the science of monetary policy: a new keynesian perspective1.pdf · bernanke and blinder (1992),...

Journal of Economic Literature Vol. XXXVII (December 1999), pp. 1661–1707

Clarida, Galí, Gertler: The Science of Monetary Policy

The Science of Monetary Policy: A New Keynesian Perspective

Richard Clarida, Jordi Galí, and Mark Gertler1

“Having looked at monetary policy from both sides now, I can testify thatcentral banking in practice is as much art as science. Nonetheless, whilepracticing this dark art, I have always found the science quite useful.”2 Alan S. Blinder

1. Introduction

THERE HAS BEEN a great resurgenceof interest in the issue of how to con-

duct monetary policy. One symptom ofthis phenomenon is the enormous vol-ume of recent working papers and con-ferences on the topic. Another is thatover the past several years many leadingmacroeconomists have either proposedspecific policy rules or have at leaststaked out a position on what the generalcourse of monetary policy should be.John Taylor’s recommendation of a sim-ple interest rate rule (Taylor 1993a) is awell-known example. So too is the recentwidespread endorsement of inflation tar-geting (e.g., Ben Bernanke and FredericMishkin 1997).

Two main factors underlie this re-birth of interest. First, after a long pe-riod of near exclusive focus on the roleof nonmonetary factors in the businesscycle, a stream of empirical work begin-ning in the late 1980s has made the casethat monetary policy significantly influ-ences the short-term course of the realeconomy.3 The precise amount remainsopen to debate. On the other hand,there now seems to be broad agreementthat the choice of how to conductmonetary policy has important conse-quences for aggregate activity. It is nolonger an issue to downplay.

Second, there has been considerableimprovement in the underlying theoret-ical frameworks used for policy analysis.To provide theoretical underpinnings,the literature has incorporated the tech-niques of dynamic general equilibriumtheory pioneered in real business cycle

1661

1 Clarida: Columbia University and NBER; Galí:New York University, Universitat Pompeu Fabra,CEPR, and NBER; Gertler: New York Universityand NBER. Thanks to Ben Bernanke, Bob King,Ben McCallum, Albert Marcet, Rick Mishkin,Athanasios Orphanides, Glenn Rudebusch, ChrisSims, Lars Svensson, Andres Velasco, and severalanonymous referees for helpful comments, and toTommaso Monacelli for excellent research assis-tance. Authors Galí and Gertler are grateful to theC.V. Starr Center for Applied Economics, and(Galí) to CREI for financial support. e-mail:[email protected]

2 Blinder 1997, p. 17.

3 Examples include Romer and Romer (1988),Bernanke and Blinder (1992), Galí (1992), Ber-nanke and Mihov (1997a), Christiano, Eichen-baum, and Evans (1996, 1998) and Leeper, Simsand Zha (1996). Much of the literature has fo-cused on the effects of monetary policy shocks.Bernanke, Gertler, and Watson (1997) present evi-dence that suggests that the monetary policy rulemay have important effects on real activity.

analysis. A key point of departure fromreal business cycle theory (as we latermake clear) is the explicit incorporationof frictions such as nominal price rigidi-ties that are needed to make the frame-work suitable for evaluation of monetarypolicy.

This paper summarizes what we havelearned from this recent research onmonetary policy. We review the prog-ress that has been made and also iden-tify the central questions that remain.To organize the discussion, we expositthe monetary policy design problem in asimple theoretical model. We start witha stripped-down baseline model in or-der to characterize a number of broadprinciples that underlie optimal policymanagement. We then consider the im-plications of adding various real worldcomplications. Finally, we assess howthe predictions from theory square withpolicy-making in practice.

Throughout, we concentrate on ex-positing results that are robust across awide variety of macroeconomic frame-works. As Ben McCallum (1997b) em-phasizes, the key stumbling block forpolicy formation is limited knowledgeof the way the macroeconomy works.Results that are highly model-specificare of limited use. This literature, how-ever, contains a number of useful prin-ciples about optimal policy that are rea-sonably general in applicability. In thisrespect there is a “science of monetarypolicy,” as Alan Blinder suggests in thequote above. We provide support forthis contention in the pages that follow.

At the same time, we should makeclear that the approach we take is basedon the idea that temporary nominalprice rigidities provide the key frictionthat gives rise to nonneutral effects ofmonetary policy. The propositions wederive are broadly applicable within thisclass of models. This approach haswidespread support in both theoretical

and applied work, as we discuss later.4There are, however, important strandsof the literature that either reject theidea of nominal price rigidities (e.g.,real business cycle theory) or focus onother types of nominal rigidities, suchas frictions in money demand.5 For thisreason, we append “New KeynesianPerspective” to the title. In particular,we wish to make clear that we adopt theKeynesian approach of stressing nomi-nal price rigidities, but at the same timebase our analysis on frameworks that in-corporate the recent methodological ad-vances in macroeconomic modeling(hence the term “New”).

Section 2 lays out the formal policyproblem. We describe the baselinetheoretical model and the objectives ofpolicy. Because we are interested incharacterizing policy rules in terms ofprimitive factors, the model we useevolves from first principles. Though itis quite simple, it nonetheless containsthe main ingredients of descriptivelyricher frameworks that are used for pol-icy analysis. Within the model, as inpractice (we argue), the instrument ofmonetary policy is a short-term interestrate. The policy design problem then isto characterize how the interest rateshould adjust to the current state of theeconomy.

An important complication is that pri-vate sector behavior depends on the ex-pected course of monetary policy, aswell as on current policy. The credibil-ity of monetary policy thus becomesrelevant, as a considerable contemporaryliterature has emphasized.6 At issue is

4 See, for example, the survey by Goodfriendand King (1997).

5 See, for example, Christiano, Eichenbaum,and Evans (1997). For an analysis of monetary pol-icy rules in these kinds of models—known as “lim-ited participation” frameworks—see Christianoand Gust (1999).

6 For a recent survey of the credibility litera-ture, see Persson and Tabellini (1997).

1662 Journal of Economic Literature, Vol. XXXVII (December 1999)

whether there may be gains from en-hancing credibility either by formalcommitment to a policy rule or by intro-ducing some kind of institutional ar-rangement that achieves roughly thesame end. We address the issue by ex-amining optimal policy for both cases:with and without commitment. Alongwith expositing traditional results, wealso exposit some new results regardingthe gains from commitment.

Section 3 derives the optimal policyrule in the absence of commitment. Iffor no other reason, this case is of inter-est because it captures reality: No ma-jor central bank makes any type of bind-ing commitment over the future courseof its monetary policy. A number ofbroad implications emerge from thisbaseline case. Among these: The opti-mal policy embeds inflation targeting inthe sense that it calls for gradual adjust-ment to the optimal inflation rate. Theimplication for the policy rule is thatthe central bank should adjust thenominal short rate more than one-for-one with expected future inflation. Thatis, it should adjust the nominal rate suf-ficiently to alter the real rate (and thusaggregate demand) in the direction thatis offsetting to any movement in ex-pected inflation. Finally, how the cen-tral bank should adjust the interest ratein response to output disturbances de-pends critically on the nature of the dis-turbances: It should offset demandshocks but accommodate supply shocks,as we discuss.

Section 4 turns to the case with com-mitment. Much of the literature hasemphasized that an inefficiently highsteady state inflation rate may arise inthe absence of commitment, if the cen-tral bank’s target for real output ex-ceeds the market clearing level.7 The

gain from commitment then is to elimi-nate this inflationary bias. How realisticit is to presume that a perceptive cen-tral bank will try to inadvisedly reapshort-term gains from pushing outputabove its natural level is a matter of re-cent controversy (e.g., Blinder 1997;McCallum 1997a). We demonstrate,however, that there may be gains fromcommitment simply if current price set-ting depends on expectations of the fu-ture. In this instance, a credible com-mitment to fight inflation in the futurecan improve the current output/infla-tion trade-off that a central bank faces.Specifically, it can reduce the effectivecost in terms of current output loss thatis required to lower current inflation.This result, we believe, is new in theliterature.

In practice, however, a binding com-mitment to a rule may not be feasiblesimply because not enough is knownabout the structure of the economy orthe disturbances that buffet it. Undercertain circumstances, however, a pol-icy rule that yields welfare gains rela-tive to the optimum under discretionmay be well approximated by an opti-mal policy under discretion that is ob-tained by assigning a higher relativecost to inflation than the true socialcost. A way to pursue this policy opera-tionally is simply to appoint a central bankchair with a greater distaste for infla-tion than society as a whole, as KennethRogoff (1985) originally emphasized.

Section 5 considers a number of prac-tical problems that complicate policy-making. These include: imperfect infor-mation and lags, model uncertainty andnon-smooth preferences over inflationand output. A number of pragmatic is-sues emerge, such as: whether and howto make use of intermediate targets, thechoice of a monetary policy instrument,and why central banks appear to smoothinterest rate changes. Among other

7 The potential inflationary bias under discre-tion was originally emphasized by Kydland andPrescott (1977) and Barro and Gordon (1983).

Clarida, Galí, Gertler: The Science of Monetary Policy 1663

things, the analysis makes clear whymodern central banks (especially theFederal Reserve Board) have greatlydowngraded the role of monetary aggre-gates in the implementation of policy.The section also shows how the recentlyadvocated “opportunistic” approach tofighting inflation may emerge under anon-smooth policy objective function.The opportunistic approach boils downto trying to keep inflation from risingbut allowing it to ratchet down in theevent of favorable supply shocks.

As we illustrate throughout, the opti-mal policy depends on the degree ofpersistence in both inflation and out-put. The degree of inflation persistenceis critical since this factor governs theoutput/inflation trade-off that the pol-icy-maker faces. In our baseline model,persistence in inflation and output isdue entirely to serially correlated ex-ogenous shocks. In section 6 we con-sider a hybrid model that allows for en-dogenous persistence in both inflationand output. The model nests as specialcases our forward-looking baselinemodel and, also, a more traditionalbackward-looking Keynesian frame-work, similar to the one used by LarsSvensson (1997a) and others.

Section 7 moves from theory to prac-tice by considering a number of pro-posed simple rules for monetary policy,including the Taylor rule, and a forward-looking variant considered by Clarida,Galí, and Gertler (1998; forthcoming).Attention has centered around simplerules because of the need for robust-ness. A policy rule is robust if it pro-duces desirable results in a variety ofcompeting macroeconomic frameworks.This is tantamount to having the rulesatisfy the criteria for good policy man-agement that sections 2 through 6 es-tablish. Further, U.S. monetary policy maybe judged according to this same met-ric. In particular, the evidence suggests

that U.S. monetary policy in the fifteenyears or so prior to Paul Volcker did notalways follow the principles we have de-scribed. Simply put, interest rate man-agement during this era tended to ac-commodate inflation. Under Volckerand Greenspan, however, U.S. mone-tary policy adopted the kind of implicitinflation targeting that we argue isconsistent with good policy management.

The section also considers some pol-icy proposals that focus on target vari-ables, including introducing formalinflation or price-level targets andnominal GDP targeting. There is in ad-dition a brief discussion of the issue ofwhether indeterminacy may cause prac-tical problems for the implementation ofsimple interest rate rules. Finally, thereare concluding remarks in section 8.

2. A Baseline Framework for Analysisof Monetary Policy

This section characterizes the formalmonetary policy design problem. It firstpresents a simple baseline macro-economic framework, and then de-scribes the policy objective function.The issue of credibility is taken up next.In this regard, we describe the distinc-tion between optimal policies with andwithout credible commitment—whatthe literature refers to as the cases of“rules versus discretion.”

2.1 A Simple Macroeconomic Framework

Our baseline framework is a dynamicgeneral equilibrium model with moneyand temporary nominal price rigidities.In recent years this paradigm has be-come widely used for theoretical analy-sis of monetary policy.8 It has much ofthe empirical appeal of the traditional

8 See, e.g, Goodfriend and King (1997), McCal-lum and Nelson (1997), Walsh (1998), and the ref-erences therein.


IS/LM model, yet is grounded in dy-namic general equilibrium theory, inkeeping with the methodological ad-vances in modern macroeconomics.

Within the model, monetary policyaffects the real economy in the shortrun, much as in the traditional Keynes-ian IS/LM framework. A key difference,however, is that the aggregate behav-ioral equations evolve explicitly fromoptimization by households and firms.One important implication is that cur-rent economic behavior depends criti-cally on expectations of the futurecourse of monetary policy, as well as oncurrent policy. In addition, the modelaccommodates differing views abouthow the macroeconomy behaves. In thelimiting case of perfect price flexibility,for example, the cyclical dynamics re-semble those of a real business cyclemodel, with monetary policy affectingonly nominal variables.

Rather than work through the detailsof the derivation, which are readilyavailable elsewhere, we instead directlyintroduce the key aggregate relation-ships.9 For convenience, we abstractfrom investment and capital accumula-tion. This abstraction, however, doesnot affect any qualitative conclusions, aswe discuss. The model is as follows:

Let yt and zt be the stochastic compo-nents of output and the natural level ofoutput, respectively, both in logs.10 Thelatter is the level of output that wouldarise if wages and prices were perfectlyflexible. The difference between actualand potential output is an important vari-able in the model. It is thus convenientto define the “output gap” xt:

xt ≡ yt − zt

In addition, let πt be the period t infla-tion rate, defined as the percent changein the price level from t–1 to t; and let itbe the nominal interest rate. Each vari-able is similarly expressed as a deviationfrom its long-run level.

It is then possible to represent thebaseline model in terms of two equa-tions: an “IS” curve that relates the out-put gap inversely to the real interestrate; and a Phillips curve that relatesinflation positively to the output gap.

xt = − ϕ[it − Etπt + 1] + Etxt + 1 + gt (2.1)

πt = λxt + βEtπt + 1 + ut (2.2)where gt and ut are disturbances termsthat obey, respectively:

gt = µgt − 1 + gt (2.3)

ut = ρut − 1 + ut (2.4)where 0 ≤ µ,ρ ≤ 1 and where both gt andut are i.i.d. random variables with zero meanand variances σg2 and σu2, respectively.

Equation (2.1) is obtained by log-linearizing the consumption euler equa-tion that arises from the household’soptimal saving decision, after imposingthe equilibrium condition that con-sumption equals output minus govern-ment spending.11 The resulting expres-sion differs from the traditional IScurve mainly because current outputdepends on expected future output aswell as the interest rate. Higher ex-pected future output raises current out-put: Because individuals prefer to

9 See, for example, Yun (1996), Kimball (1995),King and Wolman (1995), Woodford (1996), andBernanke, Gertler, and Gilchrist (1998) for step-by-step derivations.

10 By stochastic component, we mean the devia-tion from a deterministic long-run trend.

11 Using the market clearing condition Yt = Ct + Et,where Et is government consumption, we can re-write the log-linearized consumption Euler equa-tion as:

yt − et = − ϕ[it − Etπt + 1] + Etyt + 1 − et + 1

where et ≡ − log(1 − Et

Yt) is taken to evolve ex-

ogenously. Using xt ≡ yt − zt, it is then possible toderive the demand for output as

xt = − ϕ[it − Etπt + 1] + Etxt + 1 + gt

where gt = Et∆zt + 1 − ∆et + 1.


smooth consumption, expectation ofhigher consumption next period (associ-ated with higher expected output) leadsthem to want to consume more today,which raises current output demand.The negative effect of the real rate oncurrent output, in turn, reflects in-tertemporal substitution of consump-tion. In this respect, the interest elastic-ity in the IS curve, ϕ, corresponds tothe intertemporal elasticity of substitu-tion. The disturbance gt is a function ofexpected changes in government pur-chases relative to expected changes inpotential output (see footnote 11).Since gt shifts the IS curve, it is inter-pretable as a demand shock. Finally, add-ing investment and capital to the modelchanges the details of equation (2.1).But it does not change the fundamentalqualitative aspects: output demand stilldepends inversely on the real rate andpositively on expected future output.

It is instructive to iterate equation(2.1) forward to obtain

xt = Et∑ i = 0

∞ − ϕ[it + i − πt + 1 + i] + gt + i (2.5)

Equation (2.5) makes transparent thedegree to which beliefs about the futureaffect current aggregate activity withinthis framework. The output gap de-pends not only on the current real rateand the demand shock, but also on theexpected future paths of these twovariables. To the extent monetary policyhas leverage over the short-term realrate due to nominal rigidities, equation(2.5) suggests that expected as well ascurrent policy actions affect aggregatedemand.

The Phillips curve, (2.2), evolvesfrom staggered nominal price setting, inthe spirit of Stanley Fischer (1977) and

John Taylor (1980).12 A key differenceis that the individual firm price-settingdecision, which provides the basis forthe aggregate relation, is derived froman explicit optimization problem. Thestarting point is an environment withmonopolistically competitive firms: Whenit has the opportunity, each firmchooses its nominal price to maximizeprofits subject to constraints on thefrequency of future price adjustments.

Under the standard scenario, each pe-riod the fraction 1/X of firms set pricesfor X > 1 periods. In general, however,aggregating the decision rules of firmsthat are setting prices on a staggeredbasis is cumbersome. For this reason,underlying the specific derivation ofequation (2.2) is an assumption due toGuillermo Calvo (1983) that greatlysimplifies the problem: In any given pe-riod a firm has a fixed probability θ itmust keep its price fixed during that pe-riod and, hence a probability 1 – θ thatit may adjust.13 This probability, fur-ther, is independent of the time thathas elapsed since the last time the firmchanged price. Accordingly, the averagetime over which a price is fixed is 1

1 − θ.Thus, for example, if θ = .75, prices arefixed on average for a year. The Calvoformulation thus captures the spirit ofstaggered setting, but facilitates the ag-gregation by making the timing of afirm’s price adjustment independent ofits history.

Equation (2.2) is simply a loglinearapproximation about the steady state ofthe aggregation of the individual firmpricing decisions. Since the equation re-lates the inflation rate to the output gapand expected inflation, it has the flavorof a traditional expectations-augmentedPhillips curve (see, e.g., Olivier Blanchard

12 See Galí and Gertler (1998) and Sbordone(1998) for some empirical support for this kind ofPhillips curve relation.

13 The Calvo formulation has become quitecommon in the literature. Work by Yun (1996),King and Wolman (1995), Woodford (1996) andothers has initiated the revival.


