Clarida Gali Gertler 1999

7/27/2019 Clarida Gali Gertler 1999

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Journal of Economic L it er ature

Vol. XXXVI I(December 1999), pp . 16611707

Clar ida, Gal, Gert ler: T he Science of M onetar y Poli cy

The Science of Monetary Policy:A New Keynesian Perspective

Richard Clarida, Jordi Gal, andMark Gertler1

Havi ng looked at monetary policy fr om both sides now, I can testi fy t hatcentr al banki ng i n p r acti ce is as much ar t as science. Nonetheless, wh il epr acticing t hi s dark art , I have always found the science qui te useful .

2

Alan S. Blinder

1. Introduction

THEREHASBEEN 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 proposed

specific policy rules or have at leaststaked out a position on what the generalcourse of monetary policy should be.

John Taylors 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. I t 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

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1 Clarida: Columbia University and NBER; Gal:New York University, Universitat Pompeu Fabra,CE PR, 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 to

Tommaso Monacelli for excellent research assis-tance. Authors Gal and Gertler are grateful to theC.V. Starr Center for Applied Economics, and(Gal) to CRE I for financial support. e-mail:[email protected]

2 Blinder 1997, p. 17.

3 Examples include Romer and Romer (1988),Bernanke and Blinder (1992), Gal (1992), Ber-nanke and Mihov (1997a), Christiano, Eichen-baum, and Evans (1996, 1998) and Leeper, Simsand Zha (1996). M uch 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.


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analysis. A key point of departure fromreal business cycle theory (as we later

make 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 with

a 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 make

clear 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.4

There are, however, important strands

of 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 policy

problem. 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). F or an analysis of monetary pol-icy rules in these kinds of modelsknown as lim-ited participation frameworkssee Christianoand Gust (1999).

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

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whether there may be gains from en-hancing credibility either by formal

commitment 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. I ffor 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. F inally, how the cen-tral bank should adjust the interest ratein response to output disturbances de-pends critically on the nature of the dis-turbances: I t should offset demandshocks but accommodate supply shocks,as we discuss.

Section 4 turns to the case with com-mitment. Much of the literature has

emphasized that an inefficiently highsteady state inflation rate may arise inthe absence of commitment, if the cen-tral banks target for real output ex-ceeds the market clearing level.7 The

gain from commitment then is to elimi-nate this inflationary bias. How realistic

it 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. I n 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).

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things, the analysis makes clear whymodern central banks (especially the

Federal 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 of

persistence 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. I n 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,Gal, 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. I n particular, the evidence suggests

that U.S. monetary policy in the fifteenyears or so prior to Paul Volcker did not

always 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 Baseli ne Fr amewor k for Analysisof Monetary Policy

This section characterizes the formalmonetary policy design problem. I t 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 commitmentwhatthe literature refers to as the cases ofrules versus discretion.

2.1 A Simp le Macr oeconomicFramework

Our baseline framework is a dynamicgeneral equilibrium model with money

and temporary nominal price rigidities.In recent years this paradigm has be-come widely used for theoretical analy-sis of monetary policy.8 I t 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.



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IS/LM model, yet is grounded in dy-namic general equilibrium theory, in

keeping with the methodological ad-vances in modern macroeconomics.Within the model, monetary policy

affects 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 on

current policy. I n 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 ytand ztbe 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. I t is thus convenient

to define the output gap xt:xtytzt

In addition, let tbe the period tinfla-tion rate, defined as the percent change

in the price level from t1 to t; and let itbe the nominal interest rate. Each vari-able is similarly expressed as a deviationfrom its long-run level.

I t 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= [itEtt+ 1] +Etxt+ 1+gt (2.1)

t=xt+Ett+ 1+ut (2.2)

where gt and ut are disturbances termsthat obey, respectively:

gt=gt 1+g^t (2.3)

ut=ut 1+u^t (2.4)

where 0, 1 and where both g^tandu^tare i.i.d. random variables with zero meanand variances g2 and u2, respectively.

Equation (2.1) is obtained by log-linearizing the consumption euler equa-tion that arises from the householdsoptimal saving decision, after imposing

the 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.

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

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

ytet= [itEtt+ 1] +Et{yt+ 1et+ 1}

where et log(1Et

Yt) is taken to evolve ex-

ogenously. Using xtytzt, it is then possible toderive the demand for output as

xt= [itEtt+ 1] +Etxt+ 1+gt

where gt=Et{zt+ 1et+ 1}.



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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, , corresponds tothe intertemporal elasticity of substitu-tion. The disturbance gtis a function ofexpected changes in government pur-chases relative to expected changes inpotential output (see footnote 11).

