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 that central banking in practice is as much art as science. Nonetheless, while practicing this dark art, I have always found the science quite useful.”2 Alan S. Blinder

1. Introduction Two main factors underlie this re- birth of interest. First, after a long pe- HERE HAS BEEN a great resurgence riod of near exclusive focus on the role Tof interest in the issue of how to con- of nonmonetary factors in the business duct monetary policy. One symptom of cycle, a stream of empirical work begin- this phenomenon is the enormous vol- ning in the late 1980s has made the case ume of recent working papers and con- that monetary policy significantly influ- ferences on the topic. Another is that ences the short-term course of the real over the past several years many leading economy.3 The precise amount remains macroeconomists have either proposed open to debate. On the other hand, specific policy rules or have at least there now seems to be broad agreement staked out a position on what the general that the choice of how to conduct course of monetary policy should be. monetary policy has important conse- John Taylor’s recommendation of a sim- quences for aggregate activity. It is no ple interest rate rule (Taylor 1993a) is a longer an issue to downplay. well-known example. So too is the recent Second, there has been considerable widespread endorsement of inflation tar- improvement in the underlying theoret- geting (e.g., Ben Bernanke and Frederic ical frameworks used for policy analysis. Mishkin 1997). To provide theoretical underpinnings, 1 Clarida: Columbia University and NBER; Galí: the literature has incorporated the tech- New York University, Universitat Pompeu Fabra, niques of dynamic general equilibrium CEPR, and NBER; Gertler: New York University theory pioneered in real business cycle and NBER. Thanks to Ben Bernanke, Bob King, Ben McCallum, Albert Marcet, Rick Mishkin, Athanasios Orphanides, Glenn Rudebusch, Chris 3 Examples include Romer and Romer (1988), Sims, Lars Svensson, Andres Velasco, and several Bernanke and Blinder (1992), Galí (1992), Ber- anonymous referees for helpful comments, and to nanke and Mihov (1997a), Christiano, Eichen- Tommaso Monacelli for excellent research assis- baum, and Evans (1996, 1998) and Leeper, Sims tance. Authors Galí and Gertler are grateful to the and Zha (1996). Much of the literature has fo- C.V. Starr Center for Applied Economics, and cused on the effects of monetary policy shocks. (Galí) to CREI for financial support. e-mail: Bernanke, Gertler, and Watson (1997) present evi- [email protected] dence that suggests that the monetary policy rule 2 Blinder 1997, p. 17. may have important effects on real activity. 1661 1662 Journal of Economic Literature, Vol. XXXVII (December 1999) analysis. A key point of departure from and applied work, as we discuss later.4 real business cycle theory (as we later There are, however, important strands make clear) is the explicit incorporation of the literature that either reject the of frictions such as nominal price rigidi- idea of nominal price rigidities (e.g., ties that are needed to make the frame- real business cycle theory) or focus on work suitable for evaluation of monetary other types of nominal rigidities, such policy. as frictions in money demand.5 For this This paper summarizes what we have reason, we append “New Keynesian learned from this recent research on Perspective” to the title. In particular, monetary policy. We review the prog- we wish to make clear that we adopt the ress that has been made and also iden- Keynesian approach of stressing nomi- tify the central questions that remain. nal price rigidities, but at the same time To organize the discussion, we exposit base our analysis on frameworks that in- the monetary policy design problem in a corporate the recent methodological ad- simple theoretical model. We start with vances in macroeconomic modeling a stripped-down baseline model in or- (hence the term “New”). der to characterize a number of broad Section 2 lays out the formal policy principles that underlie optimal policy problem. We describe the baseline management. We then consider the im- theoretical model and the objectives of plications of adding various real world policy. Because we are interested in complications. Finally, we assess how characterizing policy rules in terms of the predictions from theory square with primitive factors, the model we use policy-making in practice. evolves from first principles. Though it Throughout, we concentrate on ex- is quite simple, it nonetheless contains positing results that are robust across a the main ingredients of descriptively wide variety of macroeconomic frame- richer frameworks that are used for pol- works. As Ben McCallum (1997b) em- icy analysis. Within the model, as in phasizes, the key stumbling block for practice (we argue), the instrument of policy formation is limited knowledge monetary policy is a short-term interest of the way the macroeconomy works. rate. The policy design problem then is Results that are highly model-specific to characterize how the interest rate are of limited use. This literature, how- should adjust to the current state of the ever, contains a number of useful prin- economy. ciples about optimal policy that are rea- An important complication is that pri- sonably general in applicability. In this vate sector behavior depends on the ex- respect there is a “science of monetary pected course of monetary policy, as policy,” as Alan Blinder suggests in the well as on current policy. The credibil- quote above. We provide support for ity of monetary policy thus becomes this contention in the pages that follow. relevant, as a considerable contemporary At the same time, we should make literature has emphasized.6 At issue is clear that the approach we take is based on the idea that temporary nominal 4 See, for example, the survey by Goodfriend price rigidities provide the key friction and King (1997). 5 See, for example, Christiano, Eichenbaum, that gives rise to nonneutral effects of and Evans (1997). For an analysis of monetary pol- monetary policy. The propositions we icy rules in these kinds of models—known as “lim- derive are broadly applicable within this ited participation” frameworks—see Christiano and Gust (1999). class of models. This approach has 6 For a recent survey of the credibility litera- widespread support in both theoretical ture, see Persson and Tabellini (1997). Clarida, Galí, Gertler: The Science of Monetary Policy 1663 whether there may be gains from en- gain from commitment then is to elimi- hancing credibility either by formal nate this inflationary bias. How realistic commitment to a policy rule or by intro- it is to presume that a perceptive cen- ducing some kind of institutional ar- tral bank will try to inadvisedly reap rangement that achieves roughly the short-term gains from pushing output same end. We address the issue by ex- above its natural level is a matter of re- amining optimal policy for both cases: cent controversy (e.g., Blinder 1997; with and without commitment. Along McCallum 1997a). We demonstrate, with expositing traditional results, we however, that there may be gains from also exposit some new results regarding commitment simply if current price set- the gains from commitment. ting depends on expectations of the fu- Section 3 derives the optimal policy ture. In this instance, a credible com- rule in the absence of commitment. If mitment to fight inflation in the future for no other reason, this case is of inter- can improve the current output/infla- est because it captures reality: No ma- tion trade-off that a central bank faces. jor central bank makes any type of bind- Specifically, it can reduce the effective ing commitment over the future course cost in terms of current output loss that of its monetary policy. A number of is required to lower current inflation. broad implications emerge from this This result, we believe, is new in the baseline case. Among these: The opti- literature. mal policy embeds inflation targeting in In practice, however, a binding com- the sense that it calls for gradual adjust- mitment to a rule may not be feasible ment to the optimal inflation rate. The simply because not enough is known implication for the policy rule is that about the structure of the economy or the central bank should adjust the the disturbances that buffet it. Under nominal short rate more than one-for- certain circumstances, however, a pol- one with expected future inflation. That icy rule that yields welfare gains rela- is, it should adjust the nominal rate suf- tive to the optimum under discretion ficiently to alter the real rate (and thus may be well approximated by an opti- aggregate demand) in the direction that mal policy under discretion that is ob- is offsetting to any movement in ex- tained by assigning a higher relative pected inflation. Finally, how the cen- cost to inflation than the true social tral bank should adjust the interest rate cost. A way to pursue this policy opera- in response to output disturbances de- tionally is simply to appoint a central bank pends critically on the nature of the dis- chair with a greater distaste for infla- turbances: It should offset demand tion than society as a whole, as Kenneth shocks but accommodate supply shocks, Rogoff (1985) originally emphasized. as we discuss. Section 5 considers a number of prac- Section 4 turns to the case with com- tical problems that complicate policy- mitment. Much of the literature has making. These include: imperfect infor- emphasized that an inefficiently high mation and lags, model uncertainty and steady state inflation rate may arise in non-smooth preferences over inflation the absence of commitment, if the cen- and output. A number of pragmatic is- tral bank’s target for real output ex- sues emerge, such as: whether and how ceeds the market clearing level.7 The to make use of intermediate targets, the choice of a monetary policy instrument, 7 The potential inflationary bias under discre- tion was originally emphasized by Kydland and and why central banks appear to smooth Prescott (1977) and Barro and Gordon (1983). interest rate changes. Among other 1664 Journal of Economic Literature, Vol. XXXVII (December 1999) things, the analysis makes clear why that U.S. monetary policy in the fifteen modern central banks (especially the years or so prior to Paul Volcker did not Federal Reserve Board) have greatly always follow the principles we have de- downgraded the role of monetary aggre- scribed. Simply put, interest rate man- gates in the implementation of policy. agement during this era tended to ac- The section also shows how the recently commodate inflation. Under Volcker advocated “opportunistic” approach to and Greenspan, however, U.S. mone- fighting inflation may emerge under a tary policy adopted the kind of implicit non-smooth policy objective function. inflation targeting that we argue is The opportunistic approach boils down consistent with good policy management. to trying to keep inflation from rising The section also considers some pol- but allowing it to ratchet down in the icy proposals that focus on target vari- event of favorable supply shocks. ables, including introducing formal As we illustrate throughout, the opti- inflation or price-level targets and mal policy depends on the degree of nominal GDP targeting. There is in ad- persistence in both inflation and out- dition a brief discussion of the issue of put. The degree of inflation persistence whether indeterminacy may cause prac- is critical since this factor governs the tical problems for the implementation of output/inflation trade-off that the pol- simple interest rate rules. Finally, there icy-maker faces. In our baseline model, are concluding remarks in section 8. persistence in inflation and output is due entirely to serially correlated ex- 2. A Baseline Framework for Analysis ogenous shocks. In section 6 we con- of Monetary Policy sider a hybrid model that allows for en- dogenous persistence in both inflation This section characterizes the formal and output. The model nests as special monetary policy design problem. It first cases our forward-looking baseline presents a simple baseline macro- model and, also, a more traditional economic framework, and then de- backward-looking Keynesian frame- scribes the policy objective function. work, similar to the one used by Lars The issue of credibility is taken up next. Svensson (1997a) and others. In this regard, we describe the distinc- Section 7 moves from theory to prac- tion between optimal policies with and tice by considering a number of pro- without credible commitment—what posed simple rules for monetary policy, the literature refers to as the cases of including the Taylor rule, and a forward- “rules versus discretion.” looking variant considered by Clarida, 2.1 A Simple Macroeconomic Galí, and Gertler (1998; forthcoming). Framework Attention has centered around simple rules because of the need for robust- Our baseline framework is a dynamic ness. A policy rule is robust if it pro- general equilibrium model with money duces desirable results in a variety of and temporary nominal price rigidities. competing macroeconomic frameworks. In recent years this paradigm has be- This is tantamount to having the rule come widely used for theoretical analy- satisfy the criteria for good policy man- sis of monetary policy.8 It has much of agement that sections 2 through 6 es- the empirical appeal of the traditional tablish. Further, U.S. monetary policy may 8 See, e.g, Goodfriend and King (1997), McCal- be judged according to this same met- lum and Nelson (1997), Walsh (1998), and the ref- ric. In particular, the evidence suggests erences therein. Clarida, Galí, Gertler: The Science of Monetary Policy 1665

IS/LM model, yet is grounded in dy- In addition, let πt be the period t infla- namic general equilibrium theory, in tion rate, defined as the percent change keeping with the methodological ad- in the price level from t–1 to t; and let it vances in modern macroeconomics. be the nominal interest rate. Each vari- Within the model, monetary policy able is similarly expressed as a deviation affects the real economy in the short from its long-run level. run, much as in the traditional Keynes- It is then possible to represent the ian IS/LM framework. A key difference, baseline model in terms of two equa- however, is that the aggregate behav- tions: an “IS” curve that relates the out- ioral equations evolve explicitly from put gap inversely to the real interest optimization by households and firms. rate; and a Phillips curve that relates One important implication is that cur- inflation positively to the output gap. rent economic behavior depends criti- xt = − ϕ[it − Etπt + 1] + Etxt + 1 + gt (2.1) cally on expectations of the future π = λ + β π + course of monetary policy, as well as on t xt Et t + 1 ut (2.2) current policy. In addition, the model where gt and ut are disturbances terms accommodates differing views about that obey, respectively: how the macroeconomy behaves. In the gt = µgt − 1 + ^gt (2.3) limiting case of perfect price flexibility, = ρ + for example, the cyclical dynamics re- ut ut − 1 ^ut (2.4) semble those of a real business cycle where 0 ≤ µ,ρ ≤ 1 and where both ^gt and model, with monetary policy affecting u^t are i.i.d. random variables with zero mean 2 2 only nominal variables. and variances σg and σu, respectively. Rather than work through the details Equation (2.1) is obtained by log- of the derivation, which are readily linearizing the consumption euler equa- available elsewhere, we instead directly tion that arises from the household’s introduce the key aggregate relation- optimal saving decision, after imposing ships.9 For convenience, we abstract the equilibrium condition that con- from investment and capital accumula- sumption equals output minus govern- tion. This abstraction, however, does ment spending.11 The resulting expres- not affect any qualitative conclusions, as sion differs from the traditional IS we discuss. The model is as follows: curve mainly because current output Let yt and zt be the stochastic compo- depends on expected future output as nents of output and the natural level of well as the interest rate. Higher ex- output, respectively, both in logs.10 The pected future output raises current out- latter is the level of output that would put: Because individuals prefer to arise if wages and prices were perfectly 11 = + flexible. The difference between actual Using the market clearing condition Yt Ct Et, where Et is government consumption, we can re- and potential output is an important vari- write the log-linearized consumption Euler equa- able in the model. It is thus convenient tion as: x − = − ϕ − π + − to define the “output gap” t: yt et [it Et t + 1] Et{yt + 1 et + 1} ≡ − xt yt zt E ≡ − ( − t) where et log 1 is taken to evolve ex- Yt 9 See, for example, Yun (1996), Kimball (1995), ogenously. Using x ≡ y − z , it is then possible to King and Wolman (1995), Woodford (1996), and t t t derive the demand for output as Bernanke, Gertler, and Gilchrist (1998) for step- = − ϕ − π + + by-step derivations. xt [it Et t + 1] Etxt + 1 gt 10 By stochastic component, we mean the devia- = ∆ − ∆ tion from a deterministic long-run trend. where gt Et{ zt + 1 et + 1}. 1666 Journal of Economic Literature, Vol. XXXVII (December 1999) smooth consumption, expectation of John Taylor (1980).12 A key difference higher consumption next period (associ- is that the individual firm price-setting ated with higher expected output) leads decision, which provides the basis for them to want to consume more today, the aggregate relation, is derived from which raises current output demand. an explicit optimization problem. The The negative effect of the real rate on starting point is an environment with current output, in turn, reflects in- monopolistically competitive firms: When tertemporal substitution of consump- it has the opportunity, each firm tion. In this respect, the interest elastic- chooses its nominal price to maximize ity in the IS curve, ϕ, corresponds to profits subject to constraints on the the intertemporal elasticity of substitu- frequency of future price adjustments. tion. The disturbance gt is a function of Under the standard scenario, each pe- expected changes in government pur- riod the fraction 1/X of firms set prices chases relative to expected changes in for X > 1 periods. In general, however, potential output (see footnote 11). aggregating the decision rules of firms Since gt shifts the IS curve, it is inter- that are setting prices on a staggered pretable as a demand shock. Finally, add- basis is cumbersome. For this reason, ing investment and capital to the model underlying the specific derivation of changes the details of equation (2.1). equation (2.2) is an assumption due to But it does not change the fundamental Guillermo Calvo (1983) that greatly qualitative aspects: output demand still simplifies the problem: In any given pe- depends inversely on the real rate and riod a firm has a fixed probability θ it positively on expected future output. must keep its price fixed during that pe- It is instructive to iterate equation riod and, hence a probability 1 – θ that (2.1) forward to obtain it may adjust.13 This probability, fur- ther, is independent of the time that ∞ = − ϕ − π + has elapsed since the last time the firm xt Et∑ { [it + i t + 1 + i] gt + i} (2.5) = changed price. Accordingly, the average i 0 1 time over which a price is fixed is 1 − θ. Equation (2.5) makes transparent the Thus, for example, if θ = .75, prices are degree to which beliefs about the future fixed on average for a year. The Calvo affect current aggregate activity within formulation thus captures the spirit of this framework. The output gap de- staggered setting, but facilitates the ag- pends not only on the current real rate gregation by making the timing of a and the demand shock, but also on the firm’s price adjustment independent of expected future paths of these two its history. variables. To the extent monetary policy Equation (2.2) is simply a loglinear has leverage over the short-term real approximation about the steady state of rate due to nominal rigidities, equation the aggregation of the individual firm (2.5) suggests that expected as well as pricing decisions. Since the equation re- current policy actions affect aggregate lates the inflation rate to the output gap demand. and expected inflation, it has the flavor The Phillips curve, (2.2), evolves of a traditional expectations-augmented from staggered nominal price setting, in Phillips curve (see, e.g., Olivier Blanchard the spirit of Stanley Fischer (1977) and 13 The Calvo formulation has become quite 12 See Galí and Gertler (1998) and Sbordone common in the literature. Work by Yun (1996), (1998) for some empirical support for this kind of King and Wolman (1995), Woodford (1996) and Phillips curve relation. others has initiated the revival. Clarida, Galí, Gertler: The Science of Monetary Policy 1667