1997). A key difference with the stan-dard Phillips curve is that expected fu-ture inflation, Etπt + 1, enters additively,as opposed to expected current infla-tion, Et − 1πt.14 The implications of thisdistinction are critical: To see, iterate(2.2) forward to obtain

πt = Et∑ i = 0

∞βi[λ xt + i + ut + i] (2.6)

In contrast to the traditional Phillipscurve, there is no arbitrary inertia orlagged dependence in inflation. Rather,inflation depends entirely on currentand expected future economic condi-tions. Roughly speaking, firms set nomi-nal price based on the expectations offuture marginal costs. The variable xt + i

captures movements in marginal costsassociated with variation in excess de-mand. The shock ut + i, which we refer toas “cost push,” captures anything else thatmight affect expected marginal costs.15

We allow for the cost push shock to en-able the model to generate variation ininflation that arises independently ofmovement in excess demand, as appearspresent in the data (see, e.g., Fuhrerand Moore 1995).

To close the model, we take thenominal interest rate as the instrumentof monetary policy, as opposed to amoney supply aggregate. As Bernankeand Ilian Mihov (1998) show, this as-sumption provides a reasonable descrip-tion of Federal Reserve operating pro-cedures since 1965, except for the briefperiod of non-borrowed reserves target-ing (1980–82) under Paul Volcker.16

With the nominal rate as the policy in-strument, it is not necessary to specify amoney market equilibrium condition(i.e., an LM curve).17 In section 5, wediscuss the implications of using insteada narrow monetary aggregate as thepolicy instrument.

Though simple, the model has thesame qualitative core features as more

14 Another key difference is that the explicitderivation restricts the coefficient λ on the outputgap. In particular, λ is decreasing in θ, which mea-sures the degree of price rigidity. Thus, the longerprices are fixed on average, the less sensitive isinflation to movements in the output gap.

15 The relation for inflation that evolves fromthe Calvo model takes the form

πt = βEtπt + 1 + δ mct

where mct denotes the deviation of (real) marginalcost from its steady state value. To then relate in-flation to the output gap, the literature typicallymakes assumptions on technology, preferences,and the structure of labor markets to justify a pro-portionate relation between real marginal cost andthe output gap, so that mct = κ xt holds, where κ isthe output elasticity of real marginal cost. In thisinstance, one can rewrite the relation for inflationin terms of the output gap, as follows:πt = βEtπt + 1 + λ xt (see Galí and Gertler (1998)for details). In this context, the disturbance ut in(2.2) is interpretable as reflecting deviations fromthe condition mct = κ xt. (Indeed the evidence inGalí and Gertler 1998 suggests that mct does notvary proportionately with xt). Deviations from thisproportionality condition could be caused, for ex-ample, by movements in nominal wages that pushreal wages away from their “equilibrium” valuesdue to frictions in the wage contracting process.

On this latter point, see Erceg, Henderson, andLevin (1998). Another interpretation of the ut shock(suggested by Mike Woodford) is that it could re-flect a shock to the gap between the natural andpotential levels of output (e.g., a markup shock).

16 Roughly speaking, Bernanke and Mihov(1998) present formal evidence showing that theFederal Reserve intervenes in the market for non-borrowed bank reserves to support its choice forthe level of the Federal Funds rate, the overnightmarket for bank reserves. (Christiano, Eichen-baum, and Evans 1998, though, take issue with theidentifying assumptions in the Bernanke-Mihovtest). Informally, Federal Reserve policy actions inrecent years routinely take the form of announcinga target for the Federal funds rate (see, e.g, Rude-busch 1995). Policy discussions, further, focus onwhether to adjust that target, and by how much.In this context, the view that the Funds rate is thepolicy instrument is widely held by both practitio-ners of monetary policy and academic researchers(see, e.g., Goodfriend 1991, Taylor 1993, andWalsh 1998).

17 With the interest rate as the policy instru-ment, the central bank adjusts the money supplyto hit the interest rate target. In this instance, thecondition that money demand equal money supplysimply determines the value of the money supplythat meets this criteria.


complex, empirically based frameworksthat are used for policy analysis.18 As inthese applied frameworks, temporarynominal price rigidities play a criticalrole. With nominal rigidities present, byvarying the nominal rate, monetary pol-icy can effectively change the short-term real rate. Through this classicmechanism it gains leverage over thenear term course of the real economy.In contrast to the traditional mecha-nism, though, beliefs about how thecentral bank will set the interest rate inthe future also matter, since bothhouseholds and firms are forward look-ing. In this kind of environment, howmonetary policy should respond in theshort run to disturbances that buffet theeconomy is a nontrivial decision. Re-solving this issue is the essence of thecontemporary debate over monetarypolicy.

2.2 The Policy Objective

The central bank objective functiontranslates the behavior of the targetvariables into a welfare measure toguide the policy choice. We assume,following much of the literature, thatthis objective function is over the tar-get variables xt and πt, and takes theform:

max − 12 Et

∑ i = 0

∞βi[α xt + i

2 + πt + i2 ]

(2.7)

where the parameter α is the relativeweight on output deviations. Sincext ≡ yt − zt, the loss function takes poten-tial output zt as the target. It also implic-itly takes zero as the target inflation, butthere is no cost in terms of generality

since inflation is expressed as a percentdeviation from trend.19

While there has been considerableprogress in motivating behavioral mac-roeconomic models from first princi-ples, until very recently, the same hasnot been true about rationalizing theobjectives of policy. Over the past sev-eral years, there have been a number ofattempts to be completely coherent informulating the policy problem bytaking as the welfare criterion the util-ity of a representative agent within themodel.20

One limitation of this approach, how-ever, is that the models that are cur-rently available do not seem to capturewhat many would argue is a major costof inflation, the uncertainty that its vari-ability generates for lifetime financialplanning and for business planning (see,e.g., Brad DeLong 1997).21 Another is-sue is that, while the widely used repre-sentative agent approach may be a rea-sonable way to motivate behavioralrelationships, it could be highly mis-leading as a guide to welfare analysis. Ifsome groups suffer more in recessionsthan others (e.g. steel workers versusprofessors) and there are incomplete in-surance and credit markets, then theutility of a hypothetical representativeagent might not provide an accuratebarometer of cyclical fluctuations inwelfare.

With certain exceptions, much of the

18 Some prominent examples include the re-cently renovated large scale model used by theFederal Reserve Board, the FRB-US model (seeBrayton, Levin, Tyron, and Williams 1997), andthe medium scale models of Taylor (1979, 1993b)and Fuhrer and Moore (1995a,b).

19 Put differently, under the optimal policy, thetarget inflation rate pins down the trend inflationrate. The loss function thus penalizes deviationsfrom this trend.

20 Some examples of this approach include Aiya-gari and Braun (1997), King and Wolman (1995),Ireland (1996a), Carlstrom and Fuerst (1995), andRotemberg and Woodford (1997).

21 Underlying this kind of cost is the observationthat contracts are typically written in nominalterms and, for reasons that are difficult to explain,not perfectly indexed to the price level. On thisissue, see the discussion in Shiller (1997) and theassociated comment by Hall (1997).


literature takes a pragmatic approach tothis issue by simply assuming that theobjective of monetary policy is to mini-mize the squared deviations of outputand inflation from their respective tar-get levels. However, Julio Rotembergand Michael Woodford (1999) andWoodford (1998) provide a formal justi-fication for this approach. Theseauthors show that an objective functionlooking something like equation (2.7)may be obtained as a quadratic approxi-mation of the utility-based welfarefunction. In this instance, the relativeweight, α , is a function of the primitiveparameters of the model.

In what follows, we simply adopt thequadratic objective given by (2.7), ap-pealing loosely to the justification of-fered in Rotemberg and Woodford(1999). Judging by the number of pa-pers written by Federal Reserve econo-mists that follow this lead, this formula-tion does not seem out of sync with theway monetary policy operates in prac-tice (at least implicitly).22 The targetlevel of output is typically taken to bethe natural level of output, based on theidea that this is the level of output thatwould obtain absent any wage and pricefrictions. Yet, if distortions exist in theeconomy (e.g., imperfect competitionor taxes), a case can be made that thewelfare maximizing level of output mayexceed its natural level. This issue be-comes important in the context ofpolicy credibility, but we defer it fornow.

What should be the target rate of in-flation is perhaps an even more ephem-eral question, as is the issue of whatshould be the relative weight assignedto output and inflation losses. In theU.S., policy-makers argue that “pricestability” should be the ultimate goal.

But they define price stability as the in-flation rate at which inflation is nolonger a public concern. In practice, itis argued that an inflation rate betweenone and three percent seems to meetthis definition (e.g., Bernanke andMishkin 1997). A further justificationfor this criteria is that the official priceindices may be overstating the true in-flation rate by a percent or two, as ar-gued recently by the Boskin Commis-sion. In this regard, interestingly, theBundesbank has had for a long time anofficial inflation target of two percent.23

They similarly argue that this positiverate of inflation is consistent with pricestability, and cite measurement error asone of the reasons (Clarida and Gertler1997).

It is clear that the experience of the1970s awakened policy-makers to thecosts of high inflation (DeLong 1997).Otherwise, there is no directly observ-able indicator of the relative weights as-signed to output and inflation objec-tives. Nor, argues Blinder (1997), isthere any obvious consensus among pol-icy-makers about what these weights re-ally are in practice. It is true that therehas been a growing consensus that theprimary aim of monetary policy shouldbe to control inflation (see, e.g., Ber-nanke and Mishkin 1997). But this dis-cussion in many respects is about whatkind of policy rule may be best, as op-posed to what the underlying welfarefunction looks like.

For our purposes, however, it is rea-sonable to take the inflation target andpreference parameters as given andsimply explore the implications foroptimal policy rules.

22 See, for example, Williams (1997) and refer-ences therein.

23 Two percent is also the upper bound of theinflation target range established by the EuropeanCentral Bank. On the other hand, Feldstein (1997)argues that the tax distortions that arise becausecorporate and personal income taxes are not in-dexed to inflation justify moving from three per-cent to zero inflation.


2.3 The Policy Problem and Discretion versus Rules

The policy problem is to choose atime path for the instrument it to engi-neer time paths of the target variablesxt and πt that maximize the objectivefunction (2.7), subject to the constraintson behavior implied by (2.1) and (2.2).This formulation is in many ways in thetradition of the classic Jan Tinbergen(1952)/Henri Theil (1961) (TT) targetsand instruments problem. As with TT,the combination of quadratic loss andlinear constraints yields a certaintyequivalent decision rule for the path ofthe instrument. The optimal feedbackrule, in general, relates the instrumentto the state of the economy.

There is, however, an important dif-ference from the classic problem: Thetarget variables depend not only on thecurrent policy but also on expectationsabout future policy: The output gap de-pends on the future path of the interestrate (equation 2.5); and, in turn, inflationdepends on the current and expectedfuture behavior of the output gap(equation 2.6). As Finn Kydland andEdward Prescott (1977) originally em-phasized, in this kind of environment,credibility of future policy intentionsbecomes a critical issue. For example, acentral bank that can credibly signal itsintent to maintain inflation low in thefuture may be able to reduce currentinflation with less cost in terms of out-put reduction than might otherwise berequired.24 In section 4, we illustratethis point explicitly.

From the standpoint of policy design,the issue is to identify whether sometype of credibility-enhancing commit-ment may be desirable. Answering thisquestion boils down to comparing opti-mal policy under discretion versus rules(using the terminology of the litera-ture). In our context, a central bank op-erating under discretion chooses thecurrent interest rate by reoptimizingevery period. Any promises made in thepast do not constrain current policy.Under a rule, it chooses a plan for thepath of the interest rates that it sticks toforever. The plan may call for adjustingthe interest rate in response to the stateof the economy, but both the natureand size of the response are etched instone.

Two points need to be emphasized.First, the key distinction between dis-cretion and rules is whether currentcommitments constrain the futurecourse of policy in any credible way. Ineach instance, the optimal outcome is afeedback policy that relates the policyinstrument to the current state of theeconomy in a very specific way. The twoapproaches differ, however, in their im-plications for the link between policyintentions and private sector beliefs.Under discretion, a perceptive privatesector forms its expectations taking intoaccount how the central bank adjustspolicy, given that the central bank isfree to reoptimize every period. The ra-tional expectations equilibrium thus hasthe property that the central bank hasno incentive to change its plans in anunexpected way, even though it has thediscretion to do so. (For this reason, thepolicy that emerges in equilibrium underdiscretion is termed “time consistent.”)In contrast, under a rule, it is simply

24 In this regard, we stress further that, incontrast to conventional wisdom, the issue ofcredibility in monetary policy is not tied to centralbank objectives over output. In the classic,Barro/Gordon (1983) formulation (and countlesspapers thereafter), the central bank’s desire topush output above potential output gives rise tothe credibility problem. However, as we makeclear in section 4, gains from commitment poten-tially emerge whenever private sector behavior

depends on beliefs about the future, even if cen-tral bank objectives over output are perfectlyaligned.


the binding commitment that makes thepolicy believable in equilibrium.

Second, (it should almost go withoutsaying that) the models we use are no-where near the point where it is possi-ble to obtain a tightly specified policyrule that could be recommended forpractical use with great confidence.Nonetheless, it is useful to workthrough the cases of discretion andrules in order to develop a set of norma-tive guidelines for policy behavior. AsTaylor (1993a) argues, common senseapplication of these guidelines may im-prove the performance of monetary pol-icy. We expand on this point later. Inaddition, understanding the qualitativedifferences between outcomes underdiscretion versus rules can provide les-sons for the institutional design ofmonetary policy. For example, as wediscuss, Rogoff’s (1985) insightfulanalysis of the benefits of a conservativecentral bank chair is a product of thistype of analysis. Finally, simply under-standing the qualitative aspects of opti-mal policy management under discre-tion can provide useful normativeinsights, as we show shortly.

We proceed in the next section to de-rive the optimal policy under discretion.In a subsequent section we then evaluatethe implications of commitment.

3. Optimal Monetary Policy withoutCommitment

We begin with the case without com-mitment (“discretion”) for two reasons.First, at a basic level this scenario ac-cords best with reality. In practice, nomajor central bank makes any kind ofbinding commitment over the course ofits future monetary policy. In this re-spect, it seems paramount to under-stand the nature of optimal policy inthis environment. Second, as we havejust discussed, to fully comprehend the

possible gains from commitment to apolicy rule and other institutional de-vices that might enhance credibility, itis necessary to understand what thebenchmark case of discretion yields.

Under discretion, each period thecentral bank chooses the triplet xt,πt,it,consisting of the two target variablesand the policy instrument, to maximizethe objective (2.7) subject to the aggre-gate supply curve (2.2) and the IScurve, (2.1). It is convenient to dividethe problem into two stages: First, thecentral bank chooses xt and πt to maxi-mize the objective (2.7), given the infla-tion equation (2.2).25 Then, conditionalon the optimal values of xt and πt, it de-termines the value of it implied by theIS curve (2.1) (i.e., the interest ratethat will support xt and πt).

Since it cannot credibly manipulatebeliefs in the absence of commitment,the central bank takes private sectorexpectations as given in solving theoptimization problem.26 (Then, condi-tional on the central bank’s optimalrule, the private sector forms beliefs ra-tionally.) Because there are no en-dogenous state variables, the first stageof the policy problem reduces to the fol-lowing sequence of static optimization

25 Since all the qualitative results we derivestem mainly from the first stage problem, what iscritical is the nature of the short run Phillipscurve. For our baseline analysis, we use the Phil-lips curve implied the New Keynesian model. Insection 6 we consider a very general Phillips curvethat is a hybrid of different approaches and showthat the qualitative results remain intact. It is inthis sense that our analysis is quite robust.

26 We are ignoring the possibility of reputationalequilibria that could support a more efficient out-come. That is, in the language of game theory, werestrict attention to Markov perfect equilibria.One issue that arises with reputational equilibria isthat there are multiplicity of possible equilibria.Rogoff (1987) argues that the fragility of the re-sulting equilibria is an unsatisfactory feature ofthis approach. See also, Ireland (1996b). On theother hand, Chari, Christiano, and Eichenbaum(1998) argue that this indeterminacy could providea source of business fluctuations.


problems:27 Each period, choose xt andπt to maximize

− 12 [α xt

2 + πt2] + Ft (3.1)

subject toπt = λxt + ft (3.2)

taking as given Ft and ft, where

Ft ≡ − 12 Et

∑ i = 1

∞βi[α xt + i

2 + πt + i2 ]

and

ft ≡ βEtπt + 1 + ut. Equations (3.1) and(3.2) simply reformulate (2.7) and (2.2)in a way that makes transparent that, un-der discretion, (a) future inflation andoutput are not affected by today’s ac-tions, and (b) the central bank cannotdirectly manipulate expectations.

The solution to the first stage prob-lem yields the following optimalitycondition:

xt = − λα πt (3.3)

This condition implies simply that thecentral bank pursue a “lean against thewind” policy: Whenever inflation isabove target, contract demand below ca-pacity (by raising the interest rate); andvice-versa when it is below target. Howaggressively the central bank should re-duce xt depends positively on the gain inreduced inflation per unit of output loss,λ, and inversely on the relative weightplaced on output losses, α .

To obtain reduced form expressionsfor xt and πt, combine the optimalitycondition (fonc) with the aggregate sup-ply curve (AS ), and then impose thatprivate sector expectations are rational:

xt = − λq ut (3.4)

πt = αq ut (3.5)where

q = 1

λ2 + α(1 − βρ)

The optimal feedback policy for the in-terest rate is then found by simply in-serting the desired value of xt in the IScurve (2.1):

it = γπ Etπt + 1 + 1ϕ gt (3.6)

where

γπ = 1 + (1−ρ)λ

ρϕα > 1

Etπt + 1 = ρ πt = ραq ut

This completes the formal description ofthe optimal policy.

From this relatively parsimonious setof expressions there emerge a numberof key results that are reasonably robustfindings of the literature:

Result 1: To the extent cost push in-flation is present, there exists a shortrun trade-off between inflation andoutput variability.

