarypolicy rule,andanIScurve. WealsoexploredsimulationswithacoreVARthatreplacedequation(10) withanexpectationsversionofthepolicyrule(1)or(2),andweobtainedverysimilarresultswith suchpolicy-consistentexpectations. 11When estimating the model, long-runexpectationsfor inflation are taken from survey data, andthosefor thefederalfundsrate fromtheforwardinterestrates implicitin the term structure ofinterestrates. IntheterminologyofKozickiandTinsley(1996),theseexpectationalvariables represent“movingendpoints”forinflationandinterestrateforecasts. 12

implythat thesystem“error corrects”sothat l i j ! m 1 (cid:25) e +t j tj (cid:0) 1 = (cid:25) e 1 tj (cid:0) 1 (13) l i j ! m 1 i e +t j tj (cid:0) 1 = i e 1 tj (cid:0) 1 (14) l i j ! m 1 y e +t j tj (cid:0) 1 = 0 : (15) Long-runexpectationvariablesplayan importantrole inthe behavioralequations described above. Take, for example, the model's modified Phillips curve— equation(8): Toforecastfuturevaluesoftheunemploymentrate,firmsrelyonan expectational model composed of the 3-equation core VAR system and an additionalequationrelatingthe unemploymentrate toits ownlags,andlagged values ofinflation,short-terminterestratesandtheoutputgap. Thus,astheylookfurther andfurtherintothefuture,theirunemploymentrateforecastbecomesincreasingly more affected by, say, their long-run inflation rate forecast. More important for the purposes of this paper, long-run inflation expectations play an important role in the workings of a policy to achieve disinflation. For instance, if the policy is fully credible, then (cid:25) e 1 tj (cid:0) 1 coincides with the long-run inflation target implicit in the disinflation effort. In contrast, if (cid:25) e 1 tj (cid:0) 1 is persistently above the monetary authority's long-run inflation target, then the private sector underestimates future unemployment rates and overestimates increases in production costs. According to (8), these misperceptions would lead to higher increases in output prices than otherwise and, consequently, a tighter monetary policy stance than in the case of fullcredibility. 5 Model Simulation Results Our goal is to compare the performances of the opportunistic and deliberate approaches to disinflation. We do this by conducting stochastic simulations of the FRB/US model. All of the simulations start from a steady state baseline with the 13

inflation target and actual inflation both at 5 percent. The stochastic simulations beginwiththeannouncementofa3percentinflationtarget. Thedeliberatepolicymakerstrivesforthis newtarget byfollowingtheTaylor-typeruleinequation(1) with (cid:25) (cid:3) t (cid:3) equalto3. Theopportunisticpolicymakeremploysthestrategydescribed byequations(2)and(3).12 Thestochasticsimulationsuseabootstrapprocedurebasedontheerrorsmade bykeymodelequations(about 50innumber)overthe1966-1995period. Weran 1,000simulationseachunderopportunisticanddeliberatemonetarypolicy. These simulationswere runinpairs (whichconsistof onewitheach typeofpolicy)that were each characterized by a different sequence of randomly selected macroeconomicshocksoverwhichthedisinflationepisodetookplace(whichistheobvious variance reduction technique). For each simulation, we recorded the number of yearsthatwererequireduntilthedisinflationwascompleteandtheultimateinflation target was achieved.13 We also recorded how much the unemployment rate deviated from its steady-state value during each disinflation episode in order to computethecostsassociatedwitheachmonetarypolicystrategy.14 Whilethesacrifice ratio and disinflationduration are commonmetrics for disinflation, we also consideramoretraditionaldiscountedquadraticlossfunctionofthetype: L o s s = 8 X = j 0 1 (cid:14) j ( ( (cid:25) +t j (cid:0) (cid:25) (cid:3) (cid:3) +t j ) 2 + y 2 +t j ) : (16) This loss function sums the (discounted) squared deviations of inflation from its 12For the policy rule parameters, we use Rudebusch's (1997) estimates for the Greenspan period— (cid:12) 1 = 0 7: 8 and (cid:12) 2 = 0 6: 8 .Ourresultsarerobusttovariationintheseparameters. 13Thedisinflationisconsideredcompleteinaquarterwhenthefour-quarterinflationrateisat orbelowtheultimatetargetandremainsthereforthenextthreequarters. 14Wemeasurethecostofdisinflation—thesacrificeratio—asthecumulativeannualdeviation of theunemploymentratefrom the naturalratedividedby the two-percentagepointdecrease in theinflationrate. Therefore,ifthedisinflationpolicystartedatquarter t = 1 andtook N quarters to reach its goal, we compute the sacrifice ratio as as ( 1 = 8 ) P N 1 ( U d e v t ) where U d e v t are the unemploymentratedeviationsfromthesteadystate. 14