1997). A key difference with the stan- We allow for the cost push shock to en- dard Phillips curve is that expected fu- able the model to generate variation in ture inflation, Etπt + 1, enters additively, inflation that arises independently of as opposed to expected current infla- movement in excess demand, as appears 14 tion, Et − 1πt. The implications of this present in the data (see, e.g., Fuhrer distinction are critical: To see, iterate and Moore 1995). (2.2) forward to obtain To close the model, we take the ∞ nominal interest rate as the instrument i πt = Et∑ β [λxt + i + ut + i] (2.6) of monetary policy, as opposed to a i = 0 money supply aggregate. As Bernanke and Ilian Mihov (1998) show, this as- In contrast to the traditional Phillips sumption provides a reasonable descrip- curve, there is no arbitrary inertia or tion of Federal Reserve operating pro- lagged dependence in inflation. Rather, cedures since 1965, except for the brief inflation depends entirely on current period of non-borrowed reserves target- and expected future economic condi- ing (1980–82) under Paul Volcker.16 tions. Roughly speaking, firms set nomi- With the nominal rate as the policy in- nal price based on the expectations of strument, it is not necessary to specify a future marginal costs. The variable xt + i money market equilibrium condition captures movements in marginal costs (i.e., an LM curve).17 In section 5, we associated with variation in excess de- discuss the implications of using instead mand. The shock ut + i, which we refer to a narrow monetary aggregate as the as “cost push,” captures anything else that policy instrument. might affect expected marginal costs.15 Though simple, the model has the same qualitative core features as more 14 Another key difference is that the explicit λ derivation restricts the coefficient on the output On this latter point, see Erceg, Henderson, and gap. In particular, λ is decreasing in θ, which mea- Levin (1998). Another interpretation of the ut shock sures the degree of price rigidity. Thus, the longer (suggested by Mike Woodford) is that it could re- prices are fixed on average, the less sensitive is flect a shock to the gap between the natural and inflation to movements in the output gap. potential levels of output (e.g., a markup shock). 15 The relation for inflation that evolves from 16 Roughly speaking, Bernanke and Mihov the Calvo model takes the form (1998) present formal evidence showing that the π = βE {π + } + δ mc Federal Reserve intervenes in the market for non- t t t 1 t borrowed bank reserves to support its choice for where mct denotes the deviation of (real) marginal the level of the Federal Funds rate, the overnight cost from its steady state value. To then relate in- market for bank reserves. (Christiano, Eichen- flation to the output gap, the literature typically baum, and Evans 1998, though, take issue with the makes assumptions on technology, preferences, identifying assumptions in the Bernanke-Mihov and the structure of labor markets to justify a pro- test). Informally, Federal Reserve policy actions in portionate relation between real marginal cost and recent years routinely take the form of announcing = κ κ the output gap, so that mct xt holds, where is a target for the Federal funds rate (see, e.g, Rude- the output elasticity of real marginal cost. In this busch 1995). Policy discussions, further, focus on instance, one can rewrite the relation for inflation whether to adjust that target, and by how much. in terms of the output gap, as follows: In this context, the view that the Funds rate is the π = β π + λ t Et{ t + 1} xt (see Galí and Gertler (1998) policy instrument is widely held by both practitio- for details). In this context, the disturbance ut in ners of monetary policy and academic researchers (2.2) is interpretable as reflecting deviations from (see, e.g., Goodfriend 1991, Taylor 1993, and = κ the condition mct xt. (Indeed the evidence in Walsh 1998). 17 Galí and Gertler 1998 suggests that mct does not With the interest rate as the policy instru- vary proportionately with xt). Deviations from this ment, the central bank adjusts the money supply proportionality condition could be caused, for ex- to hit the interest rate target. In this instance, the ample, by movements in nominal wages that push condition that money demand equal money supply real wages away from their “equilibrium” values simply determines the value of the money supply due to frictions in the wage contracting process. that meets this criteria. 1668 Journal of Economic Literature, Vol. XXXVII (December 1999) complex, empirically based frameworks since inflation is expressed as a percent that are used for policy analysis.18 As in deviation from trend.19 these applied frameworks, temporary While there has been considerable nominal price rigidities play a critical progress in motivating behavioral mac- role. With nominal rigidities present, by roeconomic models from first princi- varying the nominal rate, monetary pol- ples, until very recently, the same has icy can effectively change the short- not been true about rationalizing the term real rate. Through this classic objectives of policy. Over the past sev- mechanism it gains leverage over the eral years, there have been a number of near term course of the real economy. attempts to be completely coherent in In contrast to the traditional mecha- formulating the policy problem by nism, though, beliefs about how the taking as the welfare criterion the util- central bank will set the interest rate in ity of a representative agent within the the future also matter, since both model.20 households and firms are forward look- One limitation of this approach, how- ing. In this kind of environment, how ever, is that the models that are cur- monetary policy should respond in the rently available do not seem to capture short run to disturbances that buffet the what many would argue is a major cost economy is a nontrivial decision. Re- of inflation, the uncertainty that its vari- solving this issue is the essence of the ability generates for lifetime financial contemporary debate over monetary planning and for business planning (see, policy. e.g., Brad DeLong 1997).21 Another is- sue is that, while the widely used repre- 2.2 The Policy Objective sentative agent approach may be a rea- sonable way to motivate behavioral The central bank objective function relationships, it could be highly mis- translates the behavior of the target leading as a guide to welfare analysis. If variables into a welfare measure to some groups suffer more in recessions guide the policy choice. We assume, than others (e.g. steel workers versus following much of the literature, that professors) and there are incomplete in- this objective function is over the tar- surance and credit markets, then the get variables xt and πt, and takes the utility of a hypothetical representative form: agent might not provide an accurate  ∞  barometer of cyclical fluctuations in 1   − βi[α 2 + π2 ] welfare. max Et∑ xt + i t + i  (2.7) 2  =   i 0  With certain exceptions, much of the where the parameter α is the relative 19 Put differently, under the optimal policy, the weight on output deviations. Since target inflation rate pins down the trend inflation xt ≡ yt − zt, the loss function takes poten- rate. The loss function thus penalizes deviations tial output zt as the target. It also implic- from this trend. 20 Some examples of this approach include Aiya- itly takes zero as the target inflation, but gari and Braun (1997), King and Wolman (1995), there is no cost in terms of generality Ireland (1996a), Carlstrom and Fuerst (1995), and Rotemberg and Woodford (1997). 18 Some prominent examples include the re- 21 Underlying this kind of cost is the observation cently renovated large scale model used by the that contracts are typically written in nominal Federal Reserve Board, the FRB-US model (see terms and, for reasons that are difficult to explain, Brayton, Levin, Tyron, and Williams 1997), and not perfectly indexed to the price level. On this the medium scale models of Taylor (1979, 1993b) issue, see the discussion in Shiller (1997) and the and Fuhrer and Moore (1995a,b). associated comment by Hall (1997). Clarida, Galí, Gertler: The Science of Monetary Policy 1669 literature takes a pragmatic approach to But they define price stability as the in- this issue by simply assuming that the flation rate at which inflation is no objective of monetary policy is to mini- longer a public concern. In practice, it mize the squared deviations of output is argued that an inflation rate between and inflation from their respective tar- one and three percent seems to meet get levels. However, Julio Rotemberg this definition (e.g., Bernanke and and Michael Woodford (1999) and Mishkin 1997). A further justification Woodford (1998) provide a formal justi- for this criteria is that the official price fication for this approach. These indices may be overstating the true in- authors show that an objective function flation rate by a percent or two, as ar- looking something like equation (2.7) gued recently by the Boskin Commis- may be obtained as a quadratic approxi- sion. In this regard, interestingly, the mation of the utility-based welfare Bundesbank has had for a long time an function. In this instance, the relative official inflation target of two percent.23 weight, α, is a function of the primitive They similarly argue that this positive parameters of the model. rate of inflation is consistent with price In what follows, we simply adopt the stability, and cite measurement error as quadratic objective given by (2.7), ap- one of the reasons (Clarida and Gertler pealing loosely to the justification of- 1997). fered in Rotemberg and Woodford It is clear that the experience of the (1999). Judging by the number of pa- 1970s awakened policy-makers to the pers written by Federal Reserve econo- costs of high inflation (DeLong 1997). mists that follow this lead, this formula- Otherwise, there is no directly observ- tion does not seem out of sync with the able indicator of the relative weights as- way monetary policy operates in prac- signed to output and inflation objec- tice (at least implicitly).22 The target tives. Nor, argues Blinder (1997), is level of output is typically taken to be there any obvious consensus among pol- the natural level of output, based on the icy-makers about what these weights re- idea that this is the level of output that ally are in practice. It is true that there would obtain absent any wage and price has been a growing consensus that the frictions. Yet, if distortions exist in the primary aim of monetary policy should economy (e.g., imperfect competition be to control inflation (see, e.g., Ber- or taxes), a case can be made that the nanke and Mishkin 1997). But this dis- welfare maximizing level of output may cussion in many respects is about what exceed its natural level. This issue be- kind of policy rule may be best, as op- comes important in the context of posed to what the underlying welfare policy credibility, but we defer it for function looks like. now. For our purposes, however, it is rea- What should be the target rate of in- sonable to take the inflation target and flation is perhaps an even more ephem- preference parameters as given and eral question, as is the issue of what simply explore the implications for should be the relative weight assigned optimal policy rules. to output and inflation losses. In the 23 Two percent is also the upper bound of the U.S., policy-makers argue that “price inflation target range established by the European stability” should be the ultimate goal. Central Bank. On the other hand, Feldstein (1997) argues that the tax distortions that arise because corporate and personal income taxes are not in- 22 See, for example, Williams (1997) and refer- dexed to inflation justify moving from three per- ences therein. cent to zero inflation. 1670 Journal of Economic Literature, Vol. XXXVII (December 1999)

2.3 The Policy Problem and Discretion From the standpoint of policy design, versus Rules the issue is to identify whether some type of credibility-enhancing commit- The policy problem is to choose a ment may be desirable. Answering this time path for the instrument it to engi- question boils down to comparing opti- neer time paths of the target variables mal policy under discretion versus rules π xt and t that maximize the objective (using the terminology of the litera- function (2.7), subject to the constraints ture). In our context, a central bank op- on behavior implied by (2.1) and (2.2). erating under discretion chooses the This formulation is in many ways in the current interest rate by reoptimizing tradition of the classic Jan Tinbergen every period. Any promises made in the (1952)/Henri Theil (1961) (TT) targets past do not constrain current policy. and instruments problem. As with TT, Under a rule, it chooses a plan for the the combination of quadratic loss and path of the interest rates that it sticks to linear constraints yields a certainty forever. The plan may call for adjusting equivalent decision rule for the path of the interest rate in response to the state the instrument. The optimal feedback of the economy, but both the nature rule, in general, relates the instrument and size of the response are etched in to the state of the economy. stone. There is, however, an important dif- Two points need to be emphasized. ference from the classic problem: The First, the key distinction between dis- target variables depend not only on the cretion and rules is whether current current policy but also on expectations commitments constrain the future about future policy: The output gap de- course of policy in any credible way. In pends on the future path of the interest each instance, the optimal outcome is a rate (equation 2.5); and, in turn, inflation feedback policy that relates the policy depends on the current and expected instrument to the current state of the future behavior of the output gap economy in a very specific way. The two (equation 2.6). As Finn Kydland and approaches differ, however, in their im- Edward Prescott (1977) originally em- plications for the link between policy phasized, in this kind of environment, intentions and private sector beliefs. credibility of future policy intentions Under discretion, a perceptive private becomes a critical issue. For example, a sector forms its expectations taking into central bank that can credibly signal its account how the central bank adjusts intent to maintain inflation low in the policy, given that the central bank is future may be able to reduce current free to reoptimize every period. The ra- inflation with less cost in terms of out- tional expectations equilibrium thus has put reduction than might otherwise be the property that the central bank has required.24 In section 4, we illustrate no incentive to change its plans in an this point explicitly. unexpected way, even though it has the 24 In this regard, we stress further that, in discretion to do so. (For this reason, the contrast to conventional wisdom, the issue of policy that emerges in equilibrium under credibility in monetary policy is not tied to central discretion is termed “time consistent.”) bank objectives over output. In the classic, Barro/Gordon (1983) formulation (and countless In contrast, under a rule, it is simply papers thereafter), the central bank’s desire to push output above potential output gives rise to the credibility problem. However, as we make depends on beliefs about the future, even if cen- clear in section 4, gains from commitment poten- tral bank objectives over output are perfectly tially emerge whenever private sector behavior aligned. Clarida, Galí, Gertler: The Science of Monetary Policy 1671 the binding commitment that makes the possible gains from commitment to a policy believable in equilibrium. policy rule and other institutional de- Second, (it should almost go without vices that might enhance credibility, it saying that) the models we use are no- is necessary to understand what the where near the point where it is possi- benchmark case of discretion yields. ble to obtain a tightly specified policy Under discretion, each period the rule that could be recommended for central bank chooses the triplet {xt,πt,it}, practical use with great confidence. consisting of the two target variables Nonetheless, it is useful to work and the policy instrument, to maximize through the cases of discretion and the objective (2.7) subject to the aggre- rules in order to develop a set of norma- gate supply curve (2.2) and the IS tive guidelines for policy behavior. As curve, (2.1). It is convenient to divide Taylor (1993a) argues, common sense the problem into two stages: First, the application of these guidelines may im- central bank chooses xt and πt to maxi- prove the performance of monetary pol- mize the objective (2.7), given the infla- icy. We expand on this point later. In tion equation (2.2).25 Then, conditional addition, understanding the qualitative on the optimal values of xt and πt, it de- differences between outcomes under termines the value of it implied by the discretion versus rules can provide les- IS curve (2.1) (i.e., the interest rate sons for the institutional design of that will support xt and πt). monetary policy. For example, as we Since it cannot credibly manipulate discuss, Rogoff’s (1985) insightful beliefs in the absence of commitment, analysis of the benefits of a conservative the central bank takes private sector central bank chair is a product of this expectations as given in solving the type of analysis. Finally, simply under- optimization problem.26 (Then, condi- standing the qualitative aspects of opti- tional on the central bank’s optimal mal policy management under discre- rule, the private sector forms beliefs ra- tion can provide useful normative tionally.) Because there are no en- insights, as we show shortly. dogenous state variables, the first stage We proceed in the next section to de- of the policy problem reduces to the fol- rive the optimal policy under discretion. lowing sequence of static optimization In a subsequent section we then evaluate the implications of commitment. 25 Since all the qualitative results we derive stem mainly from the first stage problem, what is critical is the nature of the short run Phillips 3. Optimal Monetary Policy without curve. For our baseline analysis, we use the Phil- Commitment lips curve implied the New Keynesian model. In section 6 we consider a very general Phillips curve that is a hybrid of different approaches and show We begin with the case without com- that the qualitative results remain intact. It is in mitment (“discretion”) for two reasons. this sense that our analysis is quite robust. First, at a basic level this scenario ac- 26 We are ignoring the possibility of reputational equilibria that could support a more efficient out- cords best with reality. In practice, no come. That is, in the language of game theory, we major central bank makes any kind of restrict attention to Markov perfect equilibria. binding commitment over the course of One issue that arises with reputational equilibria is that there are multiplicity of possible equilibria. its future monetary policy. In this re- Rogoff (1987) argues that the fragility of the re- spect, it seems paramount to under- sulting equilibria is an unsatisfactory feature of stand the nature of optimal policy in this approach. See also, Ireland (1996b). On the other hand, Chari, Christiano, and Eichenbaum this environment. Second, as we have (1998) argue that this indeterminacy could provide just discussed, to fully comprehend the a source of business fluctuations. 1672 Journal of Economic Literature, Vol. XXXVII (December 1999)