This result was originally emphasizedby Taylor (1979) and is an importantguiding principle in many applied stud-ies of monetary policy that have fol-lowed.28 A useful way to illustrate thetrade-off implied by the model is toconstruct the corresponding efficientpolicy frontier. The device is a locus ofpoints that characterize how the uncon-ditional standard deviations of outputand inflation under the optimal policy,σx and σπ, vary with central bank prefer-ences, as defined by α . Figure 1 por-trays the efficient policy frontier for our

27 In section 6, we solve for the optimum underdiscretion for the case where an endogenous statevariable is present. Within the Markov perfectequilibrium, the central bank takes private sectorbeliefs as a given function of the endogenousstate.

28 For some recent examples, see Williams(1997), Fuhrer (1997a) and Orphanides, Small,Wilcox and Wieland (1997). An exception, how-ever, is Jovanovic and Ueda (1997) who demon-strate that in an environment of incomplete con-tracting, increased dispersion of prices may reduceoutput. Stabilizing prices in this environment thenraises output.


baseline model.29 In (σx,σπ) space thelocus is downward sloping and convexto the origin. Points to the right of thefrontier are inefficient. Points to theleft are infeasible. Along the frontierthere is a trade-off: As α rises (indicat-ing relatively greater preference foroutput stability), the optimal policy en-gineers a lower standard deviation ofoutput, but at the expense of higher in-flation volatility. The limiting cases areinstructive:

As α → 0: σx = σu

λ; σπ = 0 (3.7)

As α → ∞: σx = 0; σπ = σu

1 − βρ (3.8)

where σu is the standard deviation of thecost push innovation.

It is important to emphasize that thetrade-off emerges only if cost push in-flation is present. In the absence of costinflation (i.e., with σu = 0), there is notrade-off. In this instance, inflation de-

pends only on current and future de-mand. By adjusting interest rates to setxt = 0, ∀ t, the central bank is able to hitits inflation and output targets simulta-neously, all the time. If cost push fac-tors drive inflation, however, it is onlypossible to reduce inflation in the nearterm by contracting demand. Thisconsideration leads to the next result:

Result 2: The optimal policy incorpo-rates inflation targeting in the sensethat it requires to aim for convergenceof inflation to its target over time. Ex-treme inflation targeting, however, i.e.,adjusting policy to immediately reachan inflation target, is optimal underonly one of two circumstances: (1) costpush inflation is absent; or (2) there isno concern for output deviations (i.e.,α = 0).

In the general case, with α > 0 andσu > 0, there is gradual convergence ofinflation back to target. From equations(3.5) and (2.4), under the optimal policy

limi → ∞

Etπt + i = limi → ∞

αqρi ut = 029 Equations (3.4) and (3.5) define the frontierfor the baseline model.


In this formal sense, the optimal pol-icy embeds inflation targeting.30 Withexogenous cost push inflation, policy af-fects the gap between inflation and itstarget along the convergent path, butnot the rate of convergence. In con-trast, in the presence of endogenous in-flation persistence, policy will generallyaffect the rate of convergence as well,as we discuss later.

The conditions for extreme inflationtargeting can be seen immediately frominspection of equations (3.7) and (3.8).When σu = 0 (no cost push inflation),adjusting policy to immediately hit theinflation target is optimal, regardless ofpreferences. Since there is no trade-offin this case, it is never costly to try tominimize inflation variability. Inflationbeing the only concern of policy pro-vides the other rationale for extreme in-flation targeting. As equation (3.7) indi-cates, it is optimal to minimize inflationvariance if α = 0, even with cost pushinflation present.

Result 2 illustrates why some con-flicting views about the optimal transi-tion path to the inflation target haveemerged in the literature. MarvinGoodfriend and Robert King (1997), forexample, argue in favor of extreme in-flation targeting. Svensson (1997a,b)and Laurence Ball (1997) suggest that,in general, gradual convergence of in-flation is optimal. The difference stemsfrom the treatment of cost push infla-tion: It is absent in the Goodfriend-King paradigm, but very much a factorin the Svensson and Ball frameworks.

Results 1 and 2 pertain to the behav-ior of the target variables. We now state

several results regarding the behavior ofthe policy instrument, it.

Result 3: Under the optimal policy,in response to a rise in expected infla-tion, nominal rates should rise suffi-ciently to increase real rates. Put differ-ently, in the optimal rule for thenominal rate, the coefficient on expectedinflation should exceed unity.

Result 3 is transparent from equation(3.6). It simply reflects the implicit tar-geting feature of optimal policy de-scribed in Result 2. Whenever inflationis above target, the optimal policy re-quires raising real rates to contract de-mand. Though this principle may seemobvious, it provides a very simple crite-ria for evaluating monetary policy. Forexample, Clarida, Galí, and Gertler (forth-coming) find that U.S. monetary policyin the pre-Volcker era of 1960–79 vio-lated this strategy. Federal Reserve pol-icy tended to accommodate rather thanfight increases in expected inflation.Nominal rates adjusted, but not suffi-ciently to raise real rates. The persis-tent high inflation during this era mayhave been the end product of the fail-ure to raise real rates under these cir-cumstances. Since 1979, however, theFederal Reserve appears to have adoptedthe kind of implicit inflation targetingstrategy that equation (3.6) suggests.Over this period, the Fed has systemati-cally raised real rates in response to an-ticipated increases in inflationary ex-pectations. We return to this issue later.

Result 4: The optimal policy calls foradjusting the interest rate to perfectly off-set demand shocks, gt, but perfectly ac-commodate shocks to potential output, zt,by keeping the nominal rate constant.

That policy should offset demandshocks is transparent from the policyrule (3.6). Here the simple idea is thatcountering demand shocks pushes bothoutput and inflation in the right direc-tion. Demand shocks do not force a

30 Note here that our definition is somewhatdifferent from Svensson (1997a), who definesinflation targeting in terms of the weights on theobjective function, i.e., he defines the case withα = 0 as corresponding to strict inflation targetingand α > 0 as corresponding to flexible inflationtargeting.


short run trade-off between output andinflation.

Shocks to potential output also do notforce a short run trade-off. But they re-quire a quite different policy response.Thus, e.g., a permanent rise in produc-tivity raises potential output, but it alsoraises output demand in a perfectly off-setting manner, due to the impact onpermanent income.31 As a consequence,the output gap does not change. Inturn, there is no change in inflation.Thus, there is no reason to raise inter-est rates, despite the rise in output.32

Indeed, this kind of scenario seems todescribe well the current behavior ofmonetary policy. Output growth wassubstantially above trend in recent times,but with no apparent accompanying in-flation.33 Based on the view that the risein output may mainly reflect productivitymovements, the Federal Reserve hasresisted large interest rate increases.

The central message of Result 4 isthat an important task of monetary pol-icy is to distinguish the sources ofbusiness cycle shocks. In the simpleenvironment here with perfect ob-servability, this task is easy. Later weexplore some implications of relaxingthis assumption.

4. Credibility and the Gains from Commitment

Since the pioneering work of Kydlandand Prescott (1977), Robert Barro and

David Gordon (1983), and Rogoff(1985), a voluminous literature has de-veloped on the issue of credibility ofmonetary policy.34 From the standpointof obtaining practical insights for pol-icy, we find it useful to divide the pa-pers into two strands. The first followsdirectly from the seminal papers andhas received by far the most attentionin academic circles. It emphasizes theproblem of persistent inflationary biasunder discretion.35 The ultimate sourceof this inflationary bias is a central bankthat desires to push output above itsnatural level. The second is emphasizedmore in applied discussions of policy. Itfocuses on the idea that disinflating aneconomy may be more painful than nec-essary, if monetary policy is perceivedas not devoted to fighting inflation.Here the source of the problem issimply that wage and price settingtoday may depend upon beliefs aboutwhere prices are headed in the future,which in turn depends on the course ofmonetary policy.

These two issues are similar in asense: They both suggest that a centralbank that can establish credibility oneway or another may be able to reduceinflation at lower cost. But the sourceof the problem in each case is differentin subtle but important ways. As aconsequence the potential empiricalrelevance may differ, as we discussbelow.

We first use our model to exposit thefamous inflationary bias result. We thenillustrate formally how credibility canreduce the cost of maintaining low in-flation, and also discuss mechanisms in

31 In this experiment we are holding constantthe IS shock gt. Since gt = [(et − zt) − Et(et + 1 − zt + 1)],(see footnote 9), this boils down to assumingeither that the shock to zt is permanent (so thatEtzt + 1 − zt = 0) or that et adjusts in a way to offsetmovements in gt.

32 That monetary policy should accommodatemovements in potential GDP is a theme of therecent literature (e.g., Aiyagari and Braun 1997;Carlstrom and Fuerst 1995; Ireland 1996a; andRotemberg and Woodford 1997). This view wasalso stressed in much earlier literature. See Fried-man and Kuttner (1996) for a review.

33 See Lown and Rich (1997) for a discussion ofthe recent “inflation puzzle.”

34 For recent surveys of the literature, see Fis-cher (1995), McCallum (1997) and Persson andTabellini (1997).

35 While the inflationary bias result is bestknown example, there may also be other costs ofdiscretion. Svennson (1997c), for example, arguesalso that discretion may lead to too much inflationvariability and too little output variability.


the literature that have been suggestedto inject this credibility. An importantresult we wish to stress—and one thatwe don’t think is widely understood inthe literature—is that gains from credi-bility emerge even when the centralbank is not trying to push output aboveits natural level.36 That is, as long asprice setting depends on expectations ofthe future, as in our baseline model,there may be gains from establishingsome form of credibility to curtail infla-tion. Further, under certain plausiblerestrictions on the form of the feedbackrule, the optimal policy under commit-ment differs from that under discretionin a very simple and intuitive way. Inthis case, the solution with commitmentresembles that obtained under discre-tion using a higher effective cost ap-plied to inflation than the social welfarefunction suggests.37 In this respect, wethink, the credibility literature may havesome broad practical insights to offer.

4.1 The Classic Inflationary Bias Problem

As in Kydland and Prescott (1979),Barro and Gordon (1983), and manyother papers, we consider the possibil-ity that the target for the output gapmay be k > 0, as opposed to 0. The policyobjective function is then given by

max − 12 Et

∑ i = o

∞βi[α(xt + i − k)2 + πt + i

2 ]

(4.1)

The rationale for having the socially opti-mal level of output exceed its naturallevel may be the presence of distortionssuch as imperfect competition or taxes.For convenience, we also assume thatprice setters do not discount the future,which permits us to fix the parameter βin the Phillips curve at unity.38

In this case, the optimality condi-tion that links the target variables isgiven by:

xtk = −

λα πt

k + k (4.2)

The superscript k indicates the variableis the solution under discretion for thecase k > 0. Plugging this condition intothe IS and Phillips curves, (2.1) and(2.2), yields:

xtk = xt (4.3)

πtk = πt +

αλ k (4.4)

where xt and πt are the equilibrium val-ues of the target variables for the base-line case with k = 0 (see equations 3.4and 3.5).

Note that output is no different fromthe baseline case, but that inflation issystematically higher, by the factor α

λ k.Thus, we have the familiar result in theliterature:

Result 5. If the central bank desiresto push output above potential (i.e.,k > 0), then under discretion a subopti-mal equilibrium may emerge with infla-tion persistently above target, and nogain in output.

The model we use to illustrate this

36 A number of papers have shown that a disin-flation will be less painful if the private sector per-ceives that the central bank will carry it out. Butthey do not show formally that, under discretion,the central bank will be less inclined to do so(see., e.g. Ball 1995, and Bonfim and Rudebusch1997).

37 With inflationary bias present, it is also possi-ble to improve welfare by assigning a higher costto inflation, as Rogoff (1985) originally empha-sized. But it is not always possible to obtain theoptimum under commitment. The point we em-phasize is that with inflationary bias absent, it ispossible to replicate the solution under commit-ment (for a restricted family of policy rules) usingthe algorithm to solve for the optimum under dis-cretion with an appropriately chosen relative costof inflation. We elaborate on these issues later inthe text.

38 Otherwise, the discounting of the future byprice-setters introduces a long-run trade-off be-tween inflation and output. Under reasonable pa-rameter values this tradeoff is small and its pres-ence merely serves to complicate the algebra. SeeGoodfriend and King (1997) for a discussion.


result differs from the simple expecta-tional Phillips curve framework inwhich it has been typically studied. Butthe intuition remains the same. In thisinstance, the central bank has the in-centive to announce that it will betough in the future to lower current in-flation (since in this case, current infla-tion depends on expected future infla-tion), but then expand current demandto push output above potential. Thepresence of k in the optimality condi-tion (4.2) reflects this temptation. A ra-tional private sector, however, recog-nizes the central bank’s incentive. Inmechanical terms, it makes use of equa-tion (4.2) to forecast inflation, since thiscondition reflects the central bank’strue intentions. Put simply, equilibriuminflation rises to the point where thecentral bank no longer is tempted to ex-pand output. Because there is no long-run trade-off between inflation and out-put (i.e., xt converges to zero in thelong run, regardless of the level of infla-tion), long-run equilibrium inflation isforced systematically above target.

The analysis has both important posi-tive and normative implications. On thepositive side, the theory provides an ex-planation for why inflation may remainpersistently high, as was the case fromthe late 1960s through the early 1980s.Indeed, its ability to provide a qualita-tive account of this inflationary era is amajor reason for its popularity.

The widely stressed normative impli-cation of this analysis is that there maybe gains from making binding commit-ments over the course of monetary pol-icy or, alternatively, making institu-tional adjustments that accomplish thesame purpose. A clear example from theanalysis is that welfare would improve ifthe central bank could simply committo acting as if k were zero. There wouldbe no change in the path of output, butinflation would decline.

Imposing binding commitments in amodel, however, is much easier than do-ing so in reality. The issue then becomeswhether there may be some simple in-stitutional mechanisms that can approxi-mate the effect of the idealized policycommitment. Perhaps the most usefulanswer to the question comes from Rogoff(1985), who proposed simply the appoint-ment of a “conservative” central banker,taken in this context to mean someonewith a greater distaste for inflation (alower α), than society as a whole:

Result 6: Appointing a central bankchair who assigns a higher relative costto inflation than society as a whole re-duces the inefficient inflationary bias thatis obtained under discretion when k > 0.

One can see plainly from equation(4.4) that letting someone with prefer-ences given by αR < α run the centralbank will reduce the inflationary bias.39

The Rogoff solution, however, is not apanacea. We know from the earlieranalysis that emphasizing greater reduc-tion in inflation variance may come atthe cost of increased output variance.Appointing an extremist to the job(someone with α at or near zero) couldwind up reducing overall welfare.

How important the inflationary biasproblem emphasized in this literature isin practice, however, is a matter of con-troversy. Benjamin Friedman and Ken-neth Kuttner (1996) point out that in-flation in the major OECD countriesnow appears well under control, despitethe absence of any obvious institutionalchanges that this literature argues areneeded to enhance credibility. If thistheory is robust, they argue, it shouldaccount not only for the high inflationof the 1960s and 1970s, but also for the

39 See Svensson (1997) and Walsh (1998) for adescription of how incentive contracts for centralbankers may reduce the inflation bias; also, Faustand Svensson (1998) for a recent discussion ofreputational mechanisms.


transition to an era of low inflation dur-ing the 1980s and 1990s. A possiblecounterargument is that in fact a num-ber of countries, including the U.S., ef-fectively adopted the Rogoff solution byappointing central bank chairs withclear distaste for inflation.

Another strand of criticism focuseson the plausibility of the underlyingstory that leads to the inflationary bias.A number of prominent authors haveargued that, in practice, it is unlikelythat k > 0 will tempt a central bank tocheat. Any rational central bank, theymaintain, will recognize the long-termcosts of misleading the public to pursueshort-term gains from pushing outputabove its natural level. Simply this rec-ognition, they argue, is sufficient toconstrain its behavior (e.g. McCallum1997a; Blinder 1997). Indeed, Blinderargues, based on his own experience onthe Federal Reserve Board, that therewas no constituency in favor of pursuingoutput gains above the natural rate. Informal terms, he maintains that thosewho run U.S. monetary policy act as ifthey were instructed to set k = 0, whicheliminates the inflationary bias.

What is perhaps less understood,however, is that there are gains fromenhancing credibility even when k = 0.To the extent that price setting todaydepends on beliefs about future eco-nomic conditions, a monetary authoritythat is able to signal a clear commit-ment to controlling inflation may facean improved short-run output/inflationtrade-off. Below we illustrate this point.The reason why this is not emphasizedin much of the existing literature onthis topic is that this work either tendsto focus on steady states (as opposed toshort-run dynamics), or it employs verysimple models of price dynamics, wherecurrent prices do not depend on beliefsabout the future. In our baseline model,however, short-run price dynamics de-

pend on expectations of the future, asequation (2.2) makes clear.40

4.2 Improving the Short-Run Output/Inflation Trade-off: Gains from Commitment with k = 0.

We now illustrate that there may begains from commitment to a policy rule,even with k = 0. The first stage problemin this case is to choose a state contin-gent sequence for xt + i and πt + i to maxi-mize the objective (2.7) assuming thatthe inflation equation (2.2) holds inevery period t + i, i ≥ 0. Specifically, thecentral bank no longer takes private sec-tor expectations as given, recognizinginstead that its policy choice effectivelydetermines such expectations.

To illustrate the gains from commit-ment in a simple way, we first restrictthe form of the policy rule to the gen-eral form that arises in equilibrium un-der discretion, and solve for the opti-mum within this class of rules. We thenshow that, with commitment, anotherrule within this class dominates the op-timum under discretion. Hence this ap-proach provides a simple way to illus-trate the gains from commitment.Another positive byproduct is that therestricted optimal rule we derive is sim-ple to interpret and implement, yet stillyields gains relative to the case of dis-cretion. Because the policy is not a globaloptimum, however, we conclude thesection by solving for the unrestrictedoptimal rule.