target and output from potential duringthe first 20 years after the disinflationbegins.15 Thus,for each stochasticsimulation,we generated three pairs of observations: namely,thedurationofthedisinflation,thesacrificeratio,andthequadratic lossforeachpolicymaker. Armed with 1,000 observations on sacrifice ratios, losses, and durations of disinflationforeachpolicymaker,wethenproceededtoaddressthemainquestion askedinthispaper: GiventhestochasticcharacteristicsoftheU.S.economyover thepast3decades—asmeasuredbytheFRB/USmodel—howwellcantheopportunistic and deliberate policymakers deliver on their announced inflation targets? To address this question, we compare mean and median values of the statistics. In the comparison of sacrifice ratios and the losses, we also used paired-sample t-tests and Wilcoxon tests to gauge the statistical significance of the reported differences betweentheopportunisticanddeliberatepolicymakers. Table 1 provides a summary of our results under various assumptions about credibility. The top half of the table considers three cases of exogenous credibility: (cid:21) t = 0 (no credibility), (cid:21) t = : 5 , and (cid:21) t = 1 (perfect credibility). Consider the intermediate case first. With (cid:21) t = : 5 , the mean sacrifice rate faced by the deliberate policymaker is 1.24; therefore, the cumulative deviation of the unemployment rate from the steady-state during the two-percentage point disinflation is about 2-1/2 percentage-point-years.16 This trade-off is less favorable than the 1.08ratiofacedbytheopportunisticpolicymaker. Furthermore,giventhep-value ofzerofortheassociatedt-test,thesedifferencesarestatisticallysignificant. Similar results are obtained with the medians (where the p-values are obtained for a Wilcoxon signed-rank test). Thus, it appears that the opportunistic policymaker, bywaitingfortheappropriateshocks,isabletoreduceinflationwithlesscumula- 15Thevalueofdeltausedis0.98,andtheoutputgapisdefinedastwicetheunemploymentgap inaccordwithOkun'sLaw. 16Thissacrificeratio isveryclosetothe onecalculatedbyBall(1994). Usingasimplebackof-the-envelopecalculationwithquarterlyU.S.data,hecalculatesaratioofabout1.2percentage pointsofunemploymentperpercentagepointdisinflation. 15

tiveunemploymentthanthedeliberatepolicymaker. Ofcourse,waitingforshocks increasesthedurationofthedisinflation,whichaverages(inmean)5.56yearsfor theopportunisticpolicymakerand 3.77years for the deliberateone. (In all cases, thedifferencesinthedurationofthedisinflationsacross thetwoapproacheswere very significant, so p-values are not reported for these statistics.) Still, as measured by simple quadratic loss, with equal weights on inflation and output deviations, the opportunistic policymaker does suffer a slightly smaller loss. Again, in all cases the differences across the two approaches were very significant, so p-values are not reported for these statistics. This last conclusionmay depend on therelativeweightsassignedtooutputandinflationdeviations. Similar qualitative results are obtained for the case of perfect credibility, although both the sacrifice ratios and the disinflation durations are quantitatively smaller. In thecaseof nocredibility,however,theresultsare less clearinthat the sacrifice ratios andlossesforthedeliberate policymakeractuallyfall belowthose oftheopportunisticone. Ofcourse,asarguedabove,credibilityislikelytorespondendogenouslytothe performanceofthepolicymaker,andresultswithendogenouscredibilityaregiven inthelowerhalfoftable1. Inparticular,asactualoranticipatedprogressismade towardtheinflationtarget,thecredibilityofthattargetislikelytorise. Themechanisms for determining credibility are described in equation (4) and (5). In our simulations,we set (cid:11) = : 6 7 , which translates into a three percentage point range of credibility around the target.17 Under the backward-looking mechanism depicted in (4)—credibilityby outcome—ifactual inflationis outside of this range, thenthe target has no credibility. Credibilityis gainedincrementallyas the target is approached. In this case, as shownintable 1,the deliberatepolicymakeractually has a lower sacrifice ratio and a smaller quadratic loss than the opportunistic one. Thisisalsothetruefortheforward-lookingspecificationofcredibility(cred- 17Ourresultsarerobusttosomevariationin (cid:11) : 16