Since gtshifts 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.

I t is instructive to iterate equation(2.1) forward to obtain

xt=Eti= 0

{[it+it+ 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 as

current policy actions affect aggregatedemand.The Phillips curve, (2.2), evolves

from staggered nominal price setting, inthe spirit of Stanley Fischer (1977) and

John Taylor (1980).12 A key differenceis that the individual firm price-setting

decision, 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/Xof firms set pricesfor X> 1 periods. In general, however,aggregating the decision rules of firms

that 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 itmust keep its price fixed during that pe-riod and, hence a probability 1 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 11 .

Thus, for example, if = .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 afirms 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

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

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



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1997). A key difference with the stan-dard Phillips curve is that expected fu-

ture inflation, Ett+ 1, enters additively,as opposed to expected current infla-tion, Et 1t.14 The implications of thisdistinction are critical: To see, iterate(2.2) forward to obtain

t=Eti= 0

i[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 current

and expected future economic condi-tions. Roughly speaking, firms set nomi-nal price based on the expectations offuture marginal costs. The variable xt+icaptures 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 in

inflation 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 I lian 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 (198082) under Paul Volcker.16With the nominal rate as the policy in-strument, it is not necessary to specify amoney market equilibrium condition(i.e., an LM curve).17 I n 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

14Another key difference is that the explicitderivation restricts the coefficient on the outputgap. In particular, is decreasing in , 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.

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

t=Et{t+1}+mct

wheremctdenotes 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=xtholds, where isthe output elasticity of real marginal cost. In thisinstance, one can rewrite the relation for inflationin terms of the output gap, as follows:

t=Et{t+1}+xt (see Gal and Gertler (1998)for details). In this context, the disturbance ut in(2.2) is interpretable as reflecting deviations fromthe condition mct= xt. (I ndeed the evidence inGal and Gertler 1998 suggests that mctdoes 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 theut 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).

16Roughly 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-M ihovtest). I nformally, 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 the

policy instrument is widely held by both practitio-ners of monetary policy and academic researchers(see, e.g., Goodfriend 1991, Taylor 1993, andWalsh 1998).

17With 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.



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complex, empirically based frameworksthat are used for policy analysis.18 As in

these 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 Objecti ve

The central bank objective functiontranslates the behavior of the targetvariables into a welfare measure to

guide the policy choice. We assume,following much of the literature, thatthis objective function is over the tar-get variables xt and t, and takes theform:

max1

2Et

i= 0

i[xt+i2 +t+i2 ]

(2.7)

where the parameter is the relativeweight on output deviations. Sincextytzt, the loss function takes poten-tial output ztas the target. I t 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. I fsome 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

18Some 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).

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

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

21Underlying 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).



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literature takes a pragmatic approach tothis issue by simply assuming that the

objective 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, , 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 no

longer a public concern. I n 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 positive

rate of inflation is consistent with pricestability, and cite measurement error asone of the reasons (Clarida and Gertler1997).

I t 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 and

simply explore the implications foroptimal policy rules.

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

23Two 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.



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2.3 The Policy Pr oblem and D iscr eti onversus Rules

The policy problem is to choose atime path for the instrument itto engi-neer time paths of the target variablesxt and t 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 certainty

equivalent 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 il lustratethis point explicitly.

From the standpoint of policy design,the issue is to identify whether some

type 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 adjusting

the 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 the

discretion to do so. (For this reason, thepolicy that emerges in equilibrium underdiscretion is termed time consistent.)In contrast, under a rule, it is simply

24In 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 banks desire topush output above potential output gives rise tothe credibili ty 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.



11/47

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. As

Taylor (1993a) argues, common senseapplication of these guidelines may im-prove the performance of monetary pol-

icy. We expand on this point later. I naddition, understanding the qualitativedifferences between outcomes underdiscretion versus rules can provide les-sons for the institutional design ofmonetary policy. For example, as wediscuss, Rogoffs (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. Opti mal Monetary Poli cy 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. I n this re-spect, it seems paramount to under-stand the nature of optimal policy inthis environment. Second, as we have

just 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,t,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). I t is convenient to dividethe problem into two stages: First, thecentral bank chooses xtand t to maxi-mize the objective (2.7), given the infla-

tion equation (2.2).25 Then, conditionalon the optimal values ofxtand t, it de-termines the value of it implied by theIS curve (2.1) (i.e., the interest ratethat will support xtand t).

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 banks 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

25Since 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. I nsection 6 we consider a very general Phillips curvethat is a hybrid of different approaches and showthat the qualitative results remain intact. I t is inthis sense that our analysis is quite robust.