4.2.1 Monetary Policy under Commitment: The Optimum withina Simple Family of Policy Rules (that includes the optimal rule under discretion)

In the equilibrium without commit-ment, it is optimal for the central bank

40 This section is based on Galí and Gertler(1999).


to adjust xt solely in response to theexogenous cost push shock, ut. We ac-cordingly consider a rule for the targetvariable xt that is contingent on thefundamental shock ut, in the followingway:

xtc = − ω ut (4.5)

for all t, where ω > 0 is the coefficient ofthe feedback rule, and where xt

c denotesthe value of xt conditional on commit-ment to the policy.41 Note that the ruleincludes the optimum under discretionas a special case (i.e., the case with ω = λqshown in 3.4).

Combining equation (4.5) with thePhillips curve (2.2), in turn, implies thatinflation under the rule, πt

c, is also a lin-ear function of the cost push shock:

πtc = λ xt

c + β Etπt + 1c + ut (4.6)

= Et∑ i = 0

∞βi [λ xt + i

c + ut + i] (4.7)

= Et∑ i = 0

∞βi [− λω ut + i + ut + i] (4.8)

= 1 − λω1 − βρ

ut (4.9)

The problem for the central bank isto choose the optimal value of the feed-back parameter ω. Relative to the caseof discretion, the ability to commit toa feedback policy provides the centralbank with an improved short-run out-put/inflation trade-off. To this end, notethat it is possible to express equation(4.9) as

πtc =

λ1 − βρ

xtc +

11 − βρ

ut(4.10)

In this case, a one percent contraction inxt

c reduces πtc by the factor λ

1 − βρ. Under

discretion, reducing xt by one percentonly produces a fall in πt of λ < λ

1 − βρ.The extra kick in the case with commit-ment is due to the impact of the policyrule on expectations of the future courseof the output gap. In particular, thechoice of ω affects not only xt but alsobeliefs about the course of xt + i

c , i = 1,2, …,since Etxt + i

c = − ω ut. A central bank thatcommits to a tough policy rule (high ω),for example, is able to credibly signalthat it will sustain over time an aggres-sive response to a persistent supply shock.Since inflation depends on the futurecourse of excess demand, commitment tothe tough policy rule leads to a magni-fied drop in inflation per unit of outputloss, relative to the case of discretion.

To find the optimal value of ω, notefirst that since xt + i

c and πt + ic are each a

constant multiple of the cost push shockut + i, it is possible to express the objec-tive function as a multiple of period tloss:

max − 12 Et

∑ i = 0

∞βi[α (xt + i

c )2 + (πt + ic )2]

←→ max − 12 [α (xt

c)2 + (πtc)2]Lt (4.11)

with Lt ≡ Et

∑ i = 0

∞βi(ut + i/ut)2

> 0. The prob-

lem then is to choose ω to maximize(4.11), subject to (4.10). In this instance,the optimality condition is given by:

xtc = −

λαc

πtc

(4.12)where

αc ≡ α(1 − βρ) < α (4.13)

Since αc < α , relative to the case of dis-cretion, commitment to the rule impliesthat it is optimal for the central bank toengineer a greater contraction in outputin response to inflationary pressures.Intuitively, the more aggressive response

41 The policy rule only depends on ut becausethe central bank can adjust it to offset any impactof movements in gt on aggregate demand. Seeequation (4.16).


to inflation is the product of the im-proved output/inflation trade-off thatcommitment affords. Specifically, theoutput cost of lowering inflation declinesfrom α to αc per unit, since reducing in-flation a given amount requires, ceterisparibus, only a fraction (1 − βρ) of theoutput loss required under discretion.The decline in the effective cost of re-ducing inflation, in turn, induces themore aggressive policy response to infla-tion, as comparing equation (4.12) withequation (3.3) makes clear.

The equilibrium solutions for xtc and

πtc are easily obtained by combining

equations (4.12) and (4.10):xt

c = − λqc ut (4.14)πt

c = − αcqc ut (4.15)with

qc = 1

λ2 + αc(1 − βρ)It is interesting to observe that the

solution under commitment in this caseperfectly resembles the solution ob-tained under discretion that arises whenα is replaced with αc < α in the objec-tive function. It follows that, condi-tional on the value of the cost pushshock, ut, inflation is closer to targetand output is further, relative to theoutcome under discretion.42

It is straightforward to verify thatcommitment to the policy rule raiseswelfare.43 The tension produced bysuch gains from commitment, we think,

is compelling from an empirical stand-point. Because inflation depends on ex-pected future output gaps, the centralbank would like to convince the privatesector that it will be tough in the fu-ture, but at the same time, not to haveto contract demand much today. As thefuture comes to pass, the central bankhas the incentive to renege on itsplanned toughness and, instead, prom-ise again to undertake contractionarypolicy down the road. To see this, sup-pose that there is a positive cost pushshock. If the central bank is free to de-viate from the rule, it will always choosethe optimal policy under discretion,which calls for a smaller contraction ofoutput, relative to the case of commit-ment (again, compare 4.1 and 3.3). Arational private sector will recognizethat incentive and, unless the centralbank is able to commit credibly, will notexpect large contractions in demand inthe future either. As a result, the costpush shock generates higher inflation inthe absence of commitment. We stressagain that, in contrast to the traditionalanalysis, this gain from commitment isnot tied to the desire of the centralbank to push output above potential,but to the forward-looking nature of in-flation (and, thus, the importance of ex-pectations about future policy) in ourbaseline model.

From a policy standpoint, Rogoff’s ra-tionale for a conservative central bankercarries over perfectly to this case. In-deed with omniscience (i.e. exactknowledge of α c and the true model),an appropriately chosen central bankercould replicate the outcome undercommitment.

We summarize the findings in Result 7:Result 7: If price-setting depends on

expectations of future economic condi-tions, then a central bank that can cred-ibly commit to a rule faces an improvedshort-run trade-off between inflation

42 Importantly, with endogenous inflation per-sistence, commitment produces a faster transitionof inflation to target, as we discuss later.

43 To verify that commitment raises welfare,simply substitute the implied values for xt and πtunder the optimal rule for each case into the pol-icy objective function. However, it should be obvi-ous that commitment raises welfare, since the op-timal rule under discretion falls within the class ofrules that we permitted the central bank to choosein the case with commitment: Yet we found thatwith commitment it is optimal to choose a differ-ent parameterization of the rule than arises in theoptimum under discretion.


and output. This gain from commitmentarises even if the central bank does notprefer to have output above potential(i.e., even when k = 0). The solutionunder commitment in this case perfectlyresembles the solution that would ob-tain for a central bank with discretionthat assigned to inflation a higher costthan the true social cost.

One additional interesting feature ofthis case with commitment involves thebehavior of interest rates. This can beseen formally by simply replacing αwith α c in the interest rate rule underdiscretion (given by equation 3.6) toobtain

it = γπc Etπt + 1 +

1ϕ gt (4.16)

with

γπc ≡ 1 +

(1 − ρ)λρϕα c

> 1 + (1 − ρ)λ

ρϕα ≡ γπ

In particular, relative to the case of dis-cretion, the central bank increases thenominal interest rate by a larger amountin response to a rise in expectedinflation.

4.2.2 Monetary Policy under Commit-ment: The Unconstrained Optimum

We now provide a brief description ofthe general solution for the optimal pol-icy under commitment.44 Because thederivation is more cumbersome than forthe restricted case just described, wedefer most of the details to an appen-dix. As with the simple fundamentalbased policy, however, the general solu-tion exploits the ability that commit-ment affords to manipulate privatesector expectations of the future.

The first stage problem remains tochoose a state-contingent sequence for

xt + i and πt + i to maximize the objective(2.7) given that the aggregate supplycurve (2.2) holds in every periodt + i, i ≥ 0. We no longer restrict thechoice of xt to depend on the contempo-raneous value of the shock (i.e., ut ), butallow instead for rules that are a func-tion of the entire history of shocks. Tofind the globally optimal solution to thelinear quadratic policy problem undercommitment, we follow David Currieand Paul Levine (1993) and Woodford(1998), and form the Lagrangian:45

max − 12 Et

∑ i = 0

∞βi [αxt + i

2 + πt + i2

+ φt + i(πt + i − λxt + i − βπt + i + 1 − ut + i)]

(4.17)

where 12 φt + i is the (state-contingent)

multiplier associated with the constraint att+i. It is straightforward to show that thefirst order conditions yield the followingoptimality conditions

xt + i − xt + i − 1 = − λα πt + i,

for i = 1,2,3,... (4.18)

and

xt = − λα

πt (4.19)

Recall that under discretion the opti-mal policy has the central bank adjustthe level of the output gap in responseto inflation. The optimal policy undercommitment requires instead adjustingthe change in the output gap in re-sponse to inflation. In other words,commitment changes the level rule forxt under discretion into a differencerule for xt, as a comparison of equations

44 We thank Chris Sims and Albert Marcet forcalling to our attention that the globally optimalrule under commitment would likely not fallwithin the restricted family of rules considered inthe previous sub-section.

45 See also King and Wolman, who analyze theoptimal monetary policy under commitment in aversion of Taylor’s (1980) staggered contractsmodel.


(3.3) and (4.8) indicates.46 The one ca-veat is that in the initial period the pol-icy is implemented (i.e., period t) thecentral bank should simply adjust thelevel of the output gap xt is response toπt, as if it were following the optimalpolicy under discretion, but for thatperiod only.

Because xt + i depends in general onxt + i − 1, the (unconstrained) optimal pol-icy under commitment is in general notsimply a function of the contemporane-ous state variable ut + i. As Woodford(1998) emphasizes in a related context,the lagged dependence in the policyrule arises as a product of the centralbank’s ability under commitment to di-rectly manipulate private sector expec-tations.47 To see this for our framework,keep in mind that πt depends not onlyon current xt but also on the expectedfuture path of xt + i. Then suppose, forexample, that there is a cost push shockthat raises inflation above target at timet. The optimal response under discre-tion, as we have seen, is to reduce xt,but then let xt + i revert back to trendover time as πt + i falls back to target.The optimal policy under commitment,however, is to continue to reduce xt + i aslong as πt + i remains above target. The(credible) threat to continue to contractxt in the future, in turn, has the imme-diate effect of dampening current infla-

tion (given the dependency of πt on fu-ture values of xt). Relative to the case ofdiscretion, accordingly, the cost pushshock has a smaller impact in currentinflation.48

As with the constrained policy, theglobally optimal policy under commit-ment exploits the ability of the centralbank to influence πt with expected fu-ture values of xt + i as well as current xt.It is also easy to see that, as was thecase with the more restrictive rule, thepolicy is not time consistent. Clearly, ifit could reoptimize at t + i, the centralbank would choose the same policy itimplemented at t, the one which mimicsthe rule under discretion for the firstperiod only.

A disadvantage of the unconstrainedoptimal policy under commitment isthat it appears more complex to imple-ment than the constrained one (de-scribed by equation 4.12). As we haveseen, the constrained rule resembles inevery dimension the optimal policy un-der discretion, but with relatively moreweight placed on fighting inflation. Ac-cordingly, as we discussed, it is possibleto approximate this policy under discre-tion with an appropriately chosen cen-tral banker. The same is not true, how-ever, for the unconstrained optimalpolicy. A conservative central bankeroperating with discretion has no obvi-ous incentive to stick to the differencerule for the output gap implied byequation (4.18).

A further complication, discussed atlength in Woodford (1998), is that theinterest rate rule that implements theoptimal policy might have undesirable

46 Woodford (1998) makes the connection be-tween the lagged dependence in the optimal ruleunder commitment and the lagged dependencethat appears to arise in interest rate behavior un-der practice (see section 5.2). Roughly speaking,since the interest rate affects the output gap,lagged dependence in the latter translates intolagged dependence in the former.

47 Woodford (1998) considers a closely relatedenvironment. The difference is that in his frame-work the policy-maker confronts a trade-off be-tween inflation and the output gap ultimately be-cause his objective function includes a target forthe nominal interest rate (along with targets forthe output gap and inflation), whereas in ourframework the trade-off arises due to the costpush shock.

48 On the surface it appears that the differencerule for xt might be unstable. However, πt adjuststo ensure that this is not the case. In particular,the optimal response to a positive cost push shockis to contract xt sufficiently to push πt below tar-get. xt then adjusts back up to target over time.The appendix provides the details.


side effects. To see this, combine (4.18)and (2.1) to obtain the implied optimalinterest rate rule

it = 1 −

λαϕ

Etπt + 1 +

1ϕ gt

Notice that the coefficient associatedwith expected inflation is less than one.Under this rule, accordingly, a rise inanticipated inflation leads to a declinein the real interest rate. As we discussin section 7, if inflationary pressuresvary inversely with the real rate, a ruleof this type may permit self-fulfillingfluctuations in output and inflation thatare clearly suboptimal.49

Overall, we have:Result 8: The globally optimal policy

rule under commitment has the centralbank partially adjust demand in re-sponse to inflationary pressures. Theidea is to exploit the dependence of cur-rent inflation on expected future de-mand. In addition, while appointing aconservative central banker may raisewelfare under discretion (see Result 7),it does not appear that it is possible toattain the globally optimal rule withthis strategy. Finally, there may be somepractical complications in implementingthe globally optimal interest rate rulethat involve potential indeterminacy, asdiscussed in Woodford (1998).

We conclude that, though substantialprogress has been made, our under-standing of the full practical implica-tions of commitment for policy-makingis still at a relatively primitive stage,with plenty of territory that is worthexploring.

5. Practical Complications

In this section we consider a numberof important practical issues that com-plicate the implementation of monetarypolicy. While they may not be as exoticas the question of credibility, they areno less important for the day-to-day for-mulation of policy.

5.1 Imperfect Information

Thus far we have assumed that thecentral bank is able to control perfectlythe paths of the key target variables. Inpractice, of course, this is not the case.One important reason is imperfect ob-servability. At the time it sets interestrates, a central bank may not have allthe relevant information available aboutthe state of the economy. Certain datatake time to collect and process. Sam-pling is imperfect. Even if it has accessto data in real time, some key variablessuch as the natural level of output arenot directly observable and are likelymeasured with great error (see, e.g., thediscussion in Arturo Estrella andMishkin 1999 and Orphanides 1998).

Beyond limiting the efficacy of pol-icy, imperfect information has severalspecific implications. First, it is nolonger possible to specify rules simplyin terms of target variables. With per-fect information, a policy may be ex-pressed equivalently in terms of targetsor instruments since a one-to-one rela-tionship generally exists between thesevariables. With imperfect information,rules for targets can be expressed onlyin terms of the respective forecasts, asopposed to the ex-post values. An alter-native is to use an intermediate targetthat is directly observable, such as abroad monetary aggregate.

Second, imperfect information makesthe policy instrument choice non-trivial.With perfect information, for example,it does not matter whether the central

49 Indeterminacy does not arise in the case ofdiscretion or in the case of the constrained opti-mum under commitment, since in each instancethe implied interest rate rule has an inflation coef-ficient greater than one. To the extent that suchcoefficient is not too large, implementation ofsuch a rule will result in a unique equilibrium (seethe discussion in section 7 and also in Clarida,Galí, and Gertler (1998).


bank uses the short-term interest rateor a monetary aggregate as the policyinstrument, so long as the money de-mand function yields a monotonic rela-tion between the two variables.50 Withimperfect information, the ex post vola-tility of a variety of key variables hingeson the instrument choice, as originallyargued by William Poole (1970). Weillustrate each of these issues below.51

5.1.1 Forecasts as Targets and Intermediate Targets

We now return to the baseline modelwith no commitment, and modify it asfollows. Suppose that the central bankcannot observe the contemporaneousvalues of output, inflation, or any of therandom shocks. Then let Ωt be the cen-tral bank’s information set at the time itfixes the interest rate that prevails attime t.52 The optimality condition forpolicy now is expressed in terms of theexpected as opposed to realized targetvariables.

Ext | Ωt

= −

λα E

πt | Ωt

(5.1)

Equation (5.1) is the certainty equivalentversion of the condition for the case ofperfect information, given by equation(3.3). Certainty equivalence applies herebecause of the linear quadratic setup(that gives linear decision rules under

perfect information) and because the er-rors in forecasting the target variablesare additive.

For ease of exposition, assume thatthere is no serial correlation in thecost push shock; that is, ρ = 0, so thatut = ut. The implied equilibrium valuesof the target variables under imperfectinformation, xt

I and πtI, are given by

xtI = xt +

λλ2 + α

ut + gt = gt (5.2)

πtI =

1 +

λ2

α πt + λ gt = ut + λ gt (5.3)

where xt and πt are the optimal values ofthe target variables that emerge in caseof perfect information (when ut is seriallyuncorrelated),53 and where ut and gt arethe unexpected movements in the costpush and demand shocks, respectively. Im-perfect information clearly implies greatervolatility of inflation, since the centralbank cannot immediately act to offsetthe impact of the shocks. The net effecton the volatility of the output gap is un-clear: the inability to offset the demandshock clearly raises output volatility. Onthe other hand, the central bank cannotoffset the inflationary impact of the costpush shock, which works to reduce thevolatility of the output. There is, however,an unambiguous reduction in welfare.54

One additional result is worth noting.Since demand shocks now affect the be-havior of output, a positive short-runco-movement between inflation andoutput can emerge if gt has a variancesufficiently large relative to that of ut.

It is straightforward to generalize theanalysis to a setting where the imper-fect observability stems from lags in the

50 To clarify, a money aggregate can serve as aninstrument only if it is directly controllable. A can-didate aggregate then would be bank reserves. Abroad aggregate such as M3 would not qualify.

51 For a broad survey of the literature on mone-tary policy targets and instruments, see Friedman(1991).

52 Thus, Ωt is similarly the private sector’s infor-mation set. Specifically, we let firms observe thecurrent values of their marginal costs, but neitherfirms nor households can observe contemporane-ous aggregate variables. In this instance, the ISand Phillips curve equations are respectively givenby

xt = − ϕ[(it | Ωt) − Et − 1πt+1] + Et − 1xt + 1 + gt

πt = λxt + βEt − 1πt + 1 + ut

53 When ut is serially uncorrelated, xt = − λ

λ2 + α ut

and πt = α

λ2 + α ut.