27 problems: Each period, choose xt and πt = αq ut (3.5) π t to maximize where − 1 [α 2 + π2] + 1 xt t Ft (3.1) q = 2 λ2 + α(1 − βρ) subject to The optimal feedback policy for the in- πt = λxt + ft (3.2) terest rate is then found by simply in- serting the desired value of xt in the IS taking as given Ft and ft, where curve (2.1):  ∞  1   1 ≡ − βi[α 2 + π2 ] it = γπ Etπt + 1 + gt (3.6) Ft Et∑ xt + i t + i  and ϕ 2  =  i 1  where ≡ β π + ft Et t + 1 ut. Equations (3.1) and (1−ρ)λ γπ = + > (3.2) simply reformulate (2.7) and (2.2) 1 ρϕα 1 in a way that makes transparent that, un- π = ρ π = ρα der discretion, (a) future inflation and Et t + 1 t q ut output are not affected by today’s ac- This completes the formal description of tions, and (b) the central bank cannot the optimal policy. directly manipulate expectations. From this relatively parsimonious set The solution to the first stage prob- of expressions there emerge a number lem yields the following optimality of key results that are reasonably robust condition: findings of the literature: λ Result 1: To the extent cost push in- = − π (3.3) xt α t flation is present, there exists a short run trade-off between inflation and This condition implies simply that the output variability. central bank pursue a “lean against the This result was originally emphasized wind” policy: Whenever inflation is by Taylor (1979) and is an important above target, contract demand below ca- guiding principle in many applied stud- pacity (by raising the interest rate); and ies of monetary policy that have fol- vice-versa when it is below target. How lowed.28 A useful way to illustrate the aggressively the central bank should re- trade-off implied by the model is to duce xt depends positively on the gain in construct the corresponding efficient reduced inflation per unit of output loss, policy frontier. The device is a locus of λ , and inversely on the relative weight points that characterize how the uncon- α placed on output losses, . ditional standard deviations of output To obtain reduced form expressions and inflation under the optimal policy, π for xt and t, combine the optimality σx and σπ, vary with central bank prefer- condition (fonc) with the aggregate sup- ences, as defined by α. Figure 1 por- ply curve (AS ), and then impose that trays the efficient policy frontier for our private sector expectations are rational:

xt = − λq ut (3.4) 28 For some recent examples, see Williams (1997), Fuhrer (1997a) and Orphanides, Small, 27 In section 6, we solve for the optimum under Wilcox and Wieland (1997). An exception, how- discretion for the case where an endogenous state ever, is Jovanovic and Ueda (1997) who demon- variable is present. Within the Markov perfect strate that in an environment of incomplete con- equilibrium, the central bank takes private sector tracting, increased dispersion of prices may reduce beliefs as a given function of the endogenous output. Stabilizing prices in this environment then state. raises output. Clarida, Galí, Gertler: The Science of Monetary Policy 1673

29 baseline model. In (σx,σπ) space the pends only on current and future de- locus is downward sloping and convex mand. By adjusting interest rates to set to the origin. Points to the right of the xt = 0, ∀ t, the central bank is able to hit frontier are inefficient. Points to the its inflation and output targets simulta- left are infeasible. Along the frontier neously, all the time. If cost push fac- there is a trade-off: As α rises (indicat- tors drive inflation, however, it is only ing relatively greater preference for possible to reduce inflation in the near output stability), the optimal policy en- term by contracting demand. This gineers a lower standard deviation of consideration leads to the next result: output, but at the expense of higher in- Result 2: The optimal policy incorpo- flation volatility. The limiting cases are rates inflation targeting in the sense instructive: that it requires to aim for convergence

σu of inflation to its target over time. Ex- α → σ = σπ = (3.7) As 0: x λ ; 0 treme inflation targeting, however, i.e., adjusting policy to immediately reach σu As α → ∞: σx = 0; σπ = (3.8) an inflation target, is optimal under 1 − βρ only one of two circumstances: (1) cost where σu is the standard deviation of the push inflation is absent; or (2) there is cost push innovation. no concern for output deviations (i.e., It is important to emphasize that the α = 0). trade-off emerges only if cost push in- In the general case, with α > 0 and σ > flation is present. In the absence of cost u 0, there is gradual convergence of inflation (i.e., with σu = 0), there is no inflation back to target. From equations trade-off. In this instance, inflation de- (3.5) and (2.4), under the optimal policy π = α ρi = 29 Equations (3.4) and (3.5) define the frontier lim Et{ t + i} lim q ut 0 for the baseline model. i → ∞ i → ∞ 1674 Journal of Economic Literature, Vol. XXXVII (December 1999)

