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Optimal Monetary Stabilization Policy∗

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Optimal Monetary Stabilization Policy∗ Optimal Monetary Stabilization Policy∗ Michael Woodford Columbia University Revised October 2010 Contents 1 Optimal Policy in a Canonical New Keynesian Model . 3 1.1 The Problem Posed . 4 1.2 Optimal Equilibrium Dynamics . 7 1.3 The Value of Commitment . 13 1.4 Implementing Optimal Policy through Forecast Targeting . 17 1.5 Optimality from a \Timeless Perspective" . 24 1.6 Consequences of the Interest-Rate Lower Bound . 31 1.7 Optimal Policy Under Imperfect Information . 40 2 Stabilization and Welfare . 44 2.1 Microfoundations of the Basic New Keynesian Model . 44 2.2 Welfare and the Optimal Policy Problem . 50 2.3 Local Characterization of Optimal Dynamics . 54 2