54 To prove that imperfect information leads to areduction in welfare, evaluate the welfare functionwith xt

I and πtI versus xt and πt.


transmission of monetary policy. Thiscase is of interest since much of theavailable evidence suggests a lag of sixto nine months in the effect of a shift ininterest rates on output.55 The lag inthe effect on inflation is around a yearand a half. Suppose, for example, that ittakes j periods for a shift in the currentinterest rate to affect output and an-other k periods for an impact on infla-tion. In the left side of equation (5.1)would appear the j period ahead fore-cast of the output gap, and on the rightwould be the (suitably discounted) j + kperiod ahead forecast of inflation.

Svensson (1997a,b) has emphasizedthe practical importance of this resultfor the mechanics of inflation targeting(specifically, the kind of inflation tar-geting that the theory implies (see Re-sult 2 in section 3). A standard criticismof employing an inflation target is thatinformation about the impact of currentmonetary policy on inflation is onlyavailable with a long lag. This informa-tion lag, it is argued, makes it impossi-ble to monitor policy performance. It ispossible to circumvent this problem, ac-cording to Svensson, by focusing in-stead on the inflation forecast. Theforecast is immediately available. Itthus provides a quick way to judge thecourse of policy. A caveat to this argu-ment is that to generate the correct in-flation forecast, the central bank musthave a good structural model of theeconomy.56 VAR-based forecasts are

reasonable only if the economy hasattained a stationary equilibrium.

A traditional alternative to using thetarget variable forecasts is to focus onthe behavior of a variable that is corre-lated with the underlying targets but isinstead observable and controllable.Broad monetary aggregates are the bestknown examples of intermediate tar-gets. If demand for a particular aggre-gate is stable, then this aggregate islikely to have a stable covariance withnominal GDP. In practice, however, ex-perience with monetary targeting hasnot been successful. The U.S. and theU.K., for example, attempted to regu-late the growth of money aggregates inthe early 1980s and then quickly aban-doned the policy after the aggregateswent haywire.57 Financial innovation ineach instance was the underlying cul-prit. Even in Germany, long considereda bastion of money targeting, there havebeen problems. Unstable movements inmoney demand have forced a retreatfrom strict money growth targeting. Anumber of recent papers go further byarguing that in practice Bundesbankpolicy looks more like inflation target-ing (as defined in Result 2) than moneytargeting (Clarida and Gertler 1997;Bernanke and Mihov 1997b).

For similar reasons, policies that tar-get other kinds of simple indicators,such as commodity prices or long terminterest rates, have not been widely em-ployed. As Woodford (1994a) has em-phasized, the correlation properties ofthese simple indicators with output and55 Galí (1992), Christiano, Eichenbaum, and

Evans (1996), and Bernanke and Mihov (1997a)document the slow response of GDP to a policyshock, and the even slower response of prices.Bernanke and Gertler (1995) show that, while theoverall response of output is sluggish, certain com-ponents of spending do respond quickly, such ashousing and consumer durables. Inventories ad-just to reconcile the gap between spending andoutput.

56 Bernanke and Woodford (1997) emphasizethe need to make structural forecasts. They alsoraise some other related criticisms of using fore-

cast-based targets, including the possibility of in-determinacy under this kind of policy rule. Wediscuss this issue in section 7.

57 See Friedman and Kuttner (1996) for a de-tailed accounting of the failure of monetary target-ing to take hold in the U.S. See also Estrella andMishkin (1996). On the other hand, Feldstein andStock (1997) argue that, with periodic adjustment,a broad monetary aggregate can still be a usefulintermediate target.


inflation is likely to vary with changesin the policy rule. In the end, there isno simple substitute for employing astructural model.

To summarize, we haveResult 9: With imperfect informa-

tion, stemming either from data prob-lems or lags in the effect of policy, theoptimal policy rules are the certaintyequivalent versions of the perfect infor-mation case. Policy rules must be ex-pressed in terms of the forecasts of tar-get variables as opposed to the ex postbehavior. Using observable intermediatetargets, such as broad money aggregates isa possibility, but experience suggests thatthese indirect indicators are generallytoo unstable to be used in practice.

5.1.2 The Instrument Choice Problem: The Interest Rate versus a Narrow Monetary Aggregate

We now turn to the issue of instru-ment choice. In practice, the interestrate that major central banks adjust isan overnight rate on interbank lendingof funds to meet reserve require-ments.58 They control this rate by ma-nipulating the supply of bank reserves,i.e., the quantity of high-poweredmoney available for meeting bank re-serve requirements. The issue thatarises is whether, from an operationalstandpoint, policy should prescribepaths (or rules) for bank reserves or forinterest rates. Suppose that the demandfor bank reserves mt is given by59

mt − pt = κ yt − η it + vt (5.4)

where pt is the price level and vt is arandom disturbance to money demand.If vt is perfectly observable then it doesnot matter whether it or mt is employedas the policy instrument. Given the timepath of it implied by the optimal policy,it is possible to back out a time pathfor mt that supports this policy fromequation (5.4).

Matters change if vt is not observ-able. With the interest rate as the in-strument, the central bank lets themoney stock adjust to the money de-mand shock. There is no impact ofmoney demand shocks on output or in-flation because the central bank per-fectly accommodates them. With moneytargeting, the reverse is true: the inter-est rate and (possibly) output adjust toclear the money market. Assume forsimplicity that demand and cost pushshocks are absent (i.e., gt = 0, ut = 0), sothat the only shock is the innovation tomoney demand. Then the interest rateimplied by a money supply instrumentitm, is given by

itm = it +

1η + ϕ(κ + λ)

vt (5.5)

where it is the rate that would arise un-der interest rate targeting and vt is theunexpected movement in money demand.

The key point is that money demandshocks can induce volatile behavior ofinterest rates. This is particularly true ifmoney demand is relatively interest in-elastic in the short run, as is the casefor bank reserves. This short run volatil-ity in interest rates will then feed intooutput volatility, via the aggregate de-mand relation, equation (2.1). It is forthis reason that in practice central banksuse interbank lending rates as the pol-icy instrument, an insight due originallyto Poole (1970).60 Recent empirical

58 See Bernanke and Mihov (1997a) for a discus-sion of Federal Reserve operating procedures andhow they have changed over time.

59 In the optimizing IS/LM framework of sec-tion 2, it is possible to motivate this specificationof the money demand function from first princi-ples, assuming that utility is separable in consump-tion and real money balances and that consump-tion is the only type of good (see, e.g., Woodford1996).

60 Poole also argued that if unobservable de-mand shocks were large relative to money demandshocks, then it may be preferable to use a money


work by Bernanke and Mihov (1997a)confirms that except for the brief pe-riod of non-borrowed reserve targetingunder Volcker (1979:10–1982:10), theFederal Reserve Board has indeedtreated the Funds rate as the policy in-strument. In summary, we have

Result 10: Large unobservableshocks to money demand produce highvolatility of interest rates when a mone-tary aggregate is used as the policy in-strument. It is largely for this reasonthat an interest rate instrument may bepreferable.

The analysis thus makes clear why thenew Federal Reserve Board model doesnot even bother to include a money ag-gregate of any form (see Flint Braytonet al. 1997). Narrow aggregates are notgood policy instruments due to the im-plied interest rate volatility. Broad ag-gregates are not good intermediate tar-gets because of their unstable relationwith aggregate activity.

5.2 Policy Conservatism: Model Uncertainty vs. Exploitation of Forward-Looking Behavior

In practice, central banks adjust in-terest rates more cautiously than stan-dard models predict. Put differently,optimal policies derived in a certaintyequivalent environment generally pre-dict a much more variable path of inter-est rates than is observed in practice.An interesting illustration of this pointis Rotemberg and Woodford (1997) whoestimate a model very similar to ourbaseline model, and then compute anoptimal interest rate policy. The histori-cal interest rate displays much less vola-tility than the optimal interest rate.

This finding is not uncommon. TheFRB-US model also generates high in-terest rate volatility under an optimalrule. Because this degree of volatilityseems greater than monetary policymakers seem willing to tolerate in prac-tice, optimal rules are also computedwith constraints on the volatility ofinterest rate changes (see, e.g., JohnWilliams 1997).61

The tendency of the Federal Reserveto adjust rates cautiously is generally re-ferred to as “interest rate smoothing.”To be precise, as a number of authorshave shown, a monetary policy rule ofthe following form captures the lasttwenty or so years of data fairly well:

it = (1 − ρ)[α + β πt + γ xt] + ρ it − 1 + εt (5.6)where α is a constant interpretable asthe steady state nominal interest rate62

and where ρ ∈ [0,1] is a parameter thatreflects the degree of lagged depen-dence in the interest rate.63 Interest ratesmoothing is present in distinct respects.First, the estimated slope coefficients oninflation and the output gap, β and γ, aretypically smaller than what the optimalrule would suggest. Second, there is typi-cally partial adjustment to movements inπt and xt, reflected by the presence of thelagged interest in the fitted rule. That is,it is a weighted average of some desiredvalue that depends on the state economy(given by the term [α + βπt + γxt] ) and thelagged interest rate, where the relativeweights depend on the smoothing pa-rameter ρ. Estimates of ρ for quarterlydata are typically on the order of 0.8 or0.9, which suggests very slow adjustment

supply instrument. With a money supply instru-ment, interest rates will naturally move in an off-setting direction in response to unobserved de-mand shocks (see Result 4). In practice, the highvariability of money demand shocks seems todominate the instrument choice, however.

61 An alternative is to penalize large changes inthe nominal interest rate by including the squareddeviations of the change in the interest rate (i.e,(it − it − 1)2) in the function, as in Rudebusch andSvensson (1998).

62 Recall that πt represents deviations of infla-tion from its average (target) level.

63 See Rudebusch (1995), for example, for a dis-cussion of the persistence in short term interestrates.


in practice. The existing theory, by andlarge, does not readily account for whythe central bank should adjust rates insuch a sluggish fashion.

Indeed, understanding why centralbanks choose a smooth path of interestrates than theory would predict is animportant unresolved issue. One impli-cation is that the standard certaintyequivalence models may not adequatelycapture the constraints policy-makersface in practice. A natural possibility isthat policy-makers know far less aboutthe way the world works than ispresumed in simple policy experiments.

In general, model uncertainty is aformidable problem. Ideally, one wouldlike to take into account that the centralbank is continually learning about theeconomy as it adjusts its policy. Per-forming this exercise in a clean way isbeyond the frontier of current knowl-edge. Though, advances in computa-tional methodology have allowed someprogress to be made with relativelysimple frameworks.64

It is possible to illustrate how modeluncertainty could in principle introduceat least some degree of policy caution.Suppose the values of several parame-ters in the model are random. The cen-tral bank knows the distribution ofthese parameters but not the realiza-tion. When it adjusts policy, accord-ingly, it cannot be sure of the impact onthe economy. As originally demon-strated by William Brainard (1969), thiskind of uncertainty can introduce cau-tion in policy responses. In contrast tothe case of certainty-equivalence, policyactions now affect the conditional vari-ance of inflation and output, as well asthe conditional mean.

To be concrete, suppose that the twoparameters of the model, the interestelasticity in the IS equation and theslope coefficient on the output gap arerandom variables, now given by ϕ~t = ϕ + εt

and by λ~t = λ + η t.65 Assume further thatεt and η t are i.i.d random variables withzero means. The optimality conditionfor policy then becomes:

Ext | Ωt = λ

α + λ2ση2 Eπt | Ωt

+ (α + λ2) σε

2

ϕ rt (5.7)

where rt ≡ it − Eπt + 1 | Ωt is the ex antereal interest rate. This condition leads tothe following result:

Result 11: Parameter uncertaintymay reduce the response of the policyinstrument to disturbances in the econ-omy. It can thus motivate a smootherpath of the interest rate than the cer-tainty equivalent policy implies.

Comparing equations (5.1) and (5.7)reveals how parameter uncertainty re-duces policy activism. Under certaintyequivalence, a rise in inflation abovetarget requires the central bank to raiseinterest rates to contract demand.66

With an uncertain slope coefficienton the output gap in the AS curve, how-ever, contraction of output below po-tential raises the variability of inflation.This induces the central bank to moder-ate the contraction in demand, as re-flected by the presence of the term λ2ση

2

in the coefficient on Eπt | Ωt. Similarly,

64 Wieland (1997) analyzes policy in a frame-work where the central bank has to learn the valueof the natural rate of unemployment (which, inour analysis, corresponds to having to learn aboutpotential GDP.)

65 We are assuming that the policy-maker knowsthe first two moments of the random parameters.It may be more plausible to argue that the policy-maker in fact has little idea what the true distri-bution looks like. See Onatski and Stock (1999)who analyze the policy problem in this kind of en-vironment using robust control methods.

66 It should also be clear from equation (5.7)that with parameter uncertainty the interest rateno longer adjusts to perfectly offset demandshocks. Suppose, for example, that there is a posi-tive demand shock. The interest rate goes up, butthe parameter uncertainty moderates the extent ofthe rise, relative to the certainty equivalence case.


uncertainty about the impact of an in-crease in the interest rate on the outputgap moderates the extent of adjustmentin it. The second term on the right sideof equation (5.7) captures this latterdampening effect.

This simple form of model uncertaintythus may help explain the relatively lowvariability of interest rates in the data.One feature of interest rate smoothingit does not appear to capture, however,is the strong lagged dependence in theinterest rate. Put differently, the kindof parameter uncertainty we have dis-cussed may explain why the slope coef-ficients on inflation and the output gap,α and β, are small relative to the case ofcertainty equivalence. But it does notexplain the partial adjustment, given bythe dependence of it on it − 1.67

Rotemberg and Woodford (1997) of-fer a novel explanation for the laggeddependence that is based on the lever-age that this kind of adjustment rulemay provide the central bank over thelong term interest rate. The idea is thatlagged dependence in it permits thecentral bank to manipulate long termrates, and hence aggregate demand,with more modest movements in theshort term rate than would be otherwisebe required. This kind of rule is thusdesirable to the extent the central bank

may care about avoiding excessive vola-tility in the short term interest rate inpursuing its stabilization goals.

To illustrate, consider the specialcase of equation (5.6) with ρ = 1. In thisinstance, the difference in the interestrate (it − it − 1), as opposed to the level, isa linear function of πt and xt. Under thedifference rule, the expected futureshort rate at t + i, Etit + i, is given by

Etit + k = Et

∑

j = 1

k

(it + j − it + j − 1)

+ it

(5.8)

= Et

∑

j = 1

k

[α + βπt + j + γxt + j]

+ it

Assume that the long-term rate dependson the sum of expected short rates overthe same horizon, in keeping with the ex-pectations hypothesis of the term struc-ture. Then, in comparison with the levelrule, the difference rule increases the re-sponsiveness of the long term rate underthe feedback policy. Suppose for examplethat, in reaction to a rise in inflation abovetarget at time t, the central bank raises it

above its steady state value. Under thedifference rule the increase in the inter-est rate has a persistent effect on the pathof the expected short rate, since Et

it + i

depends additively on it. Further, if changesin inflation and output are persistent,then the path of expected short rates willactually be rising, as equation (5.8) makesclear.68 The difference rule thus en-hances the countercyclical movement ofthe long rate relative to the movement ofshort rate. Given that aggregate demanddepends on the long rate, this kind ofrule thus enables the central bank to

67 Sack (1997a,b) argues, nonetheless, that pa-rameter uncertainty can explain this phenomenonif the uncertainty of the impact of the interest rateon the economy is based on the change in the in-terest rate (it − it − 1) as opposed to the deviationfrom trend it. In the former instance, changes in itraise the conditional variability of output, whichinduces the central bank to keep it close to it − 1.On the other hand, it is not well understood howthe link between model uncertainty and policyconservatism is affected when there is activelearning about the economy. Some results suggestthat learning should induce active adjustments ofthe policy instrument to facilitate estimating thetrue model. See the discussion in Wieland (1997),for example. Also, it is possible to construct exam-ples where parameter uncertainty leads to in-creased activism. See, for example, Thomas Sar-gent (1998).

68 On the surface it appears that the interestrate might explode under the difference rule,since it will continue to increase so long as infla-tion is above target. However, the rise in the inter-est rate will dampen demand and inflation. In thecontext of our model, it does so sufficiently to pre-clude explosive behavior.


stabilize the economy with relativelymodest movements in the short rate.69

Overall, Rotemberg and Woodfordprovide a plausible explanation for whycentral banks may want to introducelagged dependence in the interest rate.Whether this story can also account forthe empirically observed modest re-sponse of the short rate to inflation andthe output gap (i.e., the low values of βand γ, the slope coefficients on πt and xt)remains to be seen.

Another explanation for policy con-servatism and the associated interestrate smoothing includes fear of disrupt-ing financial markets (see, e.g., Good-friend 1991). Sharp unanticipated in-creases in interest rates can generatecapital losses, particularly for commer-cial banks and other financial institu-tions that may be exposed to interestrate risk. This consideration might ex-plain why the Federal Reserve chose toraise rates only very gradually during1994, the tail end of a period of consid-erable financial distress (see, e.g., thediscussion in John Campbell 1995). Dis-agreement among policy-makers is an-other explanation for slow adjustmentof rates. Neither of these alternativestories have been well developed,however. In general, understandingwhy interest rate smoothing occurs inpractice is an important unresolvedissue.

5.3 Non-Smooth Preferences and Opportunism

Another aspect of policy that has re-ceived considerable attention involvesthe process of disinflation. In the base-line model, if inflation is above target,

it is always optimal to tighten monetarypolicy to gradually bring inflation backto the optimum (see Result 2 in Section3). During his tenure at the Federal Re-serve Board, however, Blinder proposedthe following alternative: If inflation isabove but near the optimum, policyshould not contract demand. Rather, itshould take an “opportunistic” ap-proach. Roughly speaking, being oppor-tunistic boils down to waiting untilachieving the inflation target could bedone at the least cost in terms of incre-mental output reduction. Blinder’soriginal concept was vague as to the de-tails. Recent work by researchers at theFederal Reserve Board has filled in anumber of the missing pieces.