26We 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, I reland (1996b). On theother hand, Chari, Christiano, and Eichenbaum(1998) argue that this indeterminacy could providea source of business fluctuations.



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problems:27 Each period, choose xtandtto maximize

12[xt2+t2]+Ft (3.1)

subject to

t=xt+ft (3.2)

taking as given Ftand ft, where

Ft1

2Et

i= 1

i[xt+i2 +t+i2 ]

and

ftEtt+ 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 todays ac-tions, and (b) the central bank cannotdirectly manipulate expectations.

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

xt=

t (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 xtdepends positively on the gain inreduced inflation per unit of output loss,, and inversely on the relative weightplaced on output losses, .

To obtain reduced form expressionsfor xt and t, combine the optimalitycondition (fonc) with the aggregate sup-ply curve (AS ), and then impose that

private sector expectations are rational:xt= qut (3.4)

t=qut (3.5)where

q= 12+(1)

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=Ett+ 1+1

gt (3.6)

where

= 1 +(1)

> 1

Ett+ 1=t=qutThis 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 t he extent cost push in-fl ati on i s present , t here exists a shor t

run trade-off between inflation and

output var i abi l i t y .

This result was originally emphasized

by 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,xand , vary with central bank prefer-ences, as defined by . Figure 1 por-trays the efficient policy frontier for our

27In 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.

28For 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.



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baseline model.29 I n (x,) 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 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 0: x=u

; = 0 (3.7)

As: x= 0; =u

1 (3.8)

where uis the standard deviation of thecost push innovation.

I t is important to emphasize that thetrade-off emerges only if cost push in-flation is present. In the absence of costinflation (i.e., with u= 0), there is notrade-off. I n 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. I f cost push fac-tors drive inflation, however, it is only

possible to reduce inflation in the nearterm by contracting demand. Thisconsideration leads to the next result:

Result 2:The optimal policy incorp o-rates inflation targeting in the sense

that i t r equir es to aim f or conver gence

of inf lati on to it s tar get over ti me. Ex-

tr eme infl ation t argeti ng, however , i.e.,

adjusting policy to immediately reach

an inflation target, is optimal under

only one of tw o cir cumstances: (1) cost

push i nfl ation i s absent; or (2) th er e is

no concer n f or output deviati ons (i .e.,

= 0).In the general case, with > 0 and

u> 0, there is gradual convergence ofinflation back to target. From equations(3.5) and (2.4), under the optimal policy

limi

Et{t+i}= limi

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



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In this formal sense, the optimal pol-icy embeds inflation targeting.30 With

exogenous 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 u= 0 (no cost push inflation),adjusting policy to immediately hit the

inflation 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 = 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 L aurence 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 opti mal poli cy,i n r esponse to a r i se in expected in fl a-

tion, nominal rates should rise suffi-

cientl y t o incr ease real r ates. Put di ffer-

ently, in the optimal rule for the

nomi nal r ate, the coeff i cient on expected

inf lati on should exceed un it y.Result 3 is transparent from equation

(3.6). I t 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, Gal, and Gertler (forth-coming) find that U.S. monetary policyin the pre-Volcker era of 196079 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 opti mal poli cy call s foradjusti ng the in terest rate to per fectly off-

set demand shocks, gt, but per fectl y ac-

commodate shocks to potent ial outpu t, zt,by keepi ng the nominal r ate 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

30Note 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 with = 0 as corresponding to strict inflation targetingand > 0 as corresponding to flexible inflationtargeting.



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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. I nturn, 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 to

describe well the current behavior ofmonetary policy. Output growth wassubstantially above trend in recent times,but with no apparent accompanying in-flation.33Based 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. L ater weexplore some implications of relaxingthis assumption.

4. Cr edibi li ty and the Gainsfr om 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. I t 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 emphasized

more in applied discussions of policy. I tfocuses 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

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

movements in gt.32That 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.

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

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

Tabellini (1997).35While the inflationary bias result is best

known 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.



16/47

the literature that have been suggestedto inject this credibility. An important

result we wish to stressand one thatwe dont think is widely understood inthe literatureis 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 I nfl ationar yBi as 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

max1

2Et

i=o

i[(xt+ik)2+t+i2 ]

(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 in the Phillips curve at unity.38

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

xtk=

tk+k (4.2)

The superscript kindicates 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)

tk=t+

k (4.4)

where xtand tare 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 k.

