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Pitfalls of Forward-Looking Monetary Policy By MICHAEL WOODFORD* A distinctive feature of the procedures re- tion targeting as a regime of discretionary cently adopted by inﬂation-targeting central policy-making, in which the central bank is banks is their forward-looking character. Fore- charged with minimization of a loss function casts of the economy’s future evolution condi- that differs from the true social objective, in tional upon alternative policies play a central order to eliminate the Kydland-Prescott inﬂa- role in the banks’ deliberations, to an extent that tion bias resulting from discretion. King’s mod- the procedures adopted are sometimes charac- iﬁed loss function changes only the (constant) terized as “forecast targeting.” This emphasis target values for the target variables, and not the upon the future consequences of policy is un- variables themselves that the bank seeks to sta- surprising in an approach that tries to maintain bilize; hence, a Markov equilibrium resulting as transparent as possible a relation between the from discretionary optimization implies a pol- banks’ decisions and the ultimate goals of mon- icy that depends only upon states relevant to the etary policy; after all, current decisions can still determination of current or future inﬂation and affect the future, but not the past. output. Nonetheless, common descriptions of how Common descriptions of “inﬂation-forecast tar- inﬂation targeting is or should be practiced go geting” (e.g., Lars E. O. Svensson, 1999) illustrate too far, in proposing purely forward-looking this feature even more clearly. Under such proce- procedures. I shall argue instead that an optimal dures, an economic model is used to generate framework for the conduct of monetary policy conditional forecast paths for the target variables must generally be history-dependent in ways from the present onward associated with alterna- precluded by these simple proposals. This fol- tive feasible policies. The bank then chooses lows from a general feature of the optimal con- among the candidate forecast paths, either evalu- trol of a forward-looking system, which is to ating them according to a loss function or select- say, one in which the private sector’s expecta- ing the path that satisﬁes some targeting criterion, tions about future policy are an important de- such as a requirement that the forecast of inﬂation terminant of the effects of monetary policy. at some future horizon equals a target value, which may depend upon the output forecast. The bank’s current action is then the one required by I. Purely Forward-Looking Procedures the chosen scenario. The procedure is repeated afresh in each decision cycle. Past states obviously By a purely forward-looking decision proce- cannot affect the action that is chosen, if they dure for monetary policy I mean one in which affect neither the set of scenarios judged to be the bank’s action at any time is conditioned possible nor the criterion used to choose among solely upon those aspects of the state of the alternative scenarios. world that are relevant for forecasting the sub- Other authors have described inﬂation- sequent evolution of the bank’s target variables, targeting policies as rules for setting a short- which I shall here suppose to be the inﬂation term interest rate as a function of forecasts of rate and the level of aggregate economic activ- the future paths of the target variables (raising ity. Examples of such proposals are common- interest rates in proportion to the forecasted place in the literature on inﬂation targeting. For excess of inﬂation over the target level). Some- example, Mervyn King (1997) describes inﬂa- times the forecast is assumed to correspond to a scenario in which the interest rate is left at its current level; in other cases it represents * Department of Economics, Princeton University, Princeton, NJ 08544. I thank Julio Rotemberg and Lars a forecast of what should happen if the pre- Svensson for many helpful discussions, and the NSF for scribed policy rule is followed. In either case, research support. if the prescribed interest rate is a function only 100 VOL. 90 NO. 2 INFLATION TARGETING 101 of the forecasts, such a decision procedure is Euler equation. The ﬁrst relation determines t purely forward-looking. given xt, inﬂation expectations (Et t 1), and an exogenous cost shock ut. The second determines II. Why Optimal Policy Must xt given Et xt 1, the expected real rate of return Be History-Dependent (determined by the central bank’s instrument it and by Et t 1), and exogenous variation in the It might seem that the property just identiﬁed Wicksellian “natural rate of interest” r n. I assume t is a simple consequence of optimization, and that social welfare requires the minimization of thus wholly