Athanasios Orphanides and DavidWilcox (1996) show that it is possible torationalize something like opportunisticpolicy by making a small adjustment ofthe policy objective function. In par-ticular, suppose that policy-makers carequite a lot about small departures ofoutput from target, at least relative tosmall departures of inflation. An exam-ple of an objective function that capturethis phenomenon is given by

max − 12 Et

∑ i = 0

∞βi(α | xt + i | + πt + i

2 )

(5.9)

With this objective function, the opti-mality condition for policy becomes:

xt = 0, if | πt | < αλ

| πt | = αλ, otherwise

(5.10)

Thus, if inflation is within α

λ units ofthe target, the optimal policy is to sim-ply stabilize output. Otherwise, policyshould keep inflation at most α

λ unitsfrom target and then wait for favorablesupply shocks that move it closer to tar-get (e.g., favorable movements in thecost push shock ut). In this respect the

69 The idea that the central bank should pursuea partial adjustment rule to exploit the depen-dence of demand on future policy is reminiscentof the globally optimal policy under commitment(see section 4.2.2). Indeed, Woodford (1998)makes this connection formally.


policy is opportunistic. A better termfor it, however, might be “inflation zonetargeting” (Bernanke and Mishkin1997). What the policy really amountsto is keeping inflation with a certainrange, as opposed to trying to move itto an exact target.

Variations on this theme allow forpreferences that generate an inflationzone target, but then has policy trade offbetween inflation and output goals wheninflation is outside the target zone. Or-phanides, David Small, Volcker Wielandand Wilcox (1997) (OSWW) provide anexample of this more general setup.

It is important to emphasize, though,that opportunistic policy behavior thatis distinct from the gradualism of thebaseline model only arises if cost pushfactors are present in inflation. This istrue because only with cost push infla-tion present does a trade-off betweenoutput and inflation emerge (see Result1). Indeed, OSWW show that opportun-istic policy rules are equivalent to con-ventional gradualist rules in the pres-ence of demand shocks, but differ whenthere are supply shocks.70

In summary, we haveResult 12: If there is more cost asso-

ciated with small departures of outputfrom target than with small departuresof inflation, then an opportunistic ap-proach to disinflation may be optimal.This policy, further, is equivalent totargeting inflation around a zone asopposed to a particular value.

6. Implications of Endogenous Inflationand Output Persistence

Within our baseline model, the dy-namics of output and inflation are dueentirely to exogenous force processes.

We now consider an alternative frame-work that allows for endogenous persis-tence in output and inflation. Our pur-pose is to show that the results derivedin the baseline framework extend to thismore general setting. In this regard, weshow that our results are not specific tothe particular benchmark model we em-ployed, but instead hold across a rea-sonably broad class of models that areused for applied macroeconomic analy-sis. The major difference is that withendogenous persistence in inflation, theequilibrium feedback monetary policy nowinfluences the speed of convergence ofinflation to its target.

Consider the following generaliza-tions of the IS and aggregate supplycurves:

xt = − ϕ[ it − Etπt + 1] + θ xt − 1

+ (1 − θ)Etxt + 1 + gt (6.1)

πt = λ xt + φ πt − 1 + (1 − φ)βEtπt + 1 + ut (6.2)

Equation (6.1) incorporates the laggedoutput gap in the IS curve. Equation(6.2) adds lagged inflation to the aggre-gate supply curve. The parameters θ andφ index the influence of lagged versus ex-pected future variables. As a result themodel nests some important specialcases. With θ = 0 and φ = 0, we recoverthe baseline model. Conversely, withθ = 1 and φ = 1, the model becomes(approximately) the backward-lookingframework that Svensson (1997a,b) andBall (1997) have used to analyze mone-tary policy. For simplicity we assume thatthe disturbances gt and ut are seriallyuncorrelated (i.e., we set µ and ρ inequation (2.3) and (2.4) equal to zero).This simple formulation does not allowfor delays in the effect of policy, but weshow later that it is easy to amend theanalysis to incorporate delayed policyeffects.

As we noted earlier, virtually all the

70 For an alternative description of the oppor-tunistic approach, see Bomfin and Rudebusch(1997). These authors emphasize the ratchetingdown of inflation and, in particular, explore therole of imperfect credibility.


major applied macroeconomic modelsallow for some form of lagged depen-dence in output and inflation. The pri-mary justification is empirical.71 By ap-pealing to some form of adjustmentcosts, it may be feasible to explicitlymotivate the appearance of xt − 1 withinthe IS curve. Motivating the appearanceof lagged inflation in the aggregate sup-ply curve, however, is a more formida-ble challenge.72 Some frameworks do soby effectively appealing to costs ofchanging the rate of inflation.73 This as-sumption, though, is clearly unattrac-tive. In the spirit of robustness, how-ever, it is important to understand theimplications of lagged dependence. Thisis particularly true given the empiricalappeal of this formulation.

We begin with the case of discretion,and then later describe briefly how theresults are affected when the centralbank can make credible promises.74 An

analytical solution is not available, ex-cept in the polar cases of φ = 0 and φ = 1.It is, however, possible to provide an in-tuitive description of the optimum. Letaπ be a parameter that measures the se-rial dependence of inflation in thereduced form. Then the optimalitycondition that governs policy is givenby:

xt = − λα πt + ∑

k = 1

∞βk Etπt + k

(6.3)

= − λ

α(1 − βaπ)πt (6.4)

withπt = aπ πt − 1 + au ut (6.5)

and0 ≤ aπ < 1

With inertia present, adjustments incurrent monetary policy affect futuretime path of inflation. As consequence,policy now responds not only to currentinflation but also to forecasts of infla-tion into the indefinite future. Howmuch depends positively on aπ, whichmeasures the degree of inflationarypersistence.

The coefficients aπ and au are func-tions of the underlying parameters(α ,λ,β,φ).75 The former, aπ, is key, sinceit measures the speed of convergence toinflation under the optimal policy. It ispossible to show that this parameter liesbetween zero and unity, implying con-vergence. The magnitude of aπ dependspositively on the degree of inflation in-ertia φ. In the baseline case of no infla-tion inertia, φ = 0, implying aπ = 0. aπ

71 For an empirical justification for includinglagged dependent variables, see Fuhrer (1996).

72 It is possible to motivate a dependency of cur-rent inflation on lagged inflation by appealing toadaptive expectations (e.g., suppose Et − 1πt =κπt − 1). Indeed, this is the traditional approach(see the discussion in Blanchard 1997). The issuethen becomes motivating the assumption of adap-tive expectations.

73 See, for example, Fuhrer and Moore(1995a,b) and Brayton, Levin, Tyron, and Williams(1997). Galí and Gertler (forthcoming) criticizethe existing empirical literature on inflation dy-namics, and provide new evidence which suggeststhat (2.2) is a good first approximation to the data.

74 As in section 3, we restrict attention toMarkov perfect equilibria. In this case, however,we must take into account that inflation is an en-dogenous state variable. In any stationary equilib-rium, therefore, expected inflation will depend onlagged inflation. What the policy maker takes asgiven, accordingly, is not the level of expected in-flation, but rather how private sector expectationsof inflation tomorrow respond to movements in in-flation today. Simply put, to solve for the equilib-rium under discretion, we assume that private sec-tor forecast of πt + 1 takes the form νππt + νuut,where νπ and νu are arbitrary constants that thepolicy-maker takes as given. In the rational expec-tations equilibrium νπ and νu equal the true funda-mental parameters in the reduced form inflation,aπ and au.

75 To obtain solutions for aπ and au, substitute

the optimality condition xt = − λ

α(1 − βaπ) πt and

the conjectured solution for πt, (6.5), into the ag-gregate supply curve. Then use the methods ofundetermined coefficients to solve for aπ and au.The equation for aπ is a cubic. The solution is theunique value between zero and unity, which corre-sponds to the unique stable root.


also depends negatively on the relativecost of inflation, measured by 1/α . As inthe baseline case, if the distaste for in-flation is high (α is low), the optimalpolicy aggressively contracts demandwhenever inflation is above target: Withendogenous persistence, this contrac-tion not only reduces inflation but alsoincreases the speed of convergence totarget. Figure 2 illustrates the relationbetween aπ and α for three differentvalues of φ: φ = 0.01 (low inertia), φ = 0.5(medium) and φ = 0.99 (high).

Combining (6.3) with (6.1) yields theimplied optimal interest rate rule:

it = γπ Etπt + 1 + γxxt − 1 + 1ϕ gt (6.6)

with

γπ = 1 + λ(1 − aπ)

ϕαaπ(1 − βaπ)

γx = θϕ

Etπt + 1 = aππt

Most of the qualitative results ob-tained in the baseline case extend tothis more general setting. As in thebaseline case, the policy-maker faces ashort-run trade-off between output andinflation (Result 1). The effect of infla-tion inertia is to make this trade-off lessfavorable. Equation (6.3) shows thatrelative to the baseline case of φ = 0, theoptimal policy requires a more aggres-sive response to any burst of inflation.The problem is that any inflation noteliminated today persists into the fu-ture, potentially requiring more outputcontraction. Figure 3 illustrates how thetrade-off becomes less favorable in thiscase by plotting the efficient policyfrontier for the three benchmark valuesof φ. In addition, since 0 ≤ aπ < 1, the op-timal policy calls for gradual adjustmentof inflation to target (Result 2). Withφ > 0, further, extreme inflation target-ing is only optimal if α = 0, as equation(6.3) and Figure 2 suggest.

From the interest rate rule given by


equation (6.6) it is apparent that the co-efficient on expected inflation exceedsunity, implying that the ex ante realrate must rise in response to higher ex-pected inflation (Result 3). Finally, theinterest rate should also adjust to per-fectly offset demand shocks, but shouldnot respond to movements in potentialoutput (Result 4.) One interesting dif-ference in this case is that the interestrate responds to the lagged output gap,since this variable now enters the IScurve. Thus, the optimal interest raterule now resembles the simple gap rulesthat have been discussed in the litera-ture. We return to this point later. Insummary, we have

Result 13: Results 1 through 4 thatdescribe optimal monetary policy underdiscretion within the baseline modelalso apply in the case with endogenousoutput and inflation persistence.

In addition to allowing for lagged de-pendence in output and inflation, thereis also strong empirical justification forincorporating delays in the effect ofpolicy. It is straightforward to extendthe analysis to include this real worldfeature. Suppose, following Svensson(1997a,b) and Ball (1997), that there isa one-period delay in the effect of thereal interest rate on the output gap and,in turn, a one-period delay in the effectof the output gap on inflation. Then theoptimality condition becomes76

Etxt + 1 = − λ

α(1 − βaπl ) Etπt + 2 (6.7)

where the parameter aπl measures the se-

rial dependence in inflation for this case.It has qualitatively similar properties toaπ in equation (6.5), with 0 ≤ aπ

l < 1. Theleft side of (6.7) reflects the one-perioddelay in the impact of policy on output,

76 In this case, the IS curve is given by xt =− ϕ[it − 1 − Et − 1πt] + θxt − 1 + (1 − θ)Et − 1xt + 1 + gt andthe aggregate supply curve is given by πt =λxt − 1 + φπt − 1 + (1 − φ)βEtπt + 1 + ut.


and the right side reflects the two-perioddelay on inflation.

Due to the delayed impact of policy,the central bank takes both the outputgap at t, xt, and the forecast of inflationat t + 1, Etπt + 1, as predetermined fromthe vantage of time t. The rest of thesolution may thus be expressed in termsof these predetermined variables:

Etπt + 2 = aπl Etπt + 1 (6.8)

it = γπl Etπt + 1 + γx xt (6.9)

with

γπl = 1 +

(γπ − 1)βaπ

l > 1

The solution closely resembles thecase without delay. Any differences justreflect the lagged influence of policy inthis environment. The nominal rate stilladjusts more than one-for-one with ex-pected inflation. Due to the lag struc-ture, though, it adjusts to the currentoutput gap, as opposed to one from theprevious period.

We conclude this section with briefdiscussion of the gains from commit-ment. It is possible to show that, as inthe baseline model, the policy rule un-der commitment resembles the rule un-der discretion that would obtain if thepolicy-maker assigned a higher relativecost to inflation (lower value of α ) thanthe true social cost. Because inflationinertia is endogenous in this case, theoptimal policy with commitment im-plies a faster transition of inflation tothe optimum relative to what occurs un-der discretion. This can be seen by not-ing that the parameter which governsthe speed of convergence of inflation,aπ, is decreasing in the relative cost ofinflation 1/α (see Figure 4).77 Simplyput, disinflations will be swifter thanotherwise if credible commitment ispossible either directly or indirectly by

installing a conservative central bankchair.

7. Simple Rules for Monetary Policy

We next discuss some normative andpositive aspects of simple feedbackrules for the interest rate that havebeen discussed in the literature. We thendiscuss how these instrument-basedrules are related to simple rules for tar-gets that have been recently proposed,including inflation targeting and nomi-nal GDP targeting. Finally, we concludewith a brief discussion of the issue ofpossible indeterminacy of interest raterules.

7.1 Simple Interest Rate Rules

Taylor (1993a) ignited the discussionof simple interest rate rules.78 He pro-posed a feedback policy of the followingform:

it∗ = α + γπ (πt − π–) + γx xt (7.1)with

α = r– + π–

γπ > 1, γx > 0where it

∗ is the target interest rate thefeedback rule defines, π– is the target in-flation rate, and r– is the long-run equi-librium real interest rate.79 Also, we nowexpress all variables in levels, as opposedto deviations from trend.

A number of other researchers haveconsidered rules like (7.1) (see, e.g.,Henderson and Mckibbon 1993). Tay-lor’s contribution is to spell out the nor-mative and positive implications. On

77 Note that the speed of convergence of infla-tion is decreasing in aπ.

78 McCallum (1988) proposed a simple rule forthe monetary base. The rule is less popular in pol-icy circles due to the implied interest rate volatil-ity (see Result 9). McCallum (1997) argues, how-ever, that the concern about interest rate volatilityis not well understood, a point with which weagree.

79 The inflation rate Taylor uses is actually therate over the previous year (as opposed to the pre-vious quarter).


the normative side, the rule is consis-tent with the main principles for opti-mal policy that we have described. Itcalls for gradual adjustment of inflationto its target (see Result 2). Specifically,it has the nominal rate adjust more thanone-for-one with the inflation rate. Tothe extent lagged inflation is a goodpredictor of future inflation, the rulethus has real rates adjusting to engineerinflation back to target (see Result 3).Finally, note that the interest rate re-sponds to the output gap as opposed tothe level of output. Thus, in at least anapproximate sense, the rule calls for acountercyclical response to demandshocks and accommodation of shocks topotential GDP that do not affect theoutput gap (see Result 4).

On the positive side, Taylor showedthat with certain parameter values, the

rule provides a reasonably good descrip-tion of policy over the period 1987–92.These are: γπ = 1.5, γx = 0.5, π– = 2, andr– = 2. Taylor used informal judgementto pick them. An interesting question iswhether a formal methodology wouldyield something different.

In this spirit, Clarida, Galí, and Gertler(forthcoming) estimate a simple rule forU.S. monetary policy, and consider howthis rule has evolved over time. Thespecific formulation is a “forward look-ing” version of the simple Taylor rule:

it∗ = α + γπ (Etπt + 1 − π–) + γx xt (7.2)

Under this rule, policy responds toexpected inflation as opposed to laggedinflation. In this respect, the formula-tion is consistent with the optimal rulesderived for both the baseline and hy-brid models (see equations 3.6 and 6.6).


Another virtue is that this formulationnests the simple Taylor rule as a specialcase. If either inflation or a linear com-bination of lagged inflation and the out-put gap is a sufficient statistic for futureinflation, then the specification col-lapses to the Taylor rule.

Because of the Federal Reserve’s ten-dency to smooth interest rate adjust-ments (see the discussion in section 5),a static relation like equation (7.2) can-not capture the serial correlation pres-ent in the data. We thus allow for thepossibility of partial adjustment to thetarget rate, according to:

it = ρ it − 1 + (1 − ρ)it∗ (7.3)

where ρ is a parameter that measures thedegree of interest rate smoothing.

We estimate different rules for thepre-Volcker (1960:1–79:2) and Volcker–Greenspan (1979:3–96:4). We do so be-cause it is widely believed that U.S.monetary policy took an important turnfor the better with the appointment ofPaul Volcker as Fed Chairman (seeFriedman and Kuttner 1996 and Gertler1996). Among other things, this periodmarks the beginning of an apparentlysuccessful and long-lasting disinflation.

We find that the simple rule given byequation (7.2) does a good job of char-acterizing policy in the Volcker–Green-span era. Further, it adheres to theguidelines for good policy that we haveestablished. The estimated pre-Volckerrule violates these guidelines. Specifi-cally, the parameter estimates along

with standard errors are given by Table1.80

The key lesson involves the parame-ter γπ, the coefficient on the inflationgap. The estimate for the pre-Volckerrule is significantly less than unity. Thissuggests that monetary policy over thisperiod was accommodating increases inexpected inflation, in clear violation ofthe guidelines suggested by Results 2and 3. For the post-1979 rule the esti-mate is significantly above unity. It thusincorporates the implicit inflation tar-geting feature that we have argued is acritical feature of good monetary policymanagement. It is also true that in theVolcker–Greenspan era the Federal Re-serve was only responding to the outputgap to the extent it had predictivepower for inflation:81 The estimated co-efficient on the output gap, γx, is notsignificantly different from zero. Pre1979:4 it is positive and significant. Thisoutcome is consistent with the conven-tional view that pre-1979, the Federal

TABLE 1ESTIMATES OF POLICY REACTION FUNCTION

γπ γx ρ

Pre-Volcker 0.83 0.27 0.68(0.07) (0.08) (0.05)

Volcker–Greenspan 2.15 0.93 0.79(0.40) (0.42) (0.04)

80 The estimates of the parameters in equation(7.2) are obtained by using an instrumental vari-ables procedure based on Generalized Methods ofMoments (GMM). See Clarida, Galí, and Gertler(forthcoming) for details. The specific numbersreported here are based on a version of this policyreaction function that has the Funds rate respondto expected inflation a year ahead and the currentoutput gap (reported in Table 2 of that paper).The results, however, are robust to reasonablevariations in the horizons for the gap variables.