Thus, we have the familiar result in theliterature:

Result 5. I f t he centr al bank desir esto push output above potential (i.e.,

k> 0), then under d iscreti on a subopt i -mal equil i bri um may emer ge wi th infl a-

tion persistently above target, and no

gain i n outp ut.The model we use to illustrate this

36A 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).

37With inflationary bias present, it is also possi-ble to improve welfare by assigning a higher cost

to 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.

38Otherwise, 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.



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result differs from the simple expecta-tional Phillips curve framework in

which 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 kin the optimality condi-tion (4.2) reflects this temptation. A ra-tional private sector, however, recog-nizes the central banks incentive. I n

mechanical terms, it makes use of equa-tion (4.2) to forecast inflation, since thiscondition reflects the central bankstrue 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 ifkwere 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 ), than society as a whole:

Result 6:Appoin ti ng a centr al bankchair who assi gns a higher r elat iv e cost

to i nfl ation t han society as a whole r e-duces the ineffi cient inf lati onar y bi as that

is obtained under discr eti on whenk> 0.One can see plainly from equation

(4.4) that letting someone with prefer-ences given by R


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transition to an era of low inflation dur-ing the 1980s and 1990s. A possible

counterargument 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-term

costs 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. I nformal 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 emphasized

in 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. I n our baseline model,however, short-run price dynamics de-

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

4.2 I mproving the Short-RunOutput /I nflati on Tr ade-off: Gains

fr om Commitment wit h 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+iand t+ito 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 Monetar y Poli cy underCommitment: The Opti mum wit hin

a Simp le Famil y of Policy Rul es(that i ncludes the optimal r ule

under di scretion)

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

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



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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= ut (4.5)

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

cdenotesthe 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 =qshown in 3.4).

Combining equation (4.5) with thePhillips curve (2.2), in turn, implies thatinflation under the rule, tc, is also a lin-ear function of the cost push shock:

tc=xtc+Ett+ 1c +ut (4.6)

=Eti= 0

i[xt+ic +ut+i] (4.7)

=Eti= 0

i[ut+i+ut+i] (4.8)

=11

ut (4.9)

The problem for the central bank isto choose the optimal value of the feed-back parameter . 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

tc

=

1 xtc

+

1

1 ut (4.10)In this case, a one percent contraction inxtcreduces tcby the factor 1 . Under

discretion, reducing xt by one percentonly produces a fall in t of 0. The prob-

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

xtc=

c

tc(4.12)

where

c

(1 )


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to inflation is the product of the im-proved output/inflation trade-off that

commitment affords. Specifically, theoutput cost of lowering inflation declinesfrom to cper unit, since reducing in-flation a given amount requires, ceterisparibus, only a fraction (1) 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 xtcand

tc are easily obtained by combining

equations (4.12) and (4.10):xtc= qcut (4.14)

tc= cqcut (4.15)with

qc=1

2+c(1 )I t is interesting to observe that the

solution under commitment in this caseperfectly resembles the solution ob-tained under discretion that arises when is replaced with c


21/47

and output. This gain fr om commitment

ar i ses even if th e cent r al bank does not

prefer to have output above potential(i.e., even when k=0). The solut i onunder commi tment i n th i s case perf ectl y

resembles the solution that would ob-

tain f or a centr al bank wit h di screti on

that assi gned to i nfl ati on a hi gher cost

than the tr ue social cost.

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

obtain

it=cEtt+ 1+1

gt (4.16)

with

c 1 +(1 )

c> 1 +

(1)

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 Unconstr ained Opti mum

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 private

sector expectations of the future.The first stage problem remains tochoose a state-contingent sequence for

xt+i and t+i to maximize the objective(2.7) given that the aggregate supply

curve (2.2) holds in every periodt+i, i 0. We no longer restrict thechoice ofxtto 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 L evine (1993) and Woodford(1998), and form the Lagrangian:45

max1

2Et

i= 0

i[xt+i2

+t+i2

+t+i(t+ixt+it+i+ 1ut+i)]

(4.17)

where1

2t+i is the (state-contingent)

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

xt+ixt+i 1=

t+i,

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

and

xt=

t (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

44We 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.

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



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(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 xtis response tot, as i fit 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 policy

rule arises as a product of the centralbanks ability under commitment to di-rectly manipulate private sector expec-tations.47 To see this for our framework,keep in mind that tdepends 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 t+i falls back to target.

The optimal policy under commitment,however, is to continue to reduce xt+iaslong as t+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 ofton fu-ture values ofxt). Relative to the case of

discretion, 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 t with expected fu-ture values of xt+ias well as current xt.I t 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 it

implemented 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 the

optimal policy might have undesirable

46Woodford (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 into

lagged dependence in the former.47Woodford (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.