desirable. In particular, one might the expected value of a discounted sum of period suppose that, in the case of a social objective losses of the form that is additively separable over time, familiar 2 principles of dynamic programming imply that (1) Lt t x x2 t i 2 i t optimal policy at any point in time should de- pend only upon state variables that determine for some weights x 0, i 0. constraints upon possible paths of the target In this simple model, conditional forecasts in variables from that time onward. However, such period t of the paths of the target variables from principles apply only to the control of a system that period onward depend only upon the exog- in which the target variables evolve according enous state vector st , describing information at to laws of motion that are purely backward- t about the current and future values of the looking. When, instead, private-sector expecta- exogenous disturbances u t j , r n j . Thus any t tions of the economy’s future path are among determinate equilibrium resulting from a purely the determinants of the current values of target forward-looking procedure makes i t , t , and x t variables (as in almost any model of the mon- functions solely of st . If the disturbances are etary transmission mechanism derived from op- Markovian, this means a function only of the timizing behavior), such a conclusion is current disturbances u t and r n.t incorrect (Woodford, 1999a). Except in the special case that i 0 and The reason is simple. In general, forward- there are no cost shocks, an optimal equilibrium looking behavior implies that more desirable requires these variables to be functions of responses of the target variables (inﬂation and lagged disturbances as well. For example, in the output) to a shock can be achieved if it can be case of a transitory cost shock, a forward- arranged for private-sector expectations about looking procedure results in an equally transi- the future paths of the target variables to adjust tory increase in inﬂation and decrease in output, in the right way in response to the shock. How- with both variables expected to return to their ever, this can occur (when the private sector has average values once the disturbance is past. rational expectations) only if subsequent However, an optimal commitment would in- central-bank policy does in fact change as a volve a negative output gap that returns to zero result of the past shocks in such a way as to only slowly, so that the initial burst of inﬂation bring about the alternative evolution that it was is expected to be followed by a period of dis- desired that people would expect. However, an- inﬂation; when i 0, this eventually returns ticipation by the private sector that the central the price level to its original trend path (Clarida bank will apply a purely forward-looking pro- et al. 1999; Woodford, 1999b). This expectation cedure at later dates precludes such adjustment of subsequent disinﬂation mitigates the effects of expectations at the earlier date. of the adverse cost shock, by restraining price The history-dependence of optimal policy can increases during the period of the shock. be usefully illustrated in the context of a simple Similarly, in the case of a transitory increase optimizing model of the monetary transmission in the natural rate of interest, a forward-looking mechanism, analyzed by Richard Clarida et al. procedure results in an equally transitory (1999) and by Woodford (1999a), among others. increase in the nominal interest rate. When In this model, inﬂation t and the output gap xt i 0, an optimal commitment instead in- (output relative to its efﬁcient level) are deter- volves a more persistent increase in the nominal mined by a pair of structural relations, consisting interest rate (Woodford, 1999a). This results in of an aggregate supply curve and an intertemporal a larger response of long rates (which restrain 102 AEA PAPERS AND PROCEEDINGS MAY 2000 expenditure and hence prices despite the distur- period t to seek to minimize an objective that bance), without requiring a sharp increase in adds terms of the form 1,t 1 t 2,t 1 x t to short rates. As a result, it is possible to simul- the expected discounted sum of terms L t j for taneously achieve lower volatility of inﬂation, j 0. Here the coefﬁcients i,t 1 are deter- the output gap, and the short-term nominal in- mined as part of the bank’s period-t 1 decision terest rate. cycle and then taken as given parameters of the Purely forward-looking procedures forfeit bank’s objective in its period-t decision cycle. these gains from desirable responses of inﬂation A discretionary procedure of this kind has a expectations and interest-rate expectations to Markov equilibrium in which inﬂation and out- exogenous shocks. In addition, purely forward- put evolve as under the optimal commitment, looking