81 In particular, the output gap enters the in-strument set for expected inflation. Thus, thecoefficent γx reflects the influence of the outputgap on the interest rate that is independent of itspredictive power for inflation.


Reserve was relatively more focused onoutput stabilization and less focused oninflation.

The finding that the Fed respondeddifferently to inflation in the two eras isapparent from inspection of the data.Figure 4 plots the Federal Funds rateand the rate of CPI inflation from 1965to the present. The graph shows a clearbreak in the Funds rate process around1979.82 During most of the 1970s, theex post real rate was zero or negative.After 1979 it becomes positive. Whilemany factors influence the real rate, thetight monetary policy engineered byPaul Volcker surely provides the mostlogical explanation for this initial run-up.

Figure 5 illustrates the policy changeby plotting the estimated target value ofthe interest rate under the Volcker–Greenspan rule over the entire sampleperiod. The target rule does a good job

of capturing the broad movements inthe Funds rate for the second half ofthe sample, for which it was estimated.For the pre-Volcker period, matters aredifferent. The target (generated by theestimated Volcker–Greenspan rule) issystematically well above the historicalseries. In this concrete respect, policywas far less aggressive in fightinginflation in the earlier period.83

Figure 6 compares the ability of theforward and backward looking (Taylor)target rules to explain the post 1979data. Though we find that the data re-jects the backward looking rule in favorof the forward looking one,84 the two doa roughly similar job of accounting forthe behavior of the Funds rate. This oc-curs probably because, with U.S. data,

82 Huizinga and Mishkin (1986) present formalevidence of a structural break at this time.

83 Some but not nearly all the difference be-tween rates pre-1979 and the target values under apost-1979 rule could be accounted for by a secularchange in the real rate.

84 See Clarida, Galí, and Gertler (1998).


not much besides lagged inflation isuseful for predicting future inflation.

Finally, it is interesting to observethat the other major central banks, theBundesbank and the Bank of Japan,have behaved very similarly in the post-1979 era. In Clarida, Galí, and Gertler(1998), we estimate our specificationfor these central banks. The estimatedparameters in each case are quite closeto those obtained for the Federal Re-serve during the Volcker–Greenspanperiod. Thus, good policy managementappears to have been a global phenome-non. Perhaps this is not surprising sincethe successful disinflation has also beena world-wide event.

7.2 Simple Target Rules

There have also been proposed sim-ple rules for targets, as opposed to in-struments. Of these proposed policies,inflation targeting has received by farthe most attention (see Bernanke and

Mishkin 1997 for a recent survey). In-deed a number of central banks, mostnotably the Bank of England, have re-cently adopted formal inflation targets(see, e.g., Andrew Haldane 1996).

In one sense, inflation targeting in-volves nothing more than pursuing thekind of gradualist policy that our opti-mal policy calculation implies (see Re-sult 2). Indeed, all the leading real-world proposals call for gradualconvergence of inflation to target. Nonerecommend trying to hit the inflationtarget continuously, which is consistentwith our analysis. In this respect, therule we estimate for the period is per-fectly consistent with inflation targeting.

The rationale for inflation targeting,we think, is twofold. The first is simplyto guarantee that monetary policyavoids the mistakes of the pre-Volckerera by identifying a clear nominal an-chor for policy. (After all, Alan Green-span will not be around forever). The


inflation target is in effect the nominalanchor. Since the anchor is directly interms of inflation, it avoids the poten-tially instability problems associatedwith alternatives such as money growththat are only indirectly linked to infla-tion. For example, if there are largeshocks to money demand, then a moneygrowth target may fail precisely to pindown the equilibrium inflation rate.

The second rationale has to do withcredibility and commitment. We haveseen that it is in general optimal forpolicy-makers to place a higher weighton the costs of inflation than the truesocial loss function suggests (see Re-sults 6 and 7). The focus on inflationtargets may be viewed as a way to instilla higher effective weight on inflation inthe policy choice.

Price level targeting is another typeof simple rule that has been discussedin the literature. This policy, which maybe thought of as a more extreme versionof inflation targeting, has not receivedmuch support among policy-makers andapplied economists. There are severalproblems: First, if the price level over-shoots its target, the central bank mayhave to contract economic activity in or-der to return the price level to its goal.That is, inflation above the amount im-plied by the price level target must befollowed by inflation below this desiredamount in order to return the target.Under inflation targeting, bygones arebygones: overshooting of inflation inone year does not require forcing infla-tion below target in the following year.Second, the source of positive drift inthe price level maybe measurement er-ror (see the discussion in section 2.) Itwould be unfortunate to have measure-ment error induce tightening of mone-tary policy. Third, as McCallum (1997b)shows, the net reduction in price uncer-tainty under a price level target rule,may be small relative that obtained un-

der an inflation targeting policy. For allthese reasons, it is perhaps not surpris-ing that no major central bank hasadopted a price level target.

Another candidate variable for target-ing is nominal GDP. This approach hasalso received less attention in the re-cent literature, however. One problemis that if there are shifts in the trendgrowth of real GDP, the rule does notprovide a precise nominal anchor. An-other problem, emphasized by Ball(1997), is that the policy may be overlyrestrictive. In the hybrid model of sec-tion 5, for example, the optimal policyin general has the interest rate adjust tosome linear combination of expected in-flation, the output gap and demand dis-turbances. The weights depend uponthe underlying structural parameters ofthe model. Under nominal GDP target-ing, the central bank adjusts the inter-est rate to the sum of inflation and realGDP growth. It thus arbitrarily appliesan equal weight to each component ofnominal GDP. High nominal GDPgrowth, further, could occur when theeconomy is recovering from a recessionand is still well below full capacity. Arule that calls for raising interest ratesin response to above-target nominalGDP growth in these circumstancescould stifle the recovery.85

7.3 Indeterminacy under Interest Rate Rules

One criticism of simple interest raterules is that, under certain circum-stances, they may induce instability.That is, in many models there may notbe a determinate equilibrium underparticular parametrizations of the policy

85 See Ball (1997) and Svensson (1997b) for ex-plicit examples of how nominal GDP targetingcould produce adverse outcomes. McCallum(1997c), however, argues that these results aresensitive to the use of a backward-looking Phillipscurve. For the case in favor of nominal GDP tar-geting, see Hall and Mankiw (1994).


rule. In a classic paper, Thomas Sargentand Neil Wallace (1975), illustratedhow nominal indeterminacy may arise ifprices are perfectly flexible. Under aninterest rate rule the equilibrium pinsdown the level of real money balances.However, there are an infinite numberof combinations of the nominal moneystock and the price level that satisfy thisequilibrium condition.86 In this respect,the interest rate rule produces nominalindeterminacy.87

When there is sluggish price adjust-ment, the problem of nominal indeter-minacy vanishes. Last period’s pricelevel effectively serves a nominal an-chor. Simple interest rate rules thus donot produce price level indeterminacyin the frameworks we have analyzed.More generally, since there is little rea-son to believe that prices are perfectlyflexible, the issue of nominal indetermi-nacy does not seem important in prac-tice. On the other hand, there is poten-tially a problem of real indeterminacyin the case of price stickiness, as Wil-liam Kerr and Robert King (1996), Ber-nanke and Woodford (1997) and Clarida,Galí and Gertler (forthcoming) have re-cently emphasized.88 Two types of inde-

terminacy are possible. First, if in re-sponse to a rise in expected inflation,the nominal rate does not increase suf-ficiently to raise the real rate, then self-fulfilling bursts of inflation and outputare possible. A rise in expected infla-tion, leads to a fall in real rates that, inturn, fuels the boom. Indeed, the mone-tary policy rule that Clarida, Galí, andGertler (forthcoming) estimate for thepre-Volcker period permits exactly thiskind of sunspot behavior. The lessonhere is simply that a good monetary pol-icy rule should not accommodate rise inexpected inflation. It should insteadpursue the implicit kind of inflationtargeting that we have been emphasiz-ing. This boils down to raising nominalrates sufficiently to increase real rateswhenever expected inflation goes up.

As Bernanke and Woodford (1998)emphasize, indeterminacy is also possi-ble if the rule calls for an overly aggres-sive response of interest rates to move-ments in expected inflation. In thisinstance, there is a “policy overkill” ef-fect that emerges that may result in anoscillating equilibrium. Clarida, Galíand Gertler (forthcoming) show, how-ever, the magnitude of the policy re-sponse required to generate indetermi-nacy of this type greatly exceeds theestimates obtained in practice. This po-tential indeterminacy however doessuggest another reason why a gradualapproach to meeting an inflation targetmay be desirable.

8. Concluding Remarks

We conclude by describing severalareas where future research would bequite useful:

(1) It is always the case that moreknowledge of the way the macro-economy works can improve the perfor-mance of monetary policy. Particularlycritical, however, is a better understanding

86 McCallum (1997), however, argues that theprice level is in fact determined in this kind ofenvironment.

87 A recent literature shows that the govern-ment’s intertemporal budget constraint may re-store uniqueness under an interest rule, even inan environment with flexible prices. What is criti-cal is whether the interest on the debt is financedby taxes or money creation. See, for example,Woodford (1994), Sims (1994), and Leeper (1991).

88 These papers focus on local indeterminacy.See Jess Benhabib, Stephanie Schmidt-Grohe, andMartin Uribe (1998) for a discussion of global in-determinacy. To avoid global indeterminacy, thecentral bank may have to commit to deviate from asimple interest rate rule if the economy were toget sufficiently off track. This threat to deviate canbe stabilizing, much the way off the equilibriumpath threats induce uniqueness in game theory.Because the threat is sufficient to preclude inde-terminate behavior, further, it may never have tobe implemented in practice.


of the determinants of inflation. As wehave emphasized, the output/inflationtrade-off is highly sensitive to both thedegree and nature of the persistence ininflation. As a consequence, so too isthe speed at which monetary policyshould try to reach the optimal inflationrate. Rationalizing the observed persis-tence in inflation is thus a high priority.Work by Galí and Gertler (forthcoming)and Argia Sbordone (1998) suggests thatthe short-run aggregate supply curveemployed in our baseline model mayprovide a reasonable approximation ofreality, so long as real marginal cost(specifically real unit labor costs) is usedas the relevant real sector forcing vari-able instead of the output gap, as thetheory suggests. Galí and Gertler (forth-coming) argue further that persistencein inflation may be related to sluggishadjustment of unit labor costs vis-a-vismovements in output. Sorting out thisissue will have important repercussionsfor monetary policy.

(2) Our analysis of monetary policy,as in much of the literature, was re-stricted to closed economy models. Ex-tensions to open economy frameworksare likely to provide new insights on thedesirability of alternative monetary pol-icy rules, and raise a number of issuesof great interest, including: the choiceof exchange rate regime, the potentialbenefits from monetary policy coordi-nation, the optimal response to shocksoriginating abroad, and consumer priceindex versus domestic inflation target-ing. Recent work by Ball (1998), Svens-son (1998), and Monacelli (1999) alongthese lines will undoubtedly lay theground for further research on this front.

(3) Throughout the analysis, we as-sumed that the lower bound of zero onthe nominal interest rate was not a con-straint on the performance of monetarypolicy. In Japan, for example, the short-term nominal rate has fallen to the

point where this constraint clearly is aconsideration for policy management.Similarly, in the U.S. and Europe, theinflation rates have fallen to the pointwhere the zero bound limit could con-ceivably affect the ability to ease ratesin the event of a downturn. Under-standing how monetary policy shouldproceed in this kind of environment isan important task. When the nominalrate is at zero, the only way a centralbank can reduce the real interest rate isto generate a rise in expected inflation(see the discussion in Alexander Wol-man 1998, and the references therein).How the central bank should go aboutthis and whether cooperation from fis-cal policy is necessary are importantopen questions. As Wolman (1998) sug-gests, the conclusions are quite sensi-tive to the nature of the inflationaryprocess.

(4) A more specific issue, but none-theless an important one, is to under-stand why central banks smooth interestrate adjustments. As we discussed insection 5, optimal policies implied bymost existing macroeconomic frame-works generate paths for the interestrate that are much more volatile thanwhat is observed in reality. The possi-bility thus arises that existing modelsmay fail to adequately characterize theconstraints that policy-makers face inpractice. We suggested in section 5 thatsome form of model uncertainty mightbe able to account for this phenome-non. Another alternative is that centralbanks may be exploiting the depen-dency of demand on expected future in-terest rates, as argued by Rotembergand Woodford (1999). Whether theseexplanations or any others, such as fearof disruption of financial markets, canaccount for interest rate smoothingneeds to be determined.

(5) A somewhat related issue involveshow a central bank should deal with


financial stability. The policy rulesdiscussed in the literature do includecontingencies for financial crises. A fre-quently cited reason for why monetarypolicy should not adhere tightly to asimple rule is the need for flexibility inthe event of a financial collapse. In thewake of the October 1987 stock marketcrash, for example, most economistssupported the decision of the FederalReserve Board to reduce interest rates.This support was based largely on in-stinct, however, since there is virtuallyno formal theoretical work that rational-izes this kind of intervention. Moregenerally, concern about financial sta-bility appears to be an important con-straint on policy-making. As we sug-gested in section 5, it is one possiblereason why central banks smooth inter-est rate changes. Understanding the na-ture of this concern is clearly a fertilearea for research.

(6) Finally, with few exceptions, vir-tually all the literature ignores the issueof transition to a new policy regime.89

In particular, the rational expectationsassumption is typically employed. Policysimulations thus implicitly presume thatthe private sector catches on immedi-ately to any regime change. In reality,however, there may be a period of tran-sition where the private sector learnsabout the regime change. This kind ofscenario may be highly relevant to acentral bank that has accommodated in-flation for a sustained period of timebut is intent on embarking on a disinfla-tion. Modeling private sector learningis a challenging but nonetheless impor-tant task. Sargent (1999) provides apromising start in this direction. Morework along these lines would be highlydesirable.

Appendix: The General Solution under Commitment

At time t, the central bank commits to a statecontingent sequence for xt + i and πt + i to maximize

max − 12 Et

∑ i = o

∞βi[α xt + i

2 + πt + i2 ]

subject to the short-run aggregate supply curve

πt + i = λ xt + i + β Etπt + 1 + i + ut + i

with

ut + i = ρut + i − 1 + εt + i

Following Currie and Levine (1993) and Wood-ford (1998), form the Lagrangian:

max − 12 Et

∑ i = o

∞βi[αxt + i

2 + πt + i2 ]

+ φt + i[πt + i − λxt + i − βπt + 1 + i − ut + i]

where 12 φt + i is the multiplier associated with the

constraint at t + i. The first order necessary conditions yield:

α xt + i − λ2 φt + i = 0, ∀ i ≥ 0

πt + i + 12 φt + i −

12 φt + i − 1 = 0, ∀ i ≥ 1

πt + 12 φt = 0

Combining the first order necessary conditions toeliminate φt + i then yields the optimality condi-tions

xt + i − xt + i − 1 = − λα πt + i, ∀ i ≥ 1

xt = − λα πt

Substituting the optimality conditions in the ag-gregate supply curve to eliminate πt + i then yieldsa stochastic difference equation for xt:

xt = a xt − 1 + aβ Etxt + 1 − λa

α ut

where a ≡ α

α(1 + β) + λ2. The stationary solution to

this difference equation is given by:

xt = δ xt − 1 − λδ

α(1 − δβρ) ut (8.1)

where δ ≡ 1 − √ 1 − 4βa2

2aβ ∈( 0,1), implying the pro-

cess for xt is stable. Substituting the solution for xt

89 An exception is Brayton, Levin, Tyron, andWilliams (1997) who present simulations of policyregime changes under different assumptions aboutthe behavior of private sector expectations.


in the aggregate supply curve then yields a solu-tion for πt.

πt = δ πt − 1 + δ

(1 − δβρ) (ut − ut − 1)

Since πt = pt − pt − 1, the solution implies a station-ary process for the price level:

pt = δ pt − 1 + δ

(1 − δβρ) ut

The stationary behavior of the price level resultsfrom the fact that the optimality condition effec-tively has the central bank adjust demand in re-sponse to movements in the price level relative totrend. Given πt = pt − pt − 1, the optimality condi-tion may be expressed as

xt + i = − λα pt + i ∀ i ≥ 1

Thus, for example, the central bank contracts demandwhen the price level rises above trend: hence, thetrend-reverting behavior of the price level.

REFERENCES

Aiyagari, Rao S. and R. Anton Braun. 1998. “SomeModels to Guide the Fed,” Carnegie-RochesterConf. Ser. Public Policy, 48, pp. 1–42.

Ball, Laurence. 1995. “Disinflation with ImperfectCredibility,” J. Monet. Econ., 35:1, pp. 5–23.

———. 1997. “Efficient Rules for Monetary Pol-icy,” 1997. NBER Working Paper 5952.

———. 1998. “Policy Rules for Open Economies,”NBER Working Paper 6760.

Barro, Robert J. and David B. Gordon. 1983. “APositive Theory of Monetary Policy in a NaturalRate Model,” J. Polit. Econ., 91:4, pp. 589–610.

Benhabib, Jess; Stephanie Schmitt-Grohe, andMartin Uribe. 1998. “The Perils of TaylorRules,” mimeo, New York U.

Bernanke, Ben S. and Alan Blinder. 1992. “TheFederal Funds Rate and the Channels of Mone-tary Transmission,” Amer. Econ. Rev., 82:4, pp.901–21.

Bernanke, Ben. S. and Mark Gertler. 1995. “In-side the Black Box: The Credit Channel ofMonetary Policy Transmission,” J. Econ. Per-spect., 9:2, pp. 27–48.

Bernanke, Ben. S.; Mark Gertler, and Simon Gil-christ. 1998. “The Financial Accelerator in aQuantitative Business Cycle Framework,”NBER Working Paper 6455. Forthcoming inThe Handbook of Macroeconomics. John Taylorand Michael Woodford, eds.

Bernanke, Ben S.; Mark Gertler, and Mark Wat-son. 1997. “Systematic Monetary Policy and theEffects of Oil Price Shocks,” Brookings Pap.Econ. Act., 0:1, pp. 91–142.