In this formal sense, the optimal pol- several results regarding the behavior of icy embeds inflation targeting.30 With the policy instrument, it. exogenous cost push inflation, policy af- Result 3: Under the optimal policy, fects the gap between inflation and its in response to a rise in expected infla- target along the convergent path, but tion, nominal rates should rise suffi- not the rate of convergence. In con- ciently to increase real rates. Put differ- trast, in the presence of endogenous in- ently, in the optimal rule for the flation persistence, policy will generally nominal rate, the coefficient on expected affect the rate of convergence as well, inflation should exceed unity. as we discuss later. Result 3 is transparent from equation The conditions for extreme inflation (3.6). It simply reflects the implicit tar- targeting can be seen immediately from geting feature of optimal policy de- inspection of equations (3.7) and (3.8). scribed in Result 2. Whenever inflation When σu = 0 (no cost push inflation), is above target, the optimal policy re- adjusting policy to immediately hit the quires raising real rates to contract de- inflation target is optimal, regardless of mand. Though this principle may seem preferences. Since there is no trade-off obvious, it provides a very simple crite- in this case, it is never costly to try to ria for evaluating monetary policy. For minimize inflation variability. Inflation example, Clarida, Galí, and Gertler (forth- being the only concern of policy pro- coming) find that U.S. monetary policy vides the other rationale for extreme in- in the pre-Volcker era of 1960–79 vio- flation targeting. As equation (3.7) indi- lated this strategy. Federal Reserve pol- cates, it is optimal to minimize inflation icy tended to accommodate rather than variance if α = 0, even with cost push fight increases in expected inflation. inflation present. Nominal rates adjusted, but not suffi- Result 2 illustrates why some con- ciently to raise real rates. The persis- flicting views about the optimal transi- tent high inflation during this era may tion path to the inflation target have have been the end product of the fail- emerged in the literature. Marvin ure to raise real rates under these cir- Goodfriend and Robert King (1997), for cumstances. Since 1979, however, the example, argue in favor of extreme in- Federal Reserve appears to have adopted flation targeting. Svensson (1997a,b) the kind of implicit inflation targeting and Laurence Ball (1997) suggest that, strategy that equation (3.6) suggests. in general, gradual convergence of in- Over this period, the Fed has systemati- flation is optimal. The difference stems cally raised real rates in response to an- from the treatment of cost push infla- ticipated increases in inflationary ex- tion: It is absent in the Goodfriend- pectations. We return to this issue later. King paradigm, but very much a factor Result 4: The optimal policy calls for in the Svensson and Ball frameworks. adjusting the interest rate to perfectly off- Results 1 and 2 pertain to the behav- set demand shocks, gt, but perfectly ac- ior of the target variables. We now state commodate shocks to potential output, zt, by keeping the nominal rate constant. That policy should offset demand 30 Note here that our definition is somewhat different from Svensson (1997a), who defines shocks is transparent from the policy inflation targeting in terms of the weights on the rule (3.6). Here the simple idea is that objective function, i.e., he defines the case with countering demand shocks pushes both α = 0 as corresponding to strict inflation targeting and α > 0 as corresponding to flexible inflation output and inflation in the right direc- targeting. tion. Demand shocks do not force a Clarida, Galí, Gertler: The Science of Monetary Policy 1675 short run trade-off between output and David Gordon (1983), and Rogoff inflation. (1985), a voluminous literature has de- Shocks to potential output also do not veloped on the issue of credibility of force a short run trade-off. But they re- monetary policy.34 From the standpoint quire a quite different policy response. of obtaining practical insights for pol- Thus, e.g., a permanent rise in produc- icy, we find it useful to divide the pa- tivity raises potential output, but it also pers into two strands. The first follows raises output demand in a perfectly off- directly from the seminal papers and setting manner, due to the impact on has received by far the most attention permanent income.31 As a consequence, in academic circles. It emphasizes the the output gap does not change. In problem of persistent inflationary bias turn, there is no change in inflation. under discretion.35 The ultimate source Thus, there is no reason to raise inter- of this inflationary bias is a central bank est rates, despite the rise in output.32 that desires to push output above its Indeed, this kind of scenario seems to natural level. The second is emphasized describe well the current behavior of more in applied discussions of policy. It monetary policy. Output growth was focuses on the idea that disinflating an substantially above trend in recent times, economy may be more painful than nec- but with no apparent accompanying in- essary, if monetary policy is perceived flation.33 Based on the view that the rise as not devoted to fighting inflation. in output may mainly reflect productivity Here the source of the problem is movements, the Federal Reserve has simply that wage and price setting resisted large interest rate increases. today may depend upon beliefs about The central message of Result 4 is where prices are headed in the future, that an important task of monetary pol- which in turn depends on the course of icy is to distinguish the sources of monetary policy. business cycle shocks. In the simple These two issues are similar in a environment here with perfect ob- sense: They both suggest that a central servability, this task is easy. Later we bank that can establish credibility one explore some implications of relaxing way or another may be able to reduce this assumption. inflation at lower cost. But the source of the problem in each case is different 4. Credibility and the Gains in subtle but important ways. As a from Commitment consequence the potential empirical Since the pioneering work of Kydland relevance may differ, as we discuss and Prescott (1977), Robert Barro and below. We first use our model to exposit the 31 In this experiment we are holding constant = ( − ) − ( − ) the IS shock gt. Since gt [ et zt Et et + 1 zt + 1 ], famous inflationary bias result. We then (see footnote 9), this boils down to assuming illustrate formally how credibility can either that the shock to zt is permanent (so that − = reduce the cost of maintaining low in- Etzt + 1 zt 0) or that et adjusts in a way to offset movements in gt. flation, and also discuss mechanisms in 32 That monetary policy should accommodate movements in potential GDP is a theme of the 34 For recent surveys of the literature, see Fis- recent literature (e.g., Aiyagari and Braun 1997; cher (1995), McCallum (1997) and Persson and Carlstrom and Fuerst 1995; Ireland 1996a; and Tabellini (1997). Rotemberg and Woodford 1997). This view was 35 While the inflationary bias result is best also stressed in much earlier literature. See Fried- known example, there may also be other costs of man and Kuttner (1996) for a review. discretion. Svennson (1997c), for example, argues 33 See Lown and Rich (1997) for a discussion of also that discretion may lead to too much inflation the recent “inflation puzzle.” variability and too little output variability. 1676 Journal of Economic Literature, Vol. XXXVII (December 1999) the literature that have been suggested  ∞  1   − βi[α( − )2 + π2 ] to inject this credibility. An important max Et∑ xt + i k t + i  (4.1) 2  =  result we wish to stress—and one that i o  we don’t think is widely understood in the literature—is that gains from credi- The rationale for having the socially opti- bility emerge even when the central mal level of output exceed its natural bank is not trying to push output above level may be the presence of distortions its natural level.36 That is, as long as such as imperfect competition or taxes. price setting depends on expectations of For convenience, we also assume that the future, as in our baseline model, price setters do not discount the future, which permits us to fix the parameter β there may be gains from establishing 38 some form of credibility to curtail infla- in the Phillips curve at unity. tion. Further, under certain plausible In this case, the optimality condi- restrictions on the form of the feedback tion that links the target variables is rule, the optimal policy under commit- given by: λ ment differs from that under discretion xk = − πk + k (4.2) in a very simple and intuitive way. In t α t this case, the solution with commitment The superscript k indicates the variable resembles that obtained under discre- is the solution under discretion for the tion using a higher effective cost ap- case k > 0. Plugging this condition into plied to inflation than the social welfare the IS and Phillips curves, (2.1) and 37 function suggests. In this respect, we (2.2), yields: think, the credibility literature may have k = some broad practical insights to offer. xt xt (4.3) α 4.1 The Classic Inflationary πk = π + t t k (4.4) Bias Problem λ π As in Kydland and Prescott (1979), where xt and t are the equilibrium val- Barro and Gordon (1983), and many ues of the target variables for the base- = other papers, we consider the possibil- line case with k 0 (see equations 3.4 ity that the target for the output gap and 3.5). may be k > 0, as opposed to 0. The policy Note that output is no different from the baseline case, but that inflation is objective function is then given by α systematically higher, by the factor λ k. 36 A number of papers have shown that a disin- Thus, we have the familiar result in the flation will be less painful if the private sector per- ceives that the central bank will carry it out. But literature: they do not show formally that, under discretion, Result 5. If the central bank desires the central bank will be less inclined to do so to push output above potential (i.e., (see., e.g. Ball 1995, and Bonfim and Rudebusch > 1997). k 0), then under discretion a subopti- 37 With inflationary bias present, it is also possi- mal equilibrium may emerge with infla- ble to improve welfare by assigning a higher cost tion persistently above target, and no to inflation, as Rogoff (1985) originally empha- sized. But it is not always possible to obtain the gain in output. optimum under commitment. The point we em- The model we use to illustrate this phasize is that with inflationary bias absent, it is possible to replicate the solution under commit- 38 Otherwise, the discounting of the future by ment (for a restricted family of policy rules) using price-setters introduces a long-run trade-off be- the algorithm to solve for the optimum under dis- tween inflation and output. Under reasonable pa- cretion with an appropriately chosen relative cost rameter values this tradeoff is small and its pres- of inflation. We elaborate on these issues later in ence merely serves to complicate the algebra. See the text. Goodfriend and King (1997) for a discussion. Clarida, Galí, Gertler: The Science of Monetary Policy 1677 result differs from the simple expecta- Imposing binding commitments in a tional Phillips curve framework in model, however, is much easier than do- which it has been typically studied. But ing so in reality. The issue then becomes the intuition remains the same. In this whether there may be some simple in- instance, the central bank has the in- stitutional mechanisms that can approxi- centive to announce that it will be mate the effect of the idealized policy tough in the future to lower current in- commitment. Perhaps the most useful flation (since in this case, current infla- answer to the question comes from Rogoff tion depends on expected future infla- (1985), who proposed simply the appoint- tion), but then expand current demand ment of a “conservative” central banker, to push output above potential. The taken in this context to mean someone presence of k in the optimality condi- with a greater distaste for inflation (a tion (4.2) reflects this temptation. A ra- lower α), than society as a whole: tional private sector, however, recog- Result 6: Appointing a central bank nizes the central bank’s incentive. In chair who assigns a higher relative cost mechanical terms, it makes use of equa- to inflation than society as a whole re- tion (4.2) to forecast inflation, since this duces the inefficient inflationary bias that condition reflects the central bank’s is obtained under discretion when k > 0. true intentions. Put simply, equilibrium One can see plainly from equation inflation rises to the point where the (4.4) that letting someone with prefer- central bank no longer is tempted to ex- ences given by αR < α run the central pand output. Because there is no long- bank will reduce the inflationary bias.39 run trade-off between inflation and out- The Rogoff solution, however, is not a put (i.e., xt converges to zero in the panacea. We know from the earlier long run, regardless of the level of infla- analysis that emphasizing greater reduc- tion), long-run equilibrium inflation is tion in inflation variance may come at forced systematically above target. the cost of increased output variance. The analysis has both important posi- Appointing an extremist to the job tive and normative implications. On the (someone with α at or near zero) could positive side, the theory provides an ex- wind up reducing overall welfare. planation for why inflation may remain How important the inflationary bias persistently high, as was the case from problem emphasized in this literature is the late 1960s through the early 1980s. in practice, however, is a matter of con- Indeed, its ability to provide a qualita- troversy. Benjamin Friedman and Ken- tive account of this inflationary era is a neth Kuttner (1996) point out that in- major reason for its popularity. flation in the major OECD countries The widely stressed normative impli- now appears well under control, despite cation of this analysis is that there may the absence of any obvious institutional be gains from making binding commit- changes that this literature argues are ments over the course of monetary pol- needed to enhance credibility. If this icy or, alternatively, making institu- theory is robust, they argue, it should tional adjustments that accomplish the account not only for the high inflation same purpose. A clear example from the of the 1960s and 1970s, but also for the analysis is that welfare would improve if the central bank could simply commit 39 See Svensson (1997) and Walsh (1998) for a to acting as if k were zero. There would description of how incentive contracts for central bankers may reduce the inflation bias; also, Faust be no change in the path of output, but and Svensson (1998) for a recent discussion of inflation would decline. reputational mechanisms. 1678 Journal of Economic Literature, Vol. XXXVII (December 1999) transition to an era of low inflation dur- pend on expectations of the future, as ing the 1980s and 1990s. A possible equation (2.2) makes clear.40 counterargument is that in fact a num- ber of countries, including the U.S., ef- 4.2 Improving the Short-Run fectively adopted the Rogoff solution by Output/Inflation Trade-off: Gains appointing central bank chairs with from Commitment with k = 0. clear distaste for inflation. We now illustrate that there may be Another strand of criticism focuses gains from commitment to a policy rule, on the plausibility of the underlying even with k = 0. The first stage problem story that leads to the inflationary bias. in this case is to choose a state contin- A number of prominent authors have gent sequence for xt + i and πt + i to maxi- argued that, in practice, it is unlikely > mize the objective (2.7) assuming that that k 0 will tempt a central bank to the inflation equation (2.2) holds in cheat. Any rational central bank, they every period t + i, i ≥ 0. Specifically, the maintain, will recognize the long-term central bank no longer takes private sec- costs of misleading the public to pursue tor expectations as given, recognizing short-term gains from pushing output instead that its policy choice effectively above its natural level. Simply this rec- determines such expectations. ognition, they argue, is sufficient to To illustrate the gains from commit- constrain its behavior (e.g. McCallum ment in a simple way, we first restrict 1997a; Blinder 1997). Indeed, Blinder the form of the policy rule to the gen- argues, based on his own experience on eral form that arises in equilibrium un- the Federal Reserve Board, that there der discretion, and solve for the opti- was no constituency in favor of pursuing mum within this class of rules. We then output gains above the natural rate. In show that, with commitment, another formal terms, he maintains that those rule within this class dominates the op- who run U.S. monetary policy act as if = timum under discretion. Hence this ap- they were instructed to set k 0, which proach provides a simple way to illus- eliminates the inflationary bias. trate the gains from commitment. What is perhaps less understood, Another positive byproduct is that the however, is that there are gains from = restricted optimal rule we derive is sim- enhancing credibility even when k 0. ple to interpret and implement, yet still To the extent that price setting today yields gains relative to the case of dis- depends on beliefs about future eco- cretion. Because the policy is not a global nomic conditions, a monetary authority optimum, however, we conclude the that is able to signal a clear commit- section by solving for the unrestricted ment to controlling inflation may face optimal rule. an improved short-run output/inflation trade-off. Below we illustrate this point. 4.2.1 Monetary Policy under The reason why this is not emphasized Commitment: The Optimum within in much of the existing literature on a Simple Family of Policy Rules this topic is that this work either tends (that includes the optimal rule to focus on steady states (as opposed to under discretion) short-run dynamics), or it employs very simple models of price dynamics, where In the equilibrium without commit- current prices do not depend on beliefs ment, it is optimal for the central bank about the future. In our baseline model, 40 This section is based on Galí and Gertler however, short-run price dynamics de- (1999). Clarida, Galí, Gertler: The Science of Monetary Policy 1679 to adjust xt solely in response to the discretion, reducing xt by one percent π λ < λ exogenous cost push shock, ut. We ac- only produces a fall in t of 1 − βρ. cordingly consider a rule for the target The extra kick in the case with commit- variable xt that is contingent on the ment is due to the impact of the policy fundamental shock ut, in the following rule on expectations of the future course way: of the output gap. In particular, the c = − ω choice of ω affects not only xt but also xt ut (4.5) c = … beliefs about the course of xt + i, i 1,2, , for all t, where ω > 0 is the coefficient of c + = − ω c since Etxt i ut. A central bank that the feedback rule, and where xt denotes commits to a tough policy rule (high ω), the value of xt conditional on commit- for example, is able to credibly signal 41 ment to the policy. Note that the rule that it will sustain over time an aggres- includes the optimum under discretion ω λ sive response to a persistent supply shock. as a special case (i.e., the case with = q Since inflation depends on the future shown in 3.4). course of excess demand, commitment to Combining equation (4.5) with the the tough policy rule leads to a magni- Phillips curve (2.2), in turn, implies that πc fied drop in inflation per unit of output inflation under the rule, t , is also a lin- loss, relative to the case of discretion. ear function of the cost push shock: To find the optimal value of ω, note c πc πc = λ c + β πc + first that since xt + i and t + i are each a t xt Et t + 1 ut (4.6) constant multiple of the cost push shock ∞ ut + i, it is possible to express the objec- = βi [λ c + ] Et∑ xt + i ut + i (4.7) tive function as a multiple of period t = i 0 loss: ∞  ∞  1   i − βi[α ( c )2 + (πc )2] = Et∑ β [− λω ut + i + ut + i] (4.8) max Et∑ xt + i t + i  = 2  =  i 0 i 0  − λω 1 1 ←→ − [α ( c)2 + (πc)2] = ut (4.9) max xt t Lt 1 − βρ 2 (4.11)  ∞  The problem for the central bank is   ≡ βi( )2 > to choose the optimal value of the feed- with Lt Et∑ ut + i/ut  0. The prob-  =  back parameter ω. Relative to the case i 0  of discretion, the ability to commit to lem then is to choose ω to maximize a feedback policy provides the central (4.11), subject to (4.10). In this instance, bank with an improved short-run out- the optimality condition is given by: put/inflation trade-off. To this end, note λ c = − πc that it is possible to express equation xt t αc (4.12) (4.9) as λ where πc = c + 1 x ut αc ≡ α(1 − βρ) < α (4.13) t 1 − βρ t 1 − βρ (4.10) αc < α In this case, a one percent contraction in Since , relative to the case of dis- c πc λ cretion, commitment to the rule implies xt reduces t by the factor − βρ. Under 1 that it is optimal for the central bank to 41 The policy rule only depends on ut because engineer a greater contraction in output the central bank can adjust it to offset any impact in response to inflationary pressures. of movements in gt on aggregate demand. See equation (4.16). Intuitively, the more aggressive response 1680 Journal of Economic Literature, Vol. XXXVII (December 1999) to inflation is the product of the im- is compelling from an empirical stand- proved output/inflation trade-off that point. Because inflation depends on ex- commitment affords. Specifically, the pected future output gaps, the central output cost of lowering inflation declines bank would like to convince the private from α to αc per unit, since reducing in- sector that it will be tough in the fu- flation a given amount requires, ceteris ture, but at the same time, not to have paribus, only a fraction (1 − βρ) of the to contract demand much today. As the output loss required under discretion. future comes to pass, the central bank The decline in the effective cost of re- has the incentive to renege on its ducing inflation, in turn, induces the planned toughness and, instead, prom- more aggressive policy response to infla- ise again to undertake contractionary tion, as comparing equation (4.12) with policy down the road. To see this, sup- equation (3.3) makes clear. pose that there is a positive cost push c The equilibrium solutions for xt and shock. If the central bank is free to de- πc t are easily obtained by combining viate from the rule, it will always choose equations (4.12) and (4.10): the optimal policy under discretion, c = − λ c xt q ut (4.14) which calls for a smaller contraction of output, relative to the case of commit- πc = − αcqc u t t (4.15) ment (again, compare 4.1 and 3.3). A with rational private sector will recognize 1 that incentive and, unless the central qc = λ2 + αc(1 − βρ) bank is able to commit credibly, will not It is interesting to observe that the expect large contractions in demand in solution under commitment in this case the future either. As a result, the cost perfectly resembles the solution ob- push shock generates higher inflation in tained under discretion that arises when the absence of commitment. We stress α is replaced with αc < α in the objec- again that, in contrast to the traditional tive function. It follows that, condi- analysis, this gain from commitment is tional on the value of the cost push not tied to the desire of the central bank to push output above potential, shock, ut, inflation is closer to target and output is further, relative to the but to the forward-looking nature of in- outcome under discretion.42 flation (and, thus, the importance of ex- It is straightforward to verify that pectations about future policy) in our commitment to the policy rule raises baseline model. welfare.43 The tension produced by From a policy standpoint, Rogoff’s ra- such gains from commitment, we think, tionale for a conservative central banker carries over perfectly to this case. In- 42 Importantly, with endogenous inflation per- deed with omniscience (i.e. exact sistence, commitment produces a faster transition knowledge of αc and the true model), of inflation to target, as we discuss later. an appropriately chosen central banker 43 To verify that commitment raises welfare, π could replicate the outcome under simply substitute the implied values for xt and t under the optimal rule for each case into the pol- commitment. icy objective function. However, it should be obvi- We summarize the findings in Result 7: ous that commitment raises welfare, since the op- timal rule under discretion falls within the class of Result 7: If price-setting depends on rules that we permitted the central bank to choose expectations of future economic condi- in the case with commitment: Yet we found that tions, then a central bank that can cred- with commitment it is optimal to choose a differ- ent parameterization of the rule than arises in the ibly commit to a rule faces an improved optimum under discretion. short-run trade-off between inflation Clarida, Galí, Gertler: The Science of Monetary Policy 1681 and output. This gain from commitment xt + i and πt + i to maximize the objective arises even if the central bank does not (2.7) given that the aggregate supply prefer to have output above potential curve (2.2) holds in every period (i.e., even when k = 0). The solution t + i, i ≥ 0. We no longer restrict the under commitment in this case perfectly choice of xt to depend on the contempo- resembles the solution that would ob- raneous value of the shock (i.e., ut ), but tain for a central bank with discretion allow instead for rules that are a func- that assigned to inflation a higher cost tion of the entire history of shocks. To than the true social cost. find the globally optimal solution to the One additional interesting feature of linear quadratic policy problem under this case with commitment involves the commitment, we follow David Currie behavior of interest rates. This can be and Paul Levine (1993) and Woodford seen formally by simply replacing α (1998), and form the Lagrangian:45 with αc in the interest rate rule under  ∞ discretion (given by equation 3.6) to 1  − βi α 2 + π2 obtain max Et∑ [ xt + i t + i 2  = i 0 (4.17) c 1 = γπ π + + (4.16) it Et t 1 ϕ gt   + φt + i(πt + i − λxt + i − βπt + i + 1 − ut + i)] with   ( − ρ)λ ( − ρ)λ 1 c 1 1 φ + γπ ≡ 1 + > 1 + ≡ γπ where t i is the (state-contingent) ρϕαc ρϕα 2 multiplier associated with the constraint at In particular, relative to the case of dis- t+i. It is straightforward to show that the cretion, the central bank increases the first order conditions yield the following nominal interest rate by a larger amount optimality conditions in response to a rise in expected inflation. λ xt + i − xt + i − 1 = − πt + i, 4.2.2 Monetary Policy under Commit- α ment: The Unconstrained Optimum for i = 1,2,3,... (4.18) We now provide a brief description of and the general solution for the optimal pol- λ 44 = − π (4.19) icy under commitment. Because the xt α t derivation is more cumbersome than for the restricted case just described, we Recall that under discretion the opti- defer most of the details to an appen- mal policy has the central bank adjust dix. As with the simple fundamental the level of the output gap in response based policy, however, the general solu- to inflation. The optimal policy under tion exploits the ability that commit- commitment requires instead adjusting ment affords to manipulate private the change in the output gap in re- sector expectations of the future. sponse to inflation. In other words, The first stage problem remains to commitment changes the level rule for choose a state-contingent sequence for xt under discretion into a difference rule for xt, as a comparison of equations 44 We thank Chris Sims and Albert Marcet for calling to our attention that the globally optimal 45 See also King and Wolman, who analyze the rule under commitment would likely not fall optimal monetary policy under commitment in a within the restricted family of rules considered in version of Taylor’s (1980) staggered contracts the previous sub-section. model. 1682 Journal of Economic Literature, Vol. XXXVII (December 1999)