approaches more easily result in inde- and the coefﬁcients i,t 1 are set equal to La- terminacy of equilibrium. In the model sketched grange multipliers associated with that optimi- above, an exogenously speciﬁed nominal inter- zation problem. est-rate process results in price-level indetermi- This approach represents a relatively general nacy; a determinate equilibrium requires a solution to the problem of making optimal pol- sufﬁcient degree of dependence (of the right icy consistent with a discretionary optimization sort) of the central bank’s interest-rate operating procedure. However, the practicality of the pro- target upon endogenous variables, such as in- posal may be doubted. Since the coefﬁcients ﬂation and output (Woodford, 1999a). Further- i,t 1 result from the central bank’s calcula- more, an operational procedure must make the tions when choosing period-t 1 policy, they interest rate a function of variables that are respond to no endogenous variables (not chosen exogenous or predetermined at the time that the by the bank itself) determined in period t 1 interest rate is chosen (Svensson and Woodford, and so will be a function solely of the history of 1999). In the case of a purely forward-looking exogenous disturbances. Such a procedure once procedure, this means a function solely of the again implies an interest-rate reaction function exogenous state st , as no predetermined endog- that leads to indeterminacy (Svensson and enous variables are relevant for forecasting the Woodford, 1999). target variables. But such a procedure necessar- On both grounds one might therefore prefer ily leads to indeterminacy of the paths of both an alternative approach, in which the modiﬁed inﬂation and output. loss function involves no time-varying coefﬁ- cients, but instead a period loss function that III. Examples of History-Dependent Policy depends upon lagged as well as current values of the target variables. In this case, discretionary There are a variety of ways in which a deci- policy is history-dependent because the bank’s sion procedure for monetary policy might in- loss function is history-dependent (even though corporate the sort of history-dependence the true social loss function is not). The implied required for an optimal regime. As Svensson reaction function will make the nominal interest and Woodford (1999) stress, these include rate a function of lagged endogenous vari- history-dependent variants of inﬂation-forecast ables— dependence of which sort is necessary, targeting procedures. For example, a forecast- though not sufﬁcient, for determinacy of targeting procedure that amounts to discretion- equilibrium. ary optimization can nonetheless be sufﬁciently For example, David Vestin (1999) shows that history-dependent, if the loss function that the discretionary optimization results in more nearly central bank seeks to minimize is modiﬁed in a optimal responses to cost shocks (in the above way that introduces history-dependence. model, with i 0) if the central bank is charged A particularly straightforward approach is to with stabilization of the price level rather than the incorporate into the bank’s loss function terms inﬂation rate, even though the true social loss that represent the value, at earlier dates, of hav- function is that shown in equation (1). The pro- ing people anticipate different subsequent paths posed loss function is history-dependent, in that it of the target variables (Svensson and Woodford, effectively depends upon the cumulative sum of 1999). For example, in the simple model above, inﬂation rates over all past periods, rather than one might instead direct the central bank in only upon the current period’s inﬂation rate. This VOL. 90 NO. 2 INFLATION TARGETING 103 is desirable, as it implies that an inﬂationary shock responses to cost shocks are optimal. The tar- should cause anticipation of lower inﬂation in geting criterion is history-dependent in that (3) subsequent periods, to an extent that the price involves x t 1 . Note that if the efﬁcient level of level is expected to eventually return to its original output is a deterministic trend, and , this level. rule corresponds to nominal GDP-growth tar- Similarly, Henrik Jensen (1999) shows that a geting, as proposed by Jensen; however, the nominal GDP growth target can be preferable to latter rule is fully optimal only in this special discretionary minimization of the true social case. loss function (“inﬂation targeting”) in a similar In the more general case that i 0, Marc P. model. This makes the period loss function de- Giannoni (1999) shows that the optimal target- pend upon lagged output as well as the current ing criterion instead takes the form values of target variables. Speciﬁcally, low out- put in the previous period leads the central bank to choose low output and/or deﬂation in the (4) it i 1 