48On the surface it appears that the differencerule for xtmight be unstable. However, tadjuststo ensure that this is not the case. I n particular,the optimal response to a positive cost push shockis to contract xtsufficiently to push tbelow tar-get. xt then adjusts back up to target over time.

The appendix provides the details.



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

interest rate rule

it=1

Ett+ 1+

1

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 that

are clearly suboptimal.49

Overall, we have:Result 8:The globall y optimal policy

r ule under commi tment has the centr al

bank partially adjust demand in re-

sponse to inflationary pressures. The

id ea is to exploit the dependence of cur -

rent inflation on expected future de-

mand. I n addit i on, whi le appointi ng a

conservative central banker may raise

welf are under di screti on (see Resul t 7) ,

it does not appear t hat i t i s possi ble to

attain the globally optimal rule with

th is str ategy. Fi nall y, there may be somepr acti cal compli cati ons in i mplementi ng

the globally optimal interest rate rule

that in volve potential in determi nacy, as

di scussed i n W oodford (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. Practi cal 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 I mper fect I nformation

Thus far we have assumed that thecentral bank is able to control perfectlythe paths of the key target variables. I npractice, 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. F irst, 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, as

opposed 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

49Indeterminacy 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,Gal, and Gertler (1998).



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bank uses the short-term interest rateor a monetary aggregate as the policy

instrument, 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 For ecasts as Targets andI ntermediate 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 tbe the cen-tral banks 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| t=

Et| t

(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 variables

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

Iand tI, are given by

xtI=xt+

2+

u^t+g^t=g^t (5.2)

tI=1 +

2

t+g^t=u^t+g^t (5.3)

where xtand tare the optimal values ofthe target variables that emerge in caseof perfect information (when utis seriallyuncorrelated),53 and where u^tand g^tarethe 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. On

the 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 g^thas a variancesufficiently large relative to that ofu^t.

I t is straightforward to generalize the

analysis to a setting where the imper-fect observability stems from lags in the

50To 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.

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

52

Thus, tis similarly the private sectors infor-mation set. Specifically, we let firms observe thecurrent values of their marginal costs, but neitherfirms nor households can observe contemporane-ous aggregate variables. I n this instance, the I Sand Phillips curve equations are respectively givenby

xt= [(it| t)Et 1t+1] +Et 1xt+1+gt

t=xt+Et 1t+ 1+ut

53When utis serially uncorrelated, xt=

2+ut

and t=

2+ut.

54To prove that imperfect information leads to areduction in welfare, evaluate the welfare functionwith xtIand tIversus xtand t.



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transmission of monetary policy. Thiscase is of interest since much of the

available 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 ittakesjperiods for a shift in the currentinterest rate to affect output and an-other kperiods for an impact on infla-tion. In the left side of equation (5.1)would appear thejperiod 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. I t ispossible to circumvent this problem, ac-cording to Svensson, by focusing in-stead on the inflation forecast. Theforecast is immediately available. I tthus 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. I f demand for a particular aggre-gate is stable, then this aggregate islikely to have a stable covariance withnominal GDP. I n practice, however, ex-perience with monetary targeting hasnot been successful. The U.S. and the

U.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 and55Gal (1992), Christiano, Eichenbaum, and

Evans (1996), and Bernanke and Mihov (1997a)document the slow response of GDP to a policy

shock, 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. I nventories ad-

just to reconcile the gap between spending andoutput.

56Bernanke 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.

57See 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.



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inflation is likely to vary with changesin the policy rule. I n the end, there is

no simple substitute for employing astructural model.To summarize, we haveResult 9: With imperfect informa-

ti on, stemming eit her fr om data pr ob-

lems or l ags in the eff ect of poli cy, the

optimal policy rules are the certainty

equi valent versions of the perf ect in for -

mation case. Policy rules must be ex-

pr essed i n t erms of th e for ecasts of t ar-

get var iables as opposed t o the ex post

behavi or . Using obser vable i nt ermediate

tar gets, such as br oad money aggregates is

a possibi li ty , but experi ence suggests thatthese indi r ect i ndi cator s ar e gener ally

too unstable to be used i n pr actice.

5.1.2 The Instr ument Choi ce Problem:The Int erest Rate ver sus a Nar r ow

Monetar y Aggregate

We now turn to the issue of instru-ment choice. I n 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 reservesmtis given by59

mtpt=ytit+vt (5.4)

where pt is the price level and vt is arandom disturbance to money demand.

I fvt is perfectly observable then it doesnot matter whether itor 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

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Clarida Gali Gertler 1999