(3.3) and (4.8) indicates.46 The one ca- tion (given the dependency of πt on fu- veat is that in the initial period the pol- ture values of xt). Relative to the case of icy is implemented (i.e., period t) the discretion, accordingly, the cost push central bank should simply adjust the shock has a smaller impact in current level of the output gap xt is response to inflation.48 πt, as if it were following the optimal As with the constrained policy, the policy under discretion, but for that globally optimal policy under commit- period only. ment exploits the ability of the central Because xt + i depends in general on bank to influence πt with expected fu- xt + i − 1, the (unconstrained) optimal pol- ture values of xt + i as well as current xt. icy under commitment is in general not It is also easy to see that, as was the simply a function of the contemporane- case with the more restrictive rule, the ous state variable ut + i. As Woodford policy is not time consistent. Clearly, if (1998) emphasizes in a related context, it could reoptimize at t + i, the central the lagged dependence in the policy bank would choose the same policy it rule arises as a product of the central implemented at t, the one which mimics bank’s ability under commitment to di- the rule under discretion for the first rectly manipulate private sector expec- period only. tations.47 To see this for our framework, A disadvantage of the unconstrained keep in mind that πt depends not only optimal policy under commitment is on current xt but also on the expected that it appears more complex to imple- future path of xt + i. Then suppose, for ment than the constrained one (de- example, that there is a cost push shock scribed by equation 4.12). As we have that raises inflation above target at time seen, the constrained rule resembles in t. The optimal response under discre- every dimension the optimal policy un- tion, as we have seen, is to reduce xt, der discretion, but with relatively more but then let xt + i revert back to trend weight placed on fighting inflation. Ac- over time as πt + i falls back to target. cordingly, as we discussed, it is possible The optimal policy under commitment, to approximate this policy under discre- however, is to continue to reduce xt + i as tion with an appropriately chosen cen- long as πt + i remains above target. The tral banker. The same is not true, how- (credible) threat to continue to contract ever, for the unconstrained optimal xt in the future, in turn, has the imme- policy. A conservative central banker diate effect of dampening current infla- operating with discretion has no obvi- ous incentive to stick to the difference 46 Woodford (1998) makes the connection be- rule for the output gap implied by tween the lagged dependence in the optimal rule equation (4.18). under commitment and the lagged dependence that appears to arise in interest rate behavior un- A further complication, discussed at der practice (see section 5.2). Roughly speaking, length in Woodford (1998), is that the since the interest rate affects the output gap, interest rate rule that implements the lagged dependence in the latter translates into lagged dependence in the former. optimal policy might have undesirable 47 Woodford (1998) considers a closely related environment. The difference is that in his frame- work the policy-maker confronts a trade-off be- 48 On the surface it appears that the difference π tween inflation and the output gap ultimately be- rule for xt might be unstable. However, t adjusts cause his objective function includes a target for to ensure that this is not the case. In particular, the nominal interest rate (along with targets for the optimal response to a positive cost push shock π the output gap and inflation), whereas in our is to contract xt sufficiently to push t below tar- framework the trade-off arises due to the cost get. xt then adjusts back up to target over time. push shock. The appendix provides the details. Clarida, Galí, Gertler: The Science of Monetary Policy 1683 side effects. To see this, combine (4.18) 5. Practical Complications and (2.1) to obtain the implied optimal interest rate rule In this section we consider a number of important practical issues that com-  λ  1 =  −  π + + it 1 αϕ Et t 1 ϕ gt plicate the implementation of monetary   policy. While they may not be as exotic Notice that the coefficient associated as the question of credibility, they are with expected inflation is less than one. no less important for the day-to-day for- Under this rule, accordingly, a rise in mulation of policy. anticipated inflation leads to a decline in the real interest rate. As we discuss 5.1 Imperfect Information in section 7, if inflationary pressures Thus far we have assumed that the vary inversely with the real rate, a rule central bank is able to control perfectly of this type may permit self-fulfilling the paths of the key target variables. In fluctuations in output and inflation that practice, of course, this is not the case. 49 are clearly suboptimal. One important reason is imperfect ob- Overall, we have: servability. At the time it sets interest Result 8: The globally optimal policy rates, a central bank may not have all rule under commitment has the central the relevant information available about bank partially adjust demand in re- the state of the economy. Certain data sponse to inflationary pressures. The take time to collect and process. Sam- idea is to exploit the dependence of cur- pling is imperfect. Even if it has access rent inflation on expected future de- to data in real time, some key variables mand. In addition, while appointing a such as the natural level of output are conservative central banker may raise not directly observable and are likely welfare under discretion (see Result 7), measured with great error (see, e.g., the it does not appear that it is possible to discussion in Arturo Estrella and attain the globally optimal rule with Mishkin 1999 and Orphanides 1998). this strategy. Finally, there may be some Beyond limiting the efficacy of pol- practical complications in implementing icy, imperfect information has several the globally optimal interest rate rule specific implications. First, it is no that involve potential indeterminacy, as longer possible to specify rules simply discussed in Woodford (1998). in terms of target variables. With per- We conclude that, though substantial fect information, a policy may be ex- progress has been made, our under- pressed equivalently in terms of targets standing of the full practical implica- or instruments since a one-to-one rela- tions of commitment for policy-making tionship generally exists between these is still at a relatively primitive stage, variables. With imperfect information, with plenty of territory that is worth rules for targets can be expressed only exploring. in terms of the respective forecasts, as opposed to the ex-post values. An alter- 49 Indeterminacy does not arise in the case of native is to use an intermediate target discretion or in the case of the constrained opti- that is directly observable, such as a mum under commitment, since in each instance the implied interest rate rule has an inflation coef- broad monetary aggregate. ficient greater than one. To the extent that such Second, imperfect information makes coefficient is not too large, implementation of the policy instrument choice non-trivial. such a rule will result in a unique equilibrium (see the discussion in section 7 and also in Clarida, With perfect information, for example, Galí, and Gertler (1998). it does not matter whether the central 1684 Journal of Economic Literature, Vol. XXXVII (December 1999) bank uses the short-term interest rate perfect information) and because the er- or a monetary aggregate as the policy rors in forecasting the target variables instrument, so long as the money de- are additive. mand function yields a monotonic rela- For ease of exposition, assume that tion between the two variables.50 With there is no serial correlation in the imperfect information, the ex post vola- cost push shock; that is, ρ = 0, so that tility of a variety of key variables hinges ut = ^ut. The implied equilibrium values on the instrument choice, as originally of the target variables under imperfect I πI argued by William Poole (1970). We information, xt and t, are given by illustrate each of these issues below.51  λ  I = + + = xt xt  ^ut ^gt ^gt (5.2) 5.1.1 Forecasts as Targets and λ2 + α 