ibility by behavior) and for the credibility-by-announcement mechanism (where the credibility of the deliberate policymaker is bounded below by .2 after the announcement of the new policy). To shed some light on the movementof endogenous credibility in the three cases considered, the time paths of mean credibility (that is, the average of (cid:21) t in each quarter across simulations)are shown in figure 1. In all three cases, because the deliberate policymaker makes faster progress toward the goal of low inflation, he enjoys a faster rise in credibility and a lower sacrifice ratioandloss. 6 Concluding Remarks Thereisalonghistoryofexploringtheperformanceofvariouspolicyrulesineconomic models. Almost all of this research has been conducted in the context of linear models and rules with a fixed expectations mechanism—either rational or adaptive expectations. Such a framework is not well suited for our investigation along two dimensions. First, our opportunistic policy rule is inherently nonlinear. Whilesucha rule is verydifficult tomotivatewitha symmetricloss function and linear constraints, as noted in the introduction, it does appear to hold considerable appeal for some policymakers. Second, our interest is in a period that is clearly transitional—the disinflation—again, mirroring the interests of policymakers. Such a transitionwill likelyinvolvelearning andcredibilityand changes overtimeintheexpectationsformationprocess. Given the somewhat atypical, but clearly important, topic of our investigation, there are few clear answers in the literature to the many modeling choices required. What is the nature of learning during a policy transition? How are expectations formed? How will the success of an opportunistic policy be judged? Ourresultsareofcoursedependentuponthemodelingchoicesthatwehavemade, but still we see them as useful, not for their precise quantitative answers, but for providinga cautionarytale. Namely,thereseems tobe a fundamentaltensionbe- 17

tween credibility and opportunism. The public may well be skeptical about the importance of an ultimate inflation target when it is promulgated but not acted upon by an opportunistic central bank, and this skepticism may lead to a higher costforadisinflationpolicy. 18

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R s o T E x o g e n o u s C r e d (cid:21) : = 0 0 M e a n M e d i a n (cid:21) : = 0 5 M e a n M e d i a n (cid:21) : = 1 0 M e a n M e d i a n E n d o g e n o u s C r e B y O u t c o m e M e a n M e d i a n B y B e h a v i o r M e a n M e d i a n W i t h A n n o u n c e M e a n M e d i a n e s u lt s u n d e r t h e o a c r i(cid:12) c e r a t io ( in p e f d is in (cid:13) a t io n ) , t h e h e p - v a lu e s t e s t t h i b i l i t y d i b i l i t y m e n t p p o r t u n is t r c e n t a g e p d u r a t io n o e e q u a lit y S O p p 2 . 2 8 1 . 6 3 1 . 0 6 0 . 8 7 0 . 8 6 0 . 7 2 2 . 0 6 1 . 4 8 1 . 7 0 1 . 2 9 1 . 7 0 1 . 2 9 ic ( o p o in t y f d is in o f t h e T a b l e 1 S i m u l a t i o n R e s u l t s D u r a t i o n o f a c r i (cid:12) c e R a t i o D i s i n (cid:13) a t i o n . D e l . p - v a l u e O p p . D e l . 2 . 1 0 0 . 0 0 1 0 . 2 7 6 . 1 9 1 . 5 5 0 . 0 0 9 . 2 5 5 . 2 5 1 . 2 3 0 . 0 0 5 . 5 8 3 . 7 7 0 . 9 7 0 . 0 0 5 . 0 0 3 . 2 5 0 . 9 6 0 . 0 0 3 . 9 6 2 . 7 6 0 . 7 7 0 . 0 0 3 . 5 0 2 . 2 5 1 . 8 8 0 . 0 0 9 . 4 3 5 . 5 2 1 . 4 2 0 . 0 3 8 . 2 5 4 . 7 5 1 . 5 4 0 . 0 0 8 . 2 1 4 . 5 1 1 . 2 0 0 . 5 4 7 . 2 5 3 . 7 5 1 . 3 2 0 . 0 0 8 . 2 1 3 . 9 7 1 . 0 5 0 . 0 0 7 . 2 5 3 . 5 0 p .) a n d d e lib e r a t e ( d e l.) p o lic y s t r a t e e a r s o f u n e m p lo y m e n t r a t e d e v ia t io n s (cid:13) a t io n ( in y e a r s ) , a n d a lo s s f u n c t io n o p p o r t u n is t ic a n d d e lib e r a t e m e a n s o g ie p e d e s r m D i s c o L o s s F O p p . 2 9 5 . 3 2 6 5 . 0 2 2 3 . 2 2 1 1 . 9 2 2 5 . 1 2 1 8 . 8 2 8 8 . 3 2 5 8 . 7 2 8 3 . 2 2 5 2 . 9 2 8 3 . 2 2 5 2 . 9 s a r e g iv e r p e r c e n t c r ib e d in e d ia n s . u n t e d u n c t i o n D e l . 2 6 7 . 4 2 4 6 . 3 2 2 9 . 9 2 1 7 . 1 2 3 6 . 3 2 2 7 . 8 2 6 1 . 4 2 4 0 . 9 2 5 6 . 3 2 3 7 . 5 2 4 1 . 0 2 2 6 . 6 n f o r t h e a g e p o in t t h e t e x t . 22

Figure 1: Average Time Path of Credibility By Outcome 0.5 0.4 0.3 0.2 Opportunistic 0.1 Deliberate 0.0 2 4 6 8 10 years By Behavior 0.5 0.4 0.3 0.2 0.1 0.0 2 4 6 8 10 years With Announcement 0.6 0.5 0.4 0.3 0.2 0.1 0.0 2 4 6 8 10 years 23