t 1 2 it 1 it 2 current period. As a result, a transitory cost shock results in a more persistent contraction of t x xt xt 1 output, lowering overall inﬂation and output variability as discussed above. Finally, Woodford (1999a) shows that more for appropriately chosen coefﬁcients 1 , 2 , , nearly optimal equilibrium responses to ﬂuctu- x 0. The optimal values of these coefﬁ- ations in the natural rate of interest (in the cients depend upon the coefﬁcients of the struc- model with i 0) result from discretionary tural equations and of the loss function (4), but optimization if the central bank’s period loss they are completely independent of all parame- function is given by ters specifying the shock processes. Again this condition determines a unique nonexplosive (2) L cb t 2 t x x2 t it it 1 2 equilibrium corresponding to the optimal commitment. for an appropriate choice of 0, rather than The targeting criterion (4) provides a rule for by the true social loss function (1). Such an setting the central bank’s interest-rate instru- “interest-rate smoothing” objective induces the ment that is in the spirit of the “Taylor rule.” sort of gradual adjustment of the interest rate But it differs from John B. Taylor’s (1993) that characterizes responses under the optimal classic formulation in involving additional commitment. history-dependence: interest rates respond to The appeal of such modiﬁed central-bank the growth rate of the output gap rather than to objectives depends, of course, upon the expec- its level, and the coefﬁcients 1 , 2 0 imply tation that a discretionary optimizer will not inertial interest-rate dynamics. It is interesting efﬁciently achieve its ofﬁcial aims. An appeal- to note that both of these departures from Tay- ing alternative involves commitment to the lor’s formulation characterize at least some achievement of a speciﬁc targeting criterion. econometric estimates of actual Fed reaction Introducing history-dependence is especially functions (e.g., John P. Judd and Glenn D. straightforward under such an approach; one Rudebusch, 1998). simply needs a targeting criterion that depends This example indicates that an optimal tar- upon past values of the target variables, as well geting criterion need not involve forecasts for as their current and future values. periods beyond the one for which interest For example, in the case that i 0, Wood- rates are being set. In this case, private-sector ford (1999a) shows that a policy that ensures anticipation of subsequent central-bank action that inﬂation satisﬁes the targeting criterion substitutes for preemptive actions by the cen- tral bank. However, the optimality of this rule (3) t x / xt xt 1 0 under an arbitrary information structure de- pends upon the absence of intrinsic dynamics (where is the slope of the short-run Phillips in the model’s structural equations; more gen- curve) sufﬁces to ensure that the equilibrium erally, an optimal targeting criterion will 104 AEA PAPERS AND PROCEEDINGS MAY 2000 involve forecasts, as in Svensson (1999). nal of Monetary Economics, June 1997, Even so, an optimal procedure will not gen- 39(1), pp. 81–97. erally be purely forward-looking, but will Svensson, Lars E. O. “Inﬂation Targeting as a instead have to involve backward-looking Monetary Policy Rule.” Journal of Mone- elements of the kind illustrated here. tary Economics, June 1999, 43(3), pp. 607– 54. Svensson, Lars E. O. and Woodford, Michael. REFERENCES “Implementing Optimal Policy Through In- ﬂation-Forecast Targeting.” Mimeo, Prince- Clarida, Richard; Galı, Jordi and Gertler, Mark. ´ ton University, 1999. “The Science of Monetary Policy: A New Taylor, John B. “Discretion versus Policy Rules Keynesian Perspective.” Journal of Eco- in Practice.” Carnegie–Rochester Conference nomic Literature, December 1999, 37(4), pp. Series on Public Policy, December 1993, 39, 1661–1707. pp. 195–214. Giannoni, Marc P. “Does Model Uncertainty Vestin, David. “Price-Level Targeting versus In- Imply Caution? Robust Optimal Monetary ﬂation Targeting in a Forward-Looking Policy in a Forward-Looking Model.” Model.” Mimeo, Stockholm University, Mimeo, Princeton University, 1999. 1999. Jensen, Henrik. “Targeting Nominal Income Woodford, Michael. “Optimal Monetary Policy Growth or Inﬂation?” Mimeo, University of Inertia.” National Bureau of Economic Re- Copenhagen, 1999. search (Cambridge, MA) Working Paper No. Judd, John P. and Rudebusch, Glenn D. “Tay- 7261, August 1999a. lor’s Rule and the Fed: 1970 –1997.” Eco- . “Commentary: How Should Monetary nomic Review (Federal Reserve Bank of San Policy Be Conducted in an Era of Price Sta- Francisco), 1998, (3), pp. 3–16. bility?” in New challenges for monetary pol- King, Mervyn. “Changes in UK Monetary Pol- icy. Kansas City, MO: Federal Reserve Bank icy: Rules and Discretion in Practice.” Jour- of Kansas City, 1999b.