Intermediate Targets  λ2 πI = + π + λ = + λ t 1  t ^gt ^ut ^gt (5.3) We now return to the baseline model  α  with no commitment, and modify it as where xt and πt are the optimal values of follows. Suppose that the central bank the target variables that emerge in case cannot observe the contemporaneous of perfect information (when ut is serially values of output, inflation, or any of the 53 uncorrelated), and where ^ut and ^gt are random shocks. Then let Ωt be the cen- the unexpected movements in the cost tral bank’s information set at the time it push and demand shocks, respectively. Im- fixes the interest rate that prevails at perfect information clearly implies greater time t.52 The optimality condition for volatility of inflation, since the central policy now is expressed in terms of the bank cannot immediately act to offset expected as opposed to realized target the impact of the shocks. The net effect variables. on the volatility of the output gap is un-   λ    Ω  = − π Ω  clear: the inability to offset the demand E xt | t E t | t (5.1)   α shock clearly raises output volatility. On Equation (5.1) is the certainty equivalent the other hand, the central bank cannot version of the condition for the case of offset the inflationary impact of the cost perfect information, given by equation push shock, which works to reduce the (3.3). Certainty equivalence applies here volatility of the output. There is, however, 54 because of the linear quadratic setup an unambiguous reduction in welfare. (that gives linear decision rules under One additional result is worth noting. Since demand shocks now affect the be- 50 To clarify, a money aggregate can serve as an havior of output, a positive short-run instrument only if it is directly controllable. A can- didate aggregate then would be bank reserves. A co-movement between inflation and broad aggregate such as M3 would not qualify. output can emerge if ^gt has a variance 51 For a broad survey of the literature on mone- sufficiently large relative to that of u^t. tary policy targets and instruments, see Friedman (1991). It is straightforward to generalize the 52 Ω Thus, t is similarly the private sector’s infor- analysis to a setting where the imper- mation set. Specifically, we let firms observe the fect observability stems from lags in the current values of their marginal costs, but neither − λ 53 = firms nor households can observe contemporane- When ut is serially uncorrelated, xt 2 ut ous aggregate variables. In this instance, the IS λ + α and Phillips curve equations are respectively given α and πt = ut. by λ2 + α 54 x = − ϕ[(i | Ω ) − E − π + ] + E − x + + g To prove that imperfect information leads to a t t t t 1 t 1 t 1 t 1 t reduction in welfare, evaluate the welfare function π = λ + β π + I πI π t xt Et − 1 t + 1 ut with xt and t versus xt and t. Clarida, Galí, Gertler: The Science of Monetary Policy 1685 transmission of monetary policy. This reasonable only if the economy has case is of interest since much of the attained a stationary equilibrium. available evidence suggests a lag of six A traditional alternative to using the to nine months in the effect of a shift in target variable forecasts is to focus on interest rates on output.55 The lag in the behavior of a variable that is corre- the effect on inflation is around a year lated with the underlying targets but is and a half. Suppose, for example, that it instead observable and controllable. takes j periods for a shift in the current Broad monetary aggregates are the best interest rate to affect output and an- known examples of intermediate tar- other k periods for an impact on infla- gets. If demand for a particular aggre- tion. In the left side of equation (5.1) gate is stable, then this aggregate is would appear the j period ahead fore- likely to have a stable covariance with cast of the output gap, and on the right nominal GDP. In practice, however, ex- would be the (suitably discounted) j + k perience with monetary targeting has period ahead forecast of inflation. not been successful. The U.S. and the Svensson (1997a,b) has emphasized U.K., for example, attempted to regu- the practical importance of this result late the growth of money aggregates in for the mechanics of inflation targeting the early 1980s and then quickly aban- (specifically, the kind of inflation tar- doned the policy after the aggregates geting that the theory implies (see Re- went haywire.57 Financial innovation in sult 2 in section 3). A standard criticism each instance was the underlying cul- of employing an inflation target is that prit. Even in Germany, long considered information about the impact of current a bastion of money targeting, there have monetary policy on inflation is only been problems. Unstable movements in available with a long lag. This informa- money demand have forced a retreat tion lag, it is argued, makes it impossi- from strict money growth targeting. A ble to monitor policy performance. It is number of recent papers go further by possible to circumvent this problem, ac- arguing that in practice Bundesbank cording to Svensson, by focusing in- policy looks more like inflation target- stead on the inflation forecast. The ing (as defined in Result 2) than money forecast is immediately available. It targeting (Clarida and Gertler 1997; thus provides a quick way to judge the Bernanke and Mihov 1997b). course of policy. A caveat to this argu- For similar reasons, policies that tar- ment is that to generate the correct in- get other kinds of simple indicators, flation forecast, the central bank must such as commodity prices or long term have a good structural model of the interest rates, have not been widely em- economy.56 VAR-based forecasts are ployed. As Woodford (1994a) has em- phasized, the correlation properties of 55 Galí (1992), Christiano, Eichenbaum, and these simple indicators with output 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. cast-based targets, including the possibility of in- Bernanke and Gertler (1995) show that, while the determinacy under this kind of policy rule. We overall response of output is sluggish, certain com- discuss this issue in section 7. ponents of spending do respond quickly, such as 57 See Friedman and Kuttner (1996) for a de- housing and consumer durables. Inventories ad- tailed accounting of the failure of monetary target- just to reconcile the gap between spending and ing to take hold in the U.S. See also Estrella and output. Mishkin (1996). On the other hand, Feldstein and 56 Bernanke and Woodford (1997) emphasize Stock (1997) argue that, with periodic adjustment, the need to make structural forecasts. They also a broad monetary aggregate can still be a useful raise some other related criticisms of using fore- intermediate target. 1686 Journal of Economic Literature, Vol. XXXVII (December 1999) inflation is likely to vary with changes where pt is the price level and vt is a in the policy rule. In the end, there is random disturbance to money demand. no simple substitute for employing a If vt is perfectly observable then it does structural model. not matter whether it or mt is employed To summarize, we have as the policy instrument. Given the time Result 9: With imperfect informa- path of it implied by the optimal policy, tion, stemming either from data prob- it is possible to back out a time path lems or lags in the effect of policy, the for mt that supports this policy from optimal policy rules are the certainty equation (5.4). equivalent versions of the perfect infor- Matters change if vt is not observ- mation case. Policy rules must be ex- able. With the interest rate as the in- pressed in terms of the forecasts of tar- strument, the central bank lets the get variables as opposed to the ex post money stock adjust to the money de- behavior. Using observable intermediate mand shock. There is no impact of targets, such as broad money aggregates is money demand shocks on output or in- a possibility, but experience suggests that flation because the central bank per- these indirect indicators are generally fectly accommodates them. With money too unstable to be used in practice. targeting, the reverse is true: the inter- est rate and (possibly) output adjust to 5.1.2 The Instrument Choice Problem: clear the money market. Assume for The Interest Rate versus a Narrow simplicity that demand and cost push = = Monetary Aggregate shocks are absent (i.e., gt 0, ut 0), so that the only shock is the innovation to We now turn to the issue of instru- money demand. Then the interest rate ment choice. In practice, the interest implied by a money supply instrument m rate that major central banks adjust is it , is given by an overnight rate on interbank lending m 1 i = it + ^vt (5.5) of funds to meet reserve require- t η + ϕ(κ + λ) ments.58 They control this rate by ma- nipulating the supply of bank reserves, where it is the rate that would arise un- i.e., the quantity of high-powered der interest rate targeting and ^vt is the money available for meeting bank re- unexpected movement in money demand. serve requirements. The issue that The key point is that money demand arises is whether, from an operational shocks can induce volatile behavior of standpoint, policy should prescribe interest rates. This is particularly true if paths (or rules) for bank reserves or for money demand is relatively interest in- interest rates. Suppose that the demand elastic in the short run, as is the case 59 for bank reserves mt is given by for bank reserves. This short run volatil- ity in interest rates will then feed into mt − pt = κ yt − η it + vt (5.4) output volatility, via the aggregate de- 58 See Bernanke and Mihov (1997a) for a discus- mand relation, equation (2.1). It is for sion of Federal Reserve operating procedures and this reason that in practice central banks how they have changed over time. use interbank lending rates as the pol- 59 In the optimizing IS/LM framework of sec- tion 2, it is possible to motivate this specification icy instrument, an insight due originally of the money demand function from first princi- to Poole (1970).60 Recent empirical ples, assuming that utility is separable in consump- tion and real money balances and that consump- 60 Poole also argued that if unobservable de- tion is the only type of good (see, e.g., Woodford mand shocks were large relative to money demand 1996). shocks, then it may be preferable to use a money Clarida, Galí, Gertler: The Science of Monetary Policy 1687 work by Bernanke and Mihov (1997a) This finding is not uncommon. The confirms that except for the brief pe- FRB-US model also generates high in- riod of non-borrowed reserve targeting terest rate volatility under an optimal under Volcker (1979:10–1982:10), the rule. Because this degree of volatility Federal Reserve Board has indeed seems greater than monetary policy treated the Funds rate as the policy in- makers seem willing to tolerate in prac- strument. In summary, we have tice, optimal rules are also computed Result 10: Large unobservable with constraints on the volatility of shocks to money demand produce high interest rate changes (see, e.g., John volatility of interest rates when a mone- Williams 1997).61 tary aggregate is used as the policy in- The tendency of the Federal Reserve strument. It is largely for this reason to adjust rates cautiously is generally re- that an interest rate instrument may be ferred to as “interest rate smoothing.” preferable. To be precise, as a number of authors The analysis thus makes clear why the have shown, a monetary policy rule of new Federal Reserve Board model does the following form captures the last not even bother to include a money ag- twenty or so years of data fairly well: gregate of any form (see Flint Brayton = ( − ρ) α + β π + γ + ρ + ε et al. 1997). Narrow aggregates are not it 1 [ t xt] it − 1 t (5.6) good policy instruments due to the im- where α is a constant interpretable as plied interest rate volatility. Broad ag- the steady state nominal interest rate62 gregates are not good intermediate tar- and where ρ ∈[0,1] is a parameter that gets because of their unstable relation reflects the degree of lagged depen- with aggregate activity. dence in the interest rate.63 Interest rate smoothing is present in distinct respects. Policy Conservatism: Model 5.2 First, the estimated slope coefficients on Uncertainty vs. Exploitation of inflation and the output gap, β and γ, are Forward-Looking Behavior typically smaller than what the optimal In practice, central banks adjust in- rule would suggest. Second, there is typi- terest rates more cautiously than stan- cally partial adjustment to movements in dard models predict. Put differently, πt and xt, reflected by the presence of the optimal policies derived in a certainty lagged interest in the fitted rule. That is, equivalent environment generally pre- it is a weighted average of some desired dict a much more variable path of inter- value that depends on the state economy est rates than is observed in practice. (given by the term [α + βπt + γxt]) and the An interesting illustration of this point lagged interest rate, where the relative is Rotemberg and Woodford (1997) who weights depend on the smoothing pa- estimate a model very similar to our rameter ρ. Estimates of ρ for quarterly baseline model, and then compute an data are typically on the order of 0.8 or optimal interest rate policy. The histori- 0.9, which suggests very slow adjustment cal interest rate displays much less vola- 61 An alternative is to penalize large changes in tility than the optimal interest rate. the nominal interest rate by including the squared deviations of the change in the interest rate (i.e, − )2 (it it − 1 ) in the function, as in Rudebusch and supply instrument. With a money supply instru- Svensson (1998). 62 π ment, interest rates will naturally move in an off- Recall that t represents deviations of infla- setting direction in response to unobserved de- tion from its average (target) level. mand shocks (see Result 4). In practice, the high 63 See Rudebusch (1995), for example, for a dis- variability of money demand shocks seems to cussion of the persistence in short term interest dominate the instrument choice, however. rates. 1688 Journal of Economic Literature, Vol. XXXVII (December 1999) in practice. The existing theory, by and To be concrete, suppose that the two large, does not readily account for why parameters of the model, the interest the central bank should adjust rates in elasticity in the IS equation and the such a sluggish fashion. slope coefficient on the output gap are ~ Indeed, understanding why central random variables, now given by ϕt = ϕ + εt ~ 65 banks choose a smooth path of interest and by λt = λ + ηt. Assume further that rates than theory would predict is an εt and ηt are i.i.d random variables with important unresolved issue. One impli- zero means. The optimality condition cation is that the standard certainty for policy then becomes: equivalence models may not adequately capture the constraints policy-makers λ E{xt | Ωt} = E{πt | Ωt} α + λ2σ2 face in practice. A natural possibility is η 2 σε 2 that policy-makers know far less about + (α + λ ) rt (5.7) the way the world works than is ϕ ≡ − π Ω presumed in simple policy experiments. where rt it E{ t + 1 | t} is the ex ante In general, model uncertainty is a real interest rate. This condition leads to formidable problem. Ideally, one would the following result: like to take into account that the central Result 11: Parameter uncertainty bank is continually learning about the may reduce the response of the policy economy as it adjusts its policy. Per- instrument to disturbances in the econ- forming this exercise in a clean way is omy. It can thus motivate a smoother beyond the frontier of current knowl- path of the interest rate than the cer- edge. Though, advances in computa- tainty equivalent policy implies. tional methodology have allowed some Comparing equations (5.1) and (5.7) progress to be made with relatively reveals how parameter uncertainty re- simple frameworks.64 duces policy activism. Under certainty It is possible to illustrate how model equivalence, a rise in inflation above uncertainty could in principle introduce target requires the central bank to raise at least some degree of policy caution. interest rates to contract demand.66 Suppose the values of several parame- With an uncertain slope coefficient ters in the model are random. The cen- on the output gap in the AS curve, how- tral bank knows the distribution of ever, contraction of output below po- these parameters but not the realiza- tential raises the variability of inflation. tion. When it adjusts policy, accord- This induces the central bank to moder- ingly, it cannot be sure of the impact on ate the contraction in demand, as re- λ2σ2 the economy. As originally demon- flected by the presence of the term η π Ω strated by William Brainard (1969), this in the coefficient on E{ t | t}. Similarly, kind of uncertainty can introduce cau- 65 We are assuming that the policy-maker knows tion in policy responses. In contrast to the first two moments of the random parameters. the case of certainty-equivalence, policy It may be more plausible to argue that the policy- maker in fact has little idea what the true distri- actions now affect the conditional vari- bution looks like. See Onatski and Stock (1999) ance of inflation and output, as well as who analyze the policy problem in this kind of en- the conditional mean. vironment using robust control methods. 66 It should also be clear from equation (5.7) that with parameter uncertainty the interest rate 64 Wieland (1997) analyzes policy in a frame- no longer adjusts to perfectly offset demand work where the central bank has to learn the value shocks. Suppose, for example, that there is a posi- of the natural rate of unemployment (which, in tive demand shock. The interest rate goes up, but our analysis, corresponds to having to learn about the parameter uncertainty moderates the extent of potential GDP.) the rise, relative to the certainty equivalence case. Clarida, Galí, Gertler: The Science of Monetary Policy 1689 uncertainty about the impact of an in- may care about avoiding excessive vola- crease in the interest rate on the output tility in the short term interest rate in gap moderates the extent of adjustment pursuing its stabilization goals. in it. The second term on the right side To illustrate, consider the special of equation (5.7) captures this latter case of equation (5.6) with ρ = 1. In this dampening effect. instance, the difference in the interest This simple form of model uncertainty rate (it − it − 1), as opposed to the level, is thus may help explain the relatively low a linear function of πt and xt. Under the variability of interest rates in the data. difference rule, the expected future One feature of interest rate smoothing short rate at t + i, Et{it + i}, is given by it does not appear to capture, however,  k  is the strong lagged dependence in the   Et{it + k} = Et∑ (it + j − it + j − 1) + it interest rate. Put differently, the kind   j = 1 of parameter uncertainty we have dis-   (5.8) cussed may explain why the slope coef-  k  =  α + βπ + γ  + ficients on inflation and the output gap, Et∑ [ t + j xt + j] it  =  α and β, are small relative to the case of  j 1  certainty equivalence. But it does not Assume that the long-term rate depends explain the partial adjustment, given by on the sum of expected short rates over 67 the dependence of it on it − 1. the same horizon, in keeping with the ex- Rotemberg and Woodford (1997) of- pectations hypothesis of the term struc- fer a novel explanation for the lagged ture. Then, in comparison with the level dependence that is based on the lever- rule, the difference rule increases the re- age that this kind of adjustment rule sponsiveness of the long term rate under may provide the central bank over the the feedback policy. Suppose for example long term interest rate. The idea is that that, in reaction to a rise in inflation above lagged dependence in it permits the target at time t, the central bank raises it central bank to manipulate long term above its steady state value. Under the rates, and hence aggregate demand, difference rule the increase in the inter- with more modest movements in the est rate has a persistent effect on the path   short term rate than would be otherwise  +  of the expected short rate, since Etit i be required. This kind of rule is thus depends additively on it. Further, if changes desirable to the extent the central bank in inflation and output are persistent, 67 Sack (1997a,b) argues, nonetheless, that pa- then the path of expected short rates will rameter uncertainty can explain this phenomenon actually be rising, as equation (5.8) makes if the uncertainty of the impact of the interest rate clear.68 The difference rule thus en- on the economy is based on the change in the in- ( − ) hances the countercyclical movement of terest rate it it − 1 as opposed to the deviation from trend it. In the former instance, changes in it the long rate relative to the movement of raise the conditional variability of output, which short rate. Given that aggregate demand induces the central bank to keep it close to it − 1. On the other hand, it is not well understood how depends on the long rate, this kind of the link between model uncertainty and policy rule thus enables the central bank to conservatism is affected when there is active learning about the economy. Some results suggest that learning should induce active adjustments of 68 On the surface it appears that the interest the policy instrument to facilitate estimating the rate might explode under the difference rule, true model. See the discussion in Wieland (1997), since it will continue to increase so long as infla- for example. Also, it is possible to construct exam- tion is above target. However, the rise in the inter- ples where parameter uncertainty leads to in- est rate will dampen demand and inflation. In the creased activism. See, for example, Thomas Sar- context of our model, it does so sufficiently to pre- gent (1998). clude explosive behavior. 1690 Journal of Economic Literature, Vol. XXXVII (December 1999) stabilize the economy with relatively it is always optimal to tighten monetary modest movements in the short rate.69 policy to gradually bring inflation back Overall, Rotemberg and Woodford to the optimum (see Result 2 in Section provide a plausible explanation for why 3). During his tenure at the Federal Re- central banks may want to introduce serve Board, however, Blinder proposed lagged dependence in the interest rate. the following alternative: If inflation is Whether this story can also account for above but near the optimum, policy the empirically observed modest re- should not contract demand. Rather, it sponse of the short rate to inflation and should take an “opportunistic” ap- the output gap (i.e., the low values of β proach. Roughly speaking, being oppor- and γ, the slope coefficients on πt and xt) tunistic boils down to waiting until remains to be seen. achieving the inflation target could be Another explanation for policy con- done at the least cost in terms of incre- servatism and the associated interest mental output reduction. Blinder’s rate smoothing includes fear of disrupt- original concept was vague as to the de- ing financial markets (see, e.g., Good- tails. Recent work by researchers at the friend 1991). Sharp unanticipated in- Federal Reserve Board has filled in a creases in interest rates can generate number of the missing pieces. capital losses, particularly for commer- Athanasios Orphanides and David cial banks and other financial institu- Wilcox (1996) show that it is possible to tions that may be exposed to interest rationalize something like opportunistic rate risk. This consideration might ex- policy by making a small adjustment of plain why the Federal Reserve chose to the policy objective function. In par- raise rates only very gradually during ticular, suppose that policy-makers care 1994, the tail end of a period of consid- quite a lot about small departures of erable financial distress (see, e.g., the output from target, at least relative to discussion in John Campbell 1995). Dis- small departures of inflation. An exam- agreement among policy-makers is an- ple of an objective function that capture other explanation for slow adjustment this phenomenon is given by of rates. Neither of these alternative  ∞  stories have been well developed, 1   − βi(α + π2 ) max Et∑ | xt + i | t + i  (5.9) however. In general, understanding   2 i = 0 why interest rate smoothing occurs in   practice is an important unresolved With this objective function, the opti- issue. mality condition for policy becomes: α = π < 5.3 Non-Smooth Preferences xt 0, if | t | λ and Opportunism (5.10) α | πt | = , otherwise Another aspect of policy that has re- λ ceived considerable attention involves α Thus, if inflation is within λ units of the process of disinflation. In the base- the target, the optimal policy is to sim- line model, if inflation is above target, ply stabilize output. Otherwise, policy α 69 The idea that the central bank should pursue should keep inflation at most λ units a partial adjustment rule to exploit the depen- from target and then wait for favorable dence of demand on future policy is reminiscent supply shocks that move it closer to tar- of the globally optimal policy under commitment (see section 4.2.2). Indeed, Woodford (1998) get (e.g., favorable movements in the makes this connection formally. cost push shock ut). In this respect the Clarida, Galí, Gertler: The Science of Monetary Policy 1691 policy is opportunistic. A better term We now consider an alternative frame- for it, however, might be “inflation zone work that allows for endogenous persis- targeting” (Bernanke and Mishkin tence in output and inflation. Our pur- 1997). What the policy really amounts pose is to show that the results derived to is keeping inflation with a certain in the baseline framework extend to this range, as opposed to trying to move it more general setting. In this regard, we to an exact target. show that our results are not specific to Variations on this theme allow for the particular benchmark model we em- preferences that generate an inflation ployed, but instead hold across a rea- zone target, but then has policy trade off sonably broad class of models that are between inflation and output goals when used for applied macroeconomic analy- inflation is outside the target zone. Or- sis. The major difference is that with phanides, David Small, Volcker Wieland endogenous persistence in inflation, the and Wilcox (1997) (OSWW) provide an equilibrium feedback monetary policy now example of this more general setup. influences the speed of convergence of It is important to emphasize, though, inflation to its target. that opportunistic policy behavior that Consider the following generaliza- is distinct from the gradualism of the tions of the IS and aggregate supply baseline model only arises if cost push curves: factors are present in inflation. This is = − ϕ[ − π ] + θ true because only with cost push infla- xt it Et t + 1 xt − 1 + ( − θ) + ( ) tion present does a trade-off between 1 Etxt + 1 gt 6.1 output and inflation emerge (see Result π = λ x + φ π − 1). Indeed, OSWW show that opportun- t t t 1 + (1 − φ)βE π + + u (6.2) istic policy rules are equivalent to con- t t 1 t ventional gradualist rules in the pres- Equation (6.1) incorporates the lagged ence of demand shocks, but differ when output gap in the IS curve. Equation there are supply shocks.70 (6.2) adds lagged inflation to the aggre- In summary, we have gate supply curve. The parameters θ and Result 12: If there is more cost asso- φ index the influence of lagged versus ex- ciated with small departures of output pected future variables. As a result the from target than with small departures model nests some important special of inflation, then an opportunistic ap- cases. With θ = 0 and φ = 0, we recover proach to disinflation may be optimal. the baseline model. Conversely, with This policy, further, is equivalent to θ = 1 and φ = 1, the model becomes targeting inflation around a zone as (approximately) the backward-looking opposed to a particular value. framework that Svensson (1997a,b) and Ball (1997) have used to analyze mone- 6. Implications of Endogenous Inflation tary policy. For simplicity we assume that and Output Persistence the disturbances gt and ut are serially uncorrelated (i.e., we set µ and ρ in Within our baseline model, the dy- equation (2.3) and (2.4) equal to zero). namics of output and inflation are due This simple formulation does not allow entirely to exogenous force processes. for delays in the effect of policy, but we 70 For an alternative description of the oppor- show later that it is easy to amend the tunistic approach, see Bomfin and Rudebusch analysis to incorporate delayed policy (1997). These authors emphasize the ratcheting down of inflation and, in particular, explore the effects. role of imperfect credibility. As we noted earlier, virtually all the 1692 Journal of Economic Literature, Vol. XXXVII (December 1999) major applied macroeconomic models analytical solution is not available, ex- allow for some form of lagged depen- cept in the polar cases of φ = 0 and φ = 1. dence in output and inflation. The pri- It is, however, possible to provide an in- mary justification is empirical.71 By ap- tuitive description of the optimum. Let pealing to some form of adjustment aπ be a parameter that measures the se- costs, it may be feasible to explicitly rial dependence of inflation in the motivate the appearance of xt − 1 within reduced form. Then the optimality the IS curve. Motivating the appearance condition that governs policy is given of lagged inflation in the aggregate sup- by: ply curve, however, is a more formida- λ ∞ 72 ble challenge. Some frameworks do so = − π + ∑ βk π +  xt α  t Et t k (6.3) by effectively appealing to costs of k = 1 73 changing the rate of inflation. This as- λ sumption, though, is clearly unattrac- = − π α( − β ) t (6.4) tive. In the spirit of robustness, how- 1 aπ ever, it is important to understand the with implications of lagged dependence. This πt = aπ πt − 1 + au ut (6.5) is particularly true given the empirical and appeal of this formulation. ≤ < We begin with the case of discretion, 0 aπ 1 and then later describe briefly how the With inertia present, adjustments in results are affected when the central current monetary policy affect future bank can make credible promises.74 An time path of inflation. As consequence, policy now responds not only to current 71 For an empirical justification for including inflation but also to forecasts of infla- lagged dependent variables, see Fuhrer (1996). 72 It is possible to motivate a dependency of cur- tion into the indefinite future. How rent inflation on lagged inflation by appealing to much depends positively on aπ, which π = adaptive expectations (e.g., suppose Et − 1 t measures the degree of inflationary κπ t − 1). Indeed, this is the traditional approach (see the discussion in Blanchard 1997). The issue persistence. then becomes motivating the assumption of adap- The coefficients aπ and au are func- tive expectations. tions of the underlying parameters 73 See, for example, Fuhrer and Moore (α,λ,β,φ) 75 aπ, (1995a,b) and Brayton, Levin, Tyron, and Williams . The former, is key, since (1997). Galí and Gertler (forthcoming) criticize it measures the speed of convergence to the existing empirical literature on inflation dy- inflation under the optimal policy. It is namics, and provide new evidence which suggests that (2.2) is a good first approximation to the data. possible to show that this parameter lies 74 As in section 3, we restrict attention to between zero and unity, implying con- Markov perfect equilibria. In this case, however, vergence. The magnitude of aπ depends we must take into account that inflation is an en- dogenous state variable. In any stationary equilib- positively on the degree of inflation in- rium, therefore, expected inflation will depend on ertia φ. In the baseline case of no infla- lagged inflation. What the policy maker takes as tion inertia, φ = 0, implying aπ = 0. aπ given, accordingly, is not the level of expected in- flation, but rather how private sector expectations 75 To obtain solutions for aπ and au, substitute of inflation tomorrow respond to movements in in- λ flation today. Simply put, to solve for the equilib- the optimality condition xt = − πt and rium under discretion, we assume that private sec- α(1 − βaπ) π ν π + ν π tor forecast of t + 1 takes the form π t uut, the conjectured solution for t, (6.5), into the ag- ν ν where π and u are arbitrary constants that the gregate supply curve. Then use the methods of policy-maker takes as given. In the rational expec- undetermined coefficients to solve for aπ and au. ν ν tations equilibrium π and u equal the true funda- The equation for aπ is a cubic. The solution is the mental parameters in the reduced form inflation, unique value between zero and unity, which corre- aπ and au. sponds to the unique stable root. Clarida, Galí, Gertler: The Science of Monetary Policy 1693