Bernanke, Ben S. and Ilian Mihov. 1997. “WhatDoes the Bundesbank Target?” Europ. Econ.Rev., 41:6, pp. 1025–53.

———. 1998. “Measuring Monetary Policy,”Quart. J. Econ., 113:3, pp. 869–902.

Bernanke, Ben S. and Frederic Mishkin. 1997.“Inflation Targeting: A New Framework forMonetary Policy?” J. Econ. Perspect., 11:2, pp.97–116.

Bernanke, Ben S. and Michael Woodford. 1997.“Inflation Forecasts and Monetary Policy,” J.Money, Credit, Banking, 29:4, pp. 653–84.

Blanchard, Olivier J. 1997. Macroeconomics. Up-per Saddle River, NJ: Prentice-Hall.

Blinder, Alan S. 1997. “What Central Bankers CanLearn from Academics—and Vice-Versa,” J.Econ. Perspect., 11:2, pp. 3–19.

Bomfin, Antulio N. and Glenn D. Rudebusch.1997. “Opportunistic and Deliberate Disinfla-tion Under Imperfect Credibility,” mimeo, Fed.Res. Bank San Francisco.

Brainard, William C. 1967. “Uncertainty and theEffectiveness of Policy,” Amer. Econ. Rev., 57,pp. 411–25.

Brayton, Flint; Andrew Levin, Ralph Tryon, andJohn C. Williams. 1997. “The Evolution ofMacro Models at the Federal Reserve Board,”Finance Econ. Discuss. Paper Series, 1997–29,Fed. Res. Board.

Calvo, Guillermo. 1983. “Staggered Prices in aUtility Maximizing Framework,” J. Monet.Econ., 12:3, pp. 383–98.

Campbell, John Y. 1995. “Some Lessons from theYield Curve,” J. Econ. Perspect., 9:3, pp. 129–52.

Carlstrom, Charles T. and Timothy S. Fuerst.1995. “Interest Rate Rules vs. Money SupplyRules: A Welfare Comparison in a Cash-in-Ad-vance Model,” J. Monet. Econ., 36:2, pp. 247–68.

Chari, V.V.; Lawrence J. Christiano, and MartinEichenbaum, 1998. “Expectation Traps andDiscretion,” J. Econ. Theory, 81:2, pp. 462–92.

Christiano, Lawrence J. and Christopher J. Gust.1999. “Taylor Rules in a Limited ParticipationModel,” NBER Working Paper 7017.

Christiano, Lawrence J.; Martin Eichenbaum, andCharles Evans. 1996. “The Effects of MonetaryPolicy Shocks: Evidence from the Flow ofFunds,” Rev. Econ. Statist., 78:1, pp. 16–34.

———. 1997. “Sticky Price and Limited Participa-tion Models of Money: A Comparison,” Europ.Econ. Rev., 41:6, pp. 1201–49.

———. 1998. “Monetary Policy Shocks: WhatHave We Learned and To What End?” NBERWorking Paper 6400.

Clarida, Richard and Mark Gertler. 1997. “Howthe Bundesbank Conducts Monetary Policy,” inReducing Inflation: Motivation and Strategy.Christina Romer and David Romer, eds. Chi-cago: NBER, pp. 363–412.

Clarida, Richard; Jordi Galí, and Mark Gertler.Forthcoming. “Monetary Policy Rules and Mac-roeconomic Stability: Evidence and Some The-ory,” Quart. J. Econ.

———. 1998. “Monetary Policy Rules in Practice:Some International Evidence,” Europ. Econ.Rev., 42:6, pp. 1033–67.

Currie, David and Paul Levine. 1993. Rules, Repu-


tation and Macroeconomic Policy Coordination.Cambridge: Cambridge U. Press.

DeLong, J. Bradford. 1997. “America’s PeacetimeInflation: The 1970s,” in Reducing Inflation:Motivation and Strategy. C. Romer and D.Romer, eds. Chicago: NBER, pp. 247–80.

Erceg, Christopher J.; Dale W. Henderson, andAndrew T. Levin. 1998. “Output-Gap and PriceVolatilities: Reaffirming Tradeoffs in an Opti-mizing Model,” mimeo, Fed. Res. Board.

Estrella, Arturo and Frederic S. Mishkin. 1997. “IsThere a Role for Monetary Aggregates in theConduct of Monetary Policy?” J. Monet. Econ.,40:2, pp. 279–304.

———. 1999. “Re-Thinking the Role of NAIRU inMonetary Policy: Implications of Model Formu-lation and Uncertainty,” forthcoming in Mone-tary Policy Rules. John B. Taylor, ed.

Faust, John and Lars E. O. Svensson. 1998.“Credibility and Transparency: Monetary Policywith Unobservable Goals,” mimeo, Fed. Res.Board.

Feldstein, Martin S. 1997. “The Costs and Bene-fits of Going from Low Inflation to Price Stabil-ity,” in Reducing Inflation: Motivation andStrategy. C. Romer and D. Romer, eds. Chi-cago: NBER, pp. 123–66.

Feldstein, Martin and James H. Stock. 1996. “Meas-uring Money Growth when Financial MarketsAre Changing,” J. Monet. Econ., 37:1, pp. 3–27.

Fischer, Stanley. 1995. “Modern Approaches toCentral Banking. NBER Working Paper 5064.

Friedman, Benjamin M. 1990. “Targets and In-struments of Monetary Policy,” in Handbook ofMonetary Economics. Friedman and FrankHahn, eds. Amsterdam: North-Holland.

Friedman, Benjamin M. and Kenneth N. Kuttner.1996. “A Price Target for U.S. Monetary Policy?Lessons from the Experience with MoneyGrowth Targets,” Brookings Pap. Econ. Act., 1,pp. 77–146.

Fuhrer, Jeffrey C. 1996. “Towards a Compact,Empirically Verified Rational ExpectationsModel for Monetary Policy Analysis,” mimeo,Federal Reserve Bank of Boston.

———. 1997a. “Inflation/Output Variance Trade-offs and Optimal Monetary Policy,” J. Money,Credit, Banking, 29:2, pp. 214–23.

———. 1997b. “The (Un)Importance of ForwardLooking Behavior in Price Setting,” J. Money,Credit, Banking, 29, Aug., pp. 338–50.

Fuhrer, Jeffrey C., and George R. Moore. 1995a.“Inflation Persistence,” Quart. J. Econ., 440,Feb., pp. 127–59.

———. 1995b. “ Monetary Policy Trade-offs andthe Correlation between Nominal InterestRates and Real Output,” Amer. Econ. Rev.,85:1, pp. 219–39.

Galí, Jordi, 1992. “How Well Does the IS/LMModel Fit Post-War U.S. Data?” Quart. J.Econ., 92, pp. 709–38.

Galí, Jordi and Mark Gertler. Forthcoming. “In-flation Dynamics: A Structural EconometricAnalysis,” J. Monet. Econ.

———. 1999. “Rules vs. Discretion Revisited: TheGains from Commitment in the Absence of anInflationary Bias,” work in progress.

Gertler, Mark. 1996. “Comments on Friedmanand Kuttner,” Brookings Pap. Econ. Act., 1, pp.77–125.

Goodfriend, Marvin. 1991. “Interest Rates and theConduct of Monetary Policy,” Carnegie-Roches-ter Conf. Ser. Public Policy, 34, pp. 7–37.

Goodfriend, Marvin and Robert G. King. 1997.“The New Neoclassical Synthesis and the Roleof Monetary Policy,” in NBER MacroeconomicsAnnual. Ben Bernanke and Julio Rotemberg,eds.

Gordon, Robert J. 1997. “The Time-VaryingNAIRU and Its Implications for Economic Pol-icy,” J. Econ. Perspect., 11, Winter, pp. 11–32.

Haldane, Andrew. 1995. Inflation Targeting. Bankof England.

Hall, Robert E. 1997. “Comments on Shiller,”Brookings Pap. Econ. Act., pp. 219–23.

Hall, Robert E. and N. Gregory Mankiw. 1994.“Nominal Income Targeting,” in Monetary Pol-icy. N. G. Mankiw, ed. Chicago: U. ChicagoPress.

Henderson, Dale W. and Warren J. Mckibbon.1993. “A Comparison of Some Basic MonetaryPolicy Regimes for Open Economies,”Carnegie-Rochester Conf. Ser. Public Policy,39, pp. 221–317.

Huizinga, John and Frederic S. Mishkin. 1986.“Monetary Policy Regime Shifts and the Un-usual Behavior of Real Interest Rates,”Carnegie-Rochester Conf. Ser. Public Policy,24, pp. 231–74.

Ireland, Peter N. 1996a. “The Role of Countercy-clical Monetary Policy,” J. Polit. Econ., 104:4,pp. 704–23.

———. 1996b. “Expectations, Credibility, andTime-Consistent Monetary Policy,” mimeo,Rutgers U.

Jovanovic, Boyan and Masako Udea. 1997. “Con-tracts and Money,” J. Polit. Econ., 105, Aug.,pp. 700–708.

Kerr, William and Robert G. King. 1996. “Limitson Interest Rate Rules in the IS Model,” Econ.Quart., LXXXII, pp. 47–76.

King, Robert G. and Alexander L. Wolman. 1996.“Inflation Targeting in a St. Louis Model of the21st Century,” NBER Working Paper 5507.

———. 1998. “What Should the Monetary Author-ity Do When Prices Are Sticky?” Forthcomingin Monetary Policy Rules. John B. Taylor, ed.

Kydland, Finn E. and Edward C. Prescott. 1977.“Rules Rather Than Discretion: The Inconsis-tency of Optimal Plans,” J. Polit. Econ., 85, pp.473–91.

Leeper, Eric M. 1991. “Equilibria Under ‘Active’and ‘Passive’ Monetary and Fiscal Policies,” J.Monet. Econ., 27. pp. 129–47.

Leeper, Eric M.; Christopher Sims, and Tao Zha.1996. “What Does Monetary Policy Do?”Brookings Pap. Econ. Act., 2, pp. 1–63.

Lown, Cara S. and Robert Rich. 1997. “Is There


an Inflation Puzzle?” Fed. Res. Bank New YorkEcon. Policy Rev., 3:4, pp. 51–69.

McCallum, Bennett T. 1988. “Robustness Proper-ties of a Rule for Monetary Policy,” Carnegie-Rochester Conf. Ser. Public Policy, 29, pp. 173–204.

———. 1997a. “Crucial Issues Concerning Cen-tral Bank Independence,” J. Monet. Econ., 39,June, pp. 99–112.

———. 1997b. “Issues in the Design of MonetaryPolicy Rules,” NBER Working Paper 6016.Forthcoming in The Handbook of Macro-economics.

———. 1997c. “The Alleged Instability of Nomi-nal Income Targeting,” NBER Working Paper6291.

McCallum, Bennett T. and Edward Nelson. 1997.“An Optimizing IS-LM Specification for Mone-tary Policy and Business Cycle Analysis,” NBERWorking Paper 5875.

Monacelli, Tommaso. 1999. “Into the Mussa Puz-zle: Monetary Policy Regimes and the Real Ex-change Rate in a Small Open Economy,”mimeo, Boston College.

Onatski Alexei, and James H. Stock. 1999. “RobustMonetary Policy Under Model Uncertainty in aSmall Model of the U.S. Economy,” mimeo,Harvard U.

Orphanides, Athanasios. 1998. “Monetary PolicyEvaluation with Noisy Information,” mimeo,Fed. Res. Board.

Orphanides, Athanasios and David Wilcox. 1996.“The Opportunistic Approach to Disinflation,”Finance Econ. Discuss. Paper Series, 96–24,Fed. Res. Board.

Orphanides, Athanasios; David H. Small, VolkerWeiland, and David W. Wilcox. 1997. “A Quan-titative Exploration of the Opportunistic Ap-proach to Disinflation,” Finance Econ. Discuss.Paper Series, 36, Fed. Res. Board, WashingtonD.C.

Persson, Torsten and Guido Tabellini. 1997. “Po-litical Economics and Macroeconomic Policy,”mimeo, Inst. for International Economics,Stockholm.

Poole, William. 1970. “Optimal Choice of Mone-tary Policy Instruments in a Simple StochasticMacro Model,” Quart. J. Econ., 84, pp. 197–216.

Roberts, John M. 1997. “Is Inflation Sticky?” J.Monet. Econ., 39, pp. 173–96.

Rogoff, Kenneth. 1985. “The Optimal Degree ofCommitment to an Intermediate Monetary Tar-get,” Quart. J. Econ., 100:4, pp. 1169–89.

———. 1987. “Reputational Constraints on Mone-tary Policy,” Carnegie-Rochester Conf. Ser.Public Policy, 26, 141–81.

Romer, Christina D. and David H. Romer. 1989.“Does Monetary Policy Matter? A New Test inthe Spirit of Friedman and Schwartz,” NBERMacroeconomics Annual.

Rotemberg, Julio. 1996. “Prices, Hours and Out-put: An Empirical Analysis Based on a StickyPrice Model,” J. Monet. Econ., 37, pp. 505–34.

Rotemberg, Julio and Michael Woodford. 1997.“An Optimization-Based Econometric Frame-work for the Evaluation of Monetary Policy,”NBER Macroeconomics Annual. Ben Bernankeand J. Rotemberg, eds.

———. 1999. “Interest Rate Rules in an Esti-mated Sticky Price Model,” in Monetary PolicyRules. John B. Taylor, ed. Forthcoming.

Rudebusch, Glenn D. 1995. “Federal Reserve In-terest Rate Targeting, Rational Expectationsand the Term Structure,” J. Monet. Econ. 35:pp. 245–74.

Rudebusch, Glenn D. and Lars Svensson. 1998forthcoming. “Policy Rules for Inflation Tar-geting,” in Monetary Policy Rules. John Taylor,ed.

Sack, Brian. 1997a. “Uncertainty and GradualMonetary Policy,” mimeo, Fed. Res. Board.

———. 1997b. “Does the Fed Act Gradually? AVAR Analysis,” mimeo, Fed. Res. Board, May.

Sargent, Thomas J. 1998. “The Conquest ofAmerican Inflation,” mimeo, Econ. Dept., Stan-ford U.

———. 1999. “Comment on Ball,” forthcoming inMonetary Policy Rules. John B. Taylor, ed.

Sargent, Thomas J. and Neil Wallace. 1975. “Ra-tional Expectations, the Optimal Monetary In-strument and the Optimal Money Supply Rule,”J. Polit. Econ., 83, pp. 241–54.

Sbordone, Argia. 1998. “Prices and Unit LaborCosts: A New Test of Sticky Prices,” mimeo,Rutgers U.

Shiller, Robert J. 1997. “Public Resistance to In-dexation: A Puzzle,” Brookings Pap. Econ. Act.,pp. 159–212.

Sims, Christopher. 1994. “A Simple Model for theDetermination of the Price Level and the Inter-action of Monetary and Fiscal Policy,” Econ.Theory, 4, pp. 381–99.

Svensson, Lars E. O. 1997a. “Inflation ForecastTargeting: Implementing and Monitoring Infla-tion Targets,” Europ. Econ. Rev., 41, June, pp.1111–47.

———. 1997b. “Inflation Targeting: Some Exten-sions,” NBER Working Paper 5962, March,forthcoming in Scand. J. Econ.

———. 1997c. “Optimal Inflation Targets, Con-servative Central Banks, and Linear InflationContracts,” Amer. Econ. Rev.

———. 1998. “Inflation Targeting as a MonetaryPolicy Rule,” NBER Working Paper 6790,forthcoming in J. Monet. Econ.

———. 1998. “Open-Economy Inflation Target-ing,” mimeo, forthcoming in J. Int. Econ.

Svensson, Lars E.O. and Leonardo Leiderman.1995. Inflation Targets. London: CEPR.

Taylor, John B. 1979. “Estimation and Control ofMacroeconomic Model with Rational Expecta-tions,” Econometrica, 47, Sept., pp. 1267–86.

———. 1993a. “Discretion versus Policy Rules inPractice,” Carnegie-Rochester Conf. Ser. PublicPolicy, 39, pp. 195–214.

———. 1993b. Macroeconomic Policy in a WorldEconomy. NY: W.W. Norton.


———, ed. 1999a. Monetary Policy Rules. Chi-cago: U. Chicago Press. Forthcoming.

———. 1998b. “An Historical Analysis of Mone-tary Policy Rules,” in Monetary Policy Rules.John B. Taylor, ed. Forthcoming

Theil, Henri. 1961. Economic Forecasts and Pol-icy, 2nd ed. Amsterdam: North-Holland.

Tinbergen, Jan. 1952. On the Theory of EconomicPolicy, 2nd ed. Amsterdam: North-Holland.

Walsh. Carl. 1998. Monetary Theory and Policy.MIT Press.

Wieland, Volker. 1997. “Monetary Policy and Un-certainty about the Natural UnemploymentRate,” mimeo, Fed. Res. Board.

Williams, John C. 1997. “Simple Rules for Mone-tary Policy,” mimeo, Fed. Res. Board.

Wolman, Alexander. 1998. “Staggered Price Setting

and the Zero Lower Bound on the Nominal In-terest Rate,” mimeo, Fed. Res. Bank Richmond.

Woodford, Michael. 1994a. “Nonstandard Indica-tors for Monetary Policy,” in Monetary Policy.N. Gregory Mankiw ed. Chicago: U. ChicagoPress, pp. 95–115.

———. 1994b. “Monetary Policy and Price LevelDeterminacy in a Cash-in-Advance Economy,”Econ. Theory, 4, pp. 345–80.

———. 1996. “Control of the Public Debt: A Re-quirement for Price Stability?” NBER WorkingPaper 5684.

———. 1998. “Optimal Monetary Policy Inertia,”mimeo, Princeton U.

Yun, Tack. 1996. “Nominal Price Rigidity, MoneySupply Endogeneity, and Business Cycles,” J.Monet. Econ., 37, pp. 345–70.


the science of monetary policy: a new keynesian perspective1.pdf · bernanke and blinder (1992),...

Documents