also depends negatively on the relative Most of the qualitative results ob- cost of inflation, measured by 1/α. As in tained in the baseline case extend to the baseline case, if the distaste for in- this more general setting. As in the flation is high (α is low), the optimal baseline case, the policy-maker faces a policy aggressively contracts demand short-run trade-off between output and whenever inflation is above target: With inflation (Result 1). The effect of infla- endogenous persistence, this contrac- tion inertia is to make this trade-off less tion not only reduces inflation but also favorable. Equation (6.3) shows that increases the speed of convergence to relative to the baseline case of φ = 0, the target. Figure 2 illustrates the relation optimal policy requires a more aggres- between aπ and α for three different sive response to any burst of inflation. values of φ: φ = 0.01 (low inertia), φ = 0.5 The problem is that any inflation not (medium) and φ = 0.99 (high). eliminated today persists into the fu- Combining (6.3) with (6.1) yields the ture, potentially requiring more output implied optimal interest rate rule: contraction. Figure 3 illustrates how the 1 trade-off becomes less favorable in this = γπ π + + γ − + (6.6) it Et t 1 xxt 1 ϕ gt case by plotting the efficient policy frontier for the three benchmark values with of φ. In addition, since 0 ≤ aπ < 1, the op- λ(1 − aπ) timal policy calls for gradual adjustment γπ = 1 + ϕαaπ(1 − βaπ) of inflation to target (Result 2). With θ φ > 0, further, extreme inflation target- γ = α = x ϕ ing is only optimal if 0, as equation (6.3) and Figure 2 suggest. π = π Et t + 1 aπ t From the interest rate rule given by 1694 Journal of Economic Literature, Vol. XXXVII (December 1999)

equation (6.6) it is apparent that the co- efficient on expected inflation exceeds unity, implying that the ex ante real rate must rise in response to higher ex- pected inflation (Result 3). Finally, the interest rate should also adjust to per- fectly offset demand shocks, but should not respond to movements in potential output (Result 4.) One interesting dif- ference in this case is that the interest rate responds to the lagged output gap, since this variable now enters the IS curve. Thus, the optimal interest rate rule now resembles the simple gap rules that have been discussed in the litera- ture. We return to this point later. In summary, we have Result 13: Results 1 through 4 that describe optimal monetary policy under discretion within the baseline model also apply in the case with endogenous output and inflation persistence. In addition to allowing for lagged de- pendence in output and inflation, there is also strong empirical justification for incorporating delays in the effect of policy. It is straightforward to extend the analysis to include this real world feature. Suppose, following Svensson (1997a,b) and Ball (1997), that there is a one-period delay in the effect of the real interest rate on the output gap and, in turn, a one-period delay in the effect of the output gap on inflation. Then the optimality condition becomes76 λ + = − π + Et{xt 1} l Et{ t 2} (6.7) α(1 − βaπ)

l where the parameter aπ measures the se- rial dependence in inflation for this case. It has qualitatively similar properties to aπ in equation (6.5), with 0 ≤ aπl < 1. The left side of (6.7) reflects the one-period delay in the impact of policy on output,

76 = In this case, the IS curve is given by xt − ϕ − π + θ + ( − θ) + [it − 1 Et − 1 t] xt − 1 1 Et − 1xt + 1 gt and π = the aggregate supply curve is given by t λ + φπ + ( − φ)β π + xt − 1 t − 1 1 Et t + 1 ut. Clarida, Galí, Gertler: The Science of Monetary Policy 1695 and the right side reflects the two-period installing a conservative central bank delay on inflation. chair. Due to the delayed impact of policy, the central bank takes both the output 7. Simple Rules for Monetary Policy gap at t, xt, and the forecast of inflation We next discuss some normative and at t + 1, Et{πt + }, as predetermined from 1 positive aspects of simple feedback the vantage of time t. The rest of the rules for the interest rate that have solution may thus be expressed in terms been discussed in the literature. We then of these predetermined variables: discuss how these instrument-based π = l π Et{ t + 2} aπ Et{ t + 1} (6.8) rules are related to simple rules for tar- = γ l π + γ it π Et t + 1 x xt (6.9) gets that have been recently proposed, with including inflation targeting and nomi- nal GDP targeting. Finally, we conclude (γπ − )β γ l = + 1 > π 1 l 1 with a brief discussion of the issue of aπ possible indeterminacy of interest rate The solution closely resembles the rules. case without delay. Any differences just 7.1 Simple Interest Rate Rules reflect the lagged influence of policy in this environment. The nominal rate still Taylor (1993a) ignited the discussion adjusts more than one-for-one with ex- of simple interest rate rules.78 He pro- pected inflation. Due to the lag struc- posed a feedback policy of the following ture, though, it adjusts to the current form: output gap, as opposed to one from the ∗ – it = α + γπ (πt − π) + γx xt (7.1) previous period. We conclude this section with brief with discussion of the gains from commit- α = –r + π– ment. It is possible to show that, as in γπ > 1, γx > 0 the baseline model, the policy rule un- ∗ der commitment resembles the rule un- where it is the target interest rate the feedback rule defines, π– is the target in- der discretion that would obtain if the – policy-maker assigned a higher relative flation rate, and r is the long-run equi- 79 cost to inflation (lower value of α ) than librium real interest rate. Also, we now the true social cost. Because inflation express all variables in levels, as opposed inertia is endogenous in this case, the to deviations from trend. optimal policy with commitment im- A number of other researchers have plies a faster transition of inflation to considered rules like (7.1) (see, e.g., the optimum relative to what occurs un- Henderson and Mckibbon 1993). Tay- der discretion. This can be seen by not- lor’s contribution is to spell out the nor- ing that the parameter which governs mative and positive implications. On the speed of convergence of inflation, 78 aπ, is decreasing in the relative cost of McCallum (1988) proposed a simple rule for α 77 the monetary base. The rule is less popular in pol- inflation 1/ (see Figure 4). Simply icy circles due to the implied interest rate volatil- put, disinflations will be swifter than ity (see Result 9). McCallum (1997) argues, how- otherwise if credible commitment is ever, that the concern about interest rate volatility is not well understood, a point with which we possible either directly or indirectly by agree. 79 The inflation rate Taylor uses is actually the 77 Note that the speed of convergence of infla- rate over the previous year (as opposed to the pre- tion is decreasing in aπ. vious quarter). 1696 Journal of Economic Literature, Vol. XXXVII (December 1999)

the normative side, the rule is consis- rule provides a reasonably good descrip- tent with the main principles for opti- tion of policy over the period 1987–92. – mal policy that we have described. It These are: γπ = 1.5, γx = 0.5, π = 2, and calls for gradual adjustment of inflation –r = 2. Taylor used informal judgement to its target (see Result 2). Specifically, to pick them. An interesting question is it has the nominal rate adjust more than whether a formal methodology would one-for-one with the inflation rate. To yield something different. the extent lagged inflation is a good In this spirit, Clarida, Galí, and Gertler predictor of future inflation, the rule (forthcoming) estimate a simple rule for thus has real rates adjusting to engineer U.S. monetary policy, and consider how inflation back to target (see Result 3). this rule has evolved over time. The Finally, note that the interest rate re- specific formulation is a “forward look- sponds to the output gap as opposed to ing” version of the simple Taylor rule: the level of output. Thus, in at least an ∗ = α + γ ( π − π–) + γ approximate sense, the rule calls for a it π Et t + 1 x xt (7.2) countercyclical response to demand Under this rule, policy responds to shocks and accommodation of shocks to expected inflation as opposed to lagged potential GDP that do not affect the inflation. In this respect, the formula- output gap (see Result 4). tion is consistent with the optimal rules On the positive side, Taylor showed derived for both the baseline and hy- that with certain parameter values, the brid models (see equations 3.6 and 6.6). Clarida, Galí, Gertler: The Science of Monetary Policy 1697

TABLE 1 ESTIMATES 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)

Another virtue is that this formulation with standard errors are given by Table nests the simple Taylor rule as a special 1.80 case. If either inflation or a linear com- The key lesson involves the parame- bination of lagged inflation and the out- ter γπ, the coefficient on the inflation put gap is a sufficient statistic for future gap. The estimate for the pre-Volcker inflation, then the specification col- rule is significantly less than unity. This lapses to the Taylor rule. suggests that monetary policy over this Because of the Federal Reserve’s ten- period was accommodating increases in dency to smooth interest rate adjust- expected inflation, in clear violation of ments (see the discussion in section 5), the guidelines suggested by Results 2 a static relation like equation (7.2) can- and 3. For the post-1979 rule the esti- not capture the serial correlation pres- mate is significantly above unity. It thus ent in the data. We thus allow for the incorporates the implicit inflation tar- possibility of partial adjustment to the geting feature that we have argued is a target rate, according to: critical feature of good monetary policy = ρ + ( − ρ) ∗ management. It is also true that in the it it − 1 1 it (7.3) Volcker–Greenspan era the Federal Re- where ρ is a parameter that measures the serve was only responding to the output degree of interest rate smoothing. gap to the extent it had predictive power for inflation:81 The estimated co- We estimate different rules for the γ pre-Volcker (1960:1–79:2) and Volcker– efficient on the output gap, x, is not Greenspan (1979:3–96:4). We do so be- significantly different from zero. Pre cause it is widely believed that U.S. 1979:4 it is positive and significant. This monetary policy took an important turn outcome is consistent with the conven- for the better with the appointment of tional view that pre-1979, the Federal Paul Volcker as Fed Chairman (see Friedman and Kuttner 1996 and Gertler 80 The estimates of the parameters in equation (7.2) are obtained by using an instrumental vari- 1996). Among other things, this period ables procedure based on Generalized Methods of marks the beginning of an apparently Moments (GMM). See Clarida, Galí, and Gertler successful and long-lasting disinflation. (forthcoming) for details. The specific numbers reported here are based on a version of this policy We find that the simple rule given by reaction function that has the Funds rate respond equation (7.2) does a good job of char- to expected inflation a year ahead and the current acterizing policy in the Volcker–Green- output gap (reported in Table 2 of that paper). The results, however, are robust to reasonable span era. Further, it adheres to the variations in the horizons for the gap variables. guidelines for good policy that we have 81 In particular, the output gap enters the in- strument set for expected inflation. Thus, the established. The estimated pre-Volcker γ coefficent x reflects the influence of the output rule violates these guidelines. Specifi- gap on the interest rate that is independent of its cally, the parameter estimates along predictive power for inflation. 1698 Journal of Economic Literature, Vol. XXXVII (December 1999)

Reserve was relatively more focused on of capturing the broad movements in output stabilization and less focused on the Funds rate for the second half of inflation. the sample, for which it was estimated. The finding that the Fed responded For the pre-Volcker period, matters are differently to inflation in the two eras is different. The target (generated by the apparent from inspection of the data. estimated Volcker–Greenspan rule) is Figure 4 plots the Federal Funds rate systematically well above the historical and the rate of CPI inflation from 1965 series. In this concrete respect, policy to the present. The graph shows a clear was far less aggressive in fighting break in the Funds rate process around inflation in the earlier period.83 1979.82 During most of the 1970s, the Figure 6 compares the ability of the ex post real rate was zero or negative. forward and backward looking (Taylor) After 1979 it becomes positive. While target rules to explain the post 1979 many factors influence the real rate, the data. Though we find that the data re- tight monetary policy engineered by jects the backward looking rule in favor Paul Volcker surely provides the most of the forward looking one,84 the two do logical explanation for this initial run-up. a roughly similar job of accounting for Figure 5 illustrates the policy change the behavior of the Funds rate. This oc- by plotting the estimated target value of curs probably because, with U.S. data, the interest rate under the Volcker– Greenspan rule over the entire sample 83 Some but not nearly all the difference be- period. The target rule does a good job tween rates pre-1979 and the target values under a post-1979 rule could be accounted for by a secular 82 Huizinga and Mishkin (1986) present formal change in the real rate. evidence of a structural break at this time. 84 See Clarida, Galí, and Gertler (1998). Clarida, Galí, Gertler: The Science of Monetary Policy 1699

not much besides lagged inflation is Mishkin 1997 for a recent survey). In- useful for predicting future inflation. deed a number of central banks, most Finally, it is interesting to observe notably the Bank of England, have re- that the other major central banks, the cently adopted formal inflation targets Bundesbank and the Bank of Japan, (see, e.g., Andrew Haldane 1996). have behaved very similarly in the post- In one sense, inflation targeting in- 1979 era. In Clarida, Galí, and Gertler volves nothing more than pursuing the (1998), we estimate our specification kind of gradualist policy that our opti- for these central banks. The estimated mal policy calculation implies (see Re- parameters in each case are quite close sult 2). Indeed, all the leading real- to those obtained for the Federal Re- world proposals call for gradual serve during the Volcker–Greenspan convergence of inflation to target. None period. Thus, good policy management recommend trying to hit the inflation appears to have been a global phenome- target continuously, which is consistent non. Perhaps this is not surprising since with our analysis. In this respect, the the successful disinflation has also been rule we estimate for the period is per- a world-wide event. fectly consistent with inflation targeting. The rationale for inflation targeting, 7.2 Simple Target Rules we think, is twofold. The first is simply There have also been proposed sim- to guarantee that monetary policy ple rules for targets, as opposed to in- avoids the mistakes of the pre-Volcker struments. Of these proposed policies, era by identifying a clear nominal an- inflation targeting has received by far chor for policy. (After all, Alan Green- the most attention (see Bernanke and span will not be around forever). The 1700 Journal of Economic Literature, Vol. XXXVII (December 1999) inflation target is in effect the nominal der an inflation targeting policy. For all anchor. Since the anchor is directly in these reasons, it is perhaps not surpris- terms of inflation, it avoids the poten- ing that no major central bank has tially instability problems associated adopted a price level target. with alternatives such as money growth Another candidate variable for target- that are only indirectly linked to infla- ing is nominal GDP. This approach has tion. For example, if there are large also received less attention in the re- shocks to money demand, then a money cent literature, however. One problem growth target may fail precisely to pin is that if there are shifts in the trend down the equilibrium inflation rate. growth of real GDP, the rule does not The second rationale has to do with provide a precise nominal anchor. An- credibility and commitment. We have other problem, emphasized by Ball seen that it is in general optimal for (1997), is that the policy may be overly policy-makers to place a higher weight restrictive. In the hybrid model of sec- on the costs of inflation than the true tion 5, for example, the optimal policy social loss function suggests (see Re- in general has the interest rate adjust to sults 6 and 7). The focus on inflation some linear combination of expected in- targets may be viewed as a way to instill flation, the output gap and demand dis- a higher effective weight on inflation in turbances. The weights depend upon the policy choice. the underlying structural parameters of Price level targeting is another type the model. Under nominal GDP target- of simple rule that has been discussed ing, the central bank adjusts the inter- in the literature. This policy, which may est rate to the sum of inflation and real be thought of as a more extreme version GDP growth. It thus arbitrarily applies of inflation targeting, has not received an equal weight to each component of much support among policy-makers and nominal GDP. High nominal GDP applied economists. There are several growth, further, could occur when the problems: First, if the price level over- economy is recovering from a recession shoots its target, the central bank may and is still well below full capacity. A have to contract economic activity in or- rule that calls for raising interest rates der to return the price level to its goal. in response to above-target nominal That is, inflation above the amount im- GDP growth in these circumstances plied by the price level target must be could stifle the recovery.85 followed by inflation below this desired 7.3 Indeterminacy under Interest amount in order to return the target. Rate Rules Under inflation targeting, bygones are bygones: overshooting of inflation in One criticism of simple interest rate one year does not require forcing infla- rules is that, under certain circum- tion below target in the following year. stances, they may induce instability. Second, the source of positive drift in That is, in many models there may not the price level maybe measurement er- be a determinate equilibrium under ror (see the discussion in section 2.) It particular parametrizations of the policy would be unfortunate to have measure- 85 See Ball (1997) and Svensson (1997b) for ex- ment error induce tightening of mone- plicit examples of how nominal GDP targeting tary policy. Third, as McCallum (1997b) could produce adverse outcomes. McCallum shows, the net reduction in price uncer- (1997c), however, argues that these results are sensitive to the use of a backward-looking Phillips tainty under a price level target rule, curve. For the case in favor of nominal GDP tar- may be small relative that obtained un- geting, see Hall and Mankiw (1994). Clarida, Galí, Gertler: The Science of Monetary Policy 1701 rule. In a classic paper, Thomas Sargent terminacy are possible. First, if in re- and Neil Wallace (1975), illustrated sponse to a rise in expected inflation, how nominal indeterminacy may arise if the nominal rate does not increase suf- prices are perfectly flexible. Under an ficiently to raise the real rate, then self- interest rate rule the equilibrium pins fulfilling bursts of inflation and output down the level of real money balances. are possible. A rise in expected infla- However, there are an infinite number tion, leads to a fall in real rates that, in of combinations of the nominal money turn, fuels the boom. Indeed, the mone- stock and the price level that satisfy this tary policy rule that Clarida, Galí, and equilibrium condition.86 In this respect, Gertler (forthcoming) estimate for the the interest rate rule produces nominal pre-Volcker period permits exactly this indeterminacy.87 kind of sunspot behavior. The lesson When there is sluggish price adjust- here is simply that a good monetary pol- ment, the problem of nominal indeter- icy rule should not accommodate rise in minacy vanishes. Last period’s price expected inflation. It should instead level effectively serves a nominal an- pursue the implicit kind of inflation chor. Simple interest rate rules thus do targeting that we have been emphasiz- not produce price level indeterminacy ing. This boils down to raising nominal in the frameworks we have analyzed. rates sufficiently to increase real rates More generally, since there is little rea- whenever expected inflation goes up. son to believe that prices are perfectly As Bernanke and Woodford (1998) flexible, the issue of nominal indetermi- emphasize, indeterminacy is also possi- nacy does not seem important in prac- ble if the rule calls for an overly aggres- tice. On the other hand, there is poten- sive response of interest rates to move- tially a problem of real indeterminacy ments in expected inflation. In this in the case of price stickiness, as Wil- instance, there is a “policy overkill” ef- liam Kerr and Robert King (1996), Ber- fect that emerges that may result in an nanke and Woodford (1997) and Clarida, oscillating equilibrium. Clarida, Galí Galí and Gertler (forthcoming) have re- and Gertler (forthcoming) show, how- cently emphasized.88 Two types of inde- ever, the magnitude of the policy re- sponse required to generate indetermi- 86 McCallum (1997), however, argues that the nacy of this type greatly exceeds the price level is in fact determined in this kind of estimates obtained in practice. This po- environment. tential indeterminacy however does 87 A recent literature shows that the govern- ment’s intertemporal budget constraint may re- suggest another reason why a gradual store uniqueness under an interest rule, even in approach to meeting an inflation target an environment with flexible prices. What is criti- may be desirable. cal is whether the interest on the debt is financed by taxes or money creation. See, for example, Woodford (1994), Sims (1994), and Leeper (1991). 8. Concluding Remarks 88 These papers focus on local indeterminacy. See Jess Benhabib, Stephanie Schmidt-Grohe, and Martin Uribe (1998) for a discussion of global in- We conclude by describing several determinacy. To avoid global indeterminacy, the areas where future research would be central bank may have to commit to deviate from a quite useful: simple interest rate rule if the economy were to get sufficiently off track. This threat to deviate can (1) It is always the case that more be stabilizing, much the way off the equilibrium knowledge of the way the macro- path threats induce uniqueness in game theory. economy works can improve the perfor- Because the threat is sufficient to preclude inde- terminate behavior, further, it may never have to mance of monetary policy. Particularly be implemented in practice. critical, however, is a better understanding 1702 Journal of Economic Literature, Vol. XXXVII (December 1999) of the determinants of inflation. As we point where this constraint clearly is a have emphasized, the output/inflation consideration for policy management. trade-off is highly sensitive to both the Similarly, in the U.S. and Europe, the degree and nature of the persistence in inflation rates have fallen to the point inflation. As a consequence, so too is where the zero bound limit could con- the speed at which monetary policy ceivably affect the ability to ease rates should try to reach the optimal inflation in the event of a downturn. Under- rate. Rationalizing the observed persis- standing how monetary policy should tence in inflation is thus a high priority. proceed in this kind of environment is Work by Galí and Gertler (forthcoming) an important task. When the nominal and Argia Sbordone (1998) suggests that rate is at zero, the only way a central the short-run aggregate supply curve bank can reduce the real interest rate is employed in our baseline model may to generate a rise in expected inflation provide a reasonable approximation of (see the discussion in Alexander Wol- reality, so long as real marginal cost man 1998, and the references therein). (specifically real unit labor costs) is used How the central bank should go about as the relevant real sector forcing vari- this and whether cooperation from fis- able instead of the output gap, as the cal policy is necessary are important theory suggests. Galí and Gertler (forth- open questions. As Wolman (1998) sug- coming) argue further that persistence gests, the conclusions are quite sensi- in inflation may be related to sluggish tive to the nature of the inflationary adjustment of unit labor costs vis-a-vis process. movements in output. Sorting out this (4) A more specific issue, but none- issue will have important repercussions theless an important one, is to under- for monetary policy. stand why central banks smooth interest (2) Our analysis of monetary policy, rate adjustments. As we discussed in as in much of the literature, was re- section 5, optimal policies implied by stricted to closed economy models. Ex- most existing macroeconomic frame- tensions to open economy frameworks works generate paths for the interest are likely to provide new insights on the rate that are much more volatile than desirability of alternative monetary pol- what is observed in reality. The possi- icy rules, and raise a number of issues bility thus arises that existing models of great interest, including: the choice may fail to adequately characterize the of exchange rate regime, the potential constraints that policy-makers face in benefits from monetary policy coordi- practice. We suggested in section 5 that nation, the optimal response to shocks some form of model uncertainty might originating abroad, and consumer price be able to account for this phenome- index versus domestic inflation target- non. Another alternative is that central ing. Recent work by Ball (1998), Svens- banks may be exploiting the depen- son (1998), and Monacelli (1999) along dency of demand on expected future in- these lines will undoubtedly lay the terest rates, as argued by Rotemberg ground for further research on this front. and Woodford (1999). Whether these (3) Throughout the analysis, we as- explanations or any others, such as fear sumed that the lower bound of zero on of disruption of financial markets, can the nominal interest rate was not a con- account for interest rate smoothing straint on the performance of monetary needs to be determined. policy. In Japan, for example, the short- (5) A somewhat related issue involves term nominal rate has fallen to the how a central bank should deal with Clarida, Galí, Gertler: The Science of Monetary Policy 1703 financial stability. The policy rules Appendix: The General Solution discussed in the literature do include under Commitment contingencies for financial crises. A fre- At time t, the central bank commits to a state π quently cited reason for why monetary contingent sequence for xt + i and t + i to maximize policy should not adhere tightly to a  ∞  1   − βi α 2 + π2 simple rule is the need for flexibility in max Et∑ [ xt + i t + i] 2  =  the event of a financial collapse. In the i o  wake of the October 1987 stock market subject to the short-run aggregate supply curve π = λ + β π + crash, for example, most economists t + i xt + i Et{ t + 1 + i} ut + i supported the decision of the Federal Reserve Board to reduce interest rates. with This support was based largely on in- = ρ + ε ut + i ut + i − 1 t + i stinct, however, since there is virtually no formal theoretical work that rational- Following Currie and Levine (1993) and Wood- izes this kind of intervention. More ford (1998), form the Lagrangian:  ∞ 1  generally, concern about financial sta- − βi α 2 + π2 max Et∑ {[ xt + i t + i] 2  = bility appears to be an important con- i o   straint on policy-making. As we sug-    + φ + [π + − λx + − βπ + + − u + ]} gested in section 5, it is one possible  t i t i t i t 1 i t i  reason why central banks smooth inter-   1 where φ + is the multiplier associated with the est rate changes. Understanding the na- 2 t i ture of this concern is clearly a fertile constraint at t + i. area for research. The first order necessary conditions yield: (6) Finally, with few exceptions, vir- λ α x + − φ + = 0, ∀i ≥ 0 tually all the literature ignores the issue t i 2 t i 89 of transition to a new policy regime. 1 1 π + + φ + − φ + − = 0, ∀i ≥ 1 In particular, the rational expectations t i 2 t i 2 t i 1 assumption is typically employed. Policy π + 1 φ = t t 0 simulations thus implicitly presume that 2 the private sector catches on immedi- Combining the first order necessary conditions to φ ately to any regime change. In reality, eliminate t + i then yields the optimality condi- however, there may be a period of tran- tions λ sition where the private sector learns − = − π ∀ ≥ xt + i xt + i − 1 α t + i, i 1 about the regime change. This kind of λ = − π scenario may be highly relevant to a xt α t central bank that has accommodated in- Substituting the optimality conditions in the ag- π flation for a sustained period of time gregate supply curve to eliminate t + i then yields but is intent on embarking on a disinfla- a stochastic difference equation for xt: tion. Modeling private sector learning λa x = a x − + aβ E {x + } − u is a challenging but nonetheless impor- t t 1 t t 1 α t α tant task. Sargent (1999) provides a ≡ where a α( + β) + λ . The stationary solution to promising start in this direction. More 1 2 this difference equation is given by: work along these lines would be highly λδ = δ − desirable. xt xt − 1 ut (8.1) α(1 − δβρ) 89 An exception is Brayton, Levin, Tyron, and 1 − √1 − 4βa2 where δ ≡ ∈(0,1), implying the pro- Williams (1997) who present simulations of policy 2aβ regime changes under different assumptions about cess for x is stable. Substituting the solution for x the behavior of private sector expectations. t t 1704 Journal of Economic Literature, Vol. XXXVII (December 1999) in the aggregate supply curve then yields a solu- Bernanke, Ben S. and Frederic Mishkin. 1997. π tion for t. “Inflation Targeting: A New Framework for δ Monetary Policy?” J. Econ. Perspect., 11:2, pp. π = δ π + ( − ) 97–116. t t − 1 ut ut − 1 (1 − δβρ) Bernanke, Ben S. and Michael Woodford. 1997. π = − “Inflation Forecasts and Monetary Policy,” J. Since t pt pt − 1, the solution implies a station- Money, Credit, Banking, 29:4, pp. 653–84. ary process for the price level: Blanchard, Olivier J. 1997. Macroeconomics. Up- δ per Saddle River, NJ: Prentice-Hall. = δ + pt pt − 1 ( − δβρ) ut Blinder, Alan S. 1997. “What Central Bankers Can 1 Learn from Academics—and Vice-Versa,” J. The stationary behavior of the price level results Econ. Perspect., 11:2, pp. 3–19. from the fact that the optimality condition effec- Bomfin, Antulio N. and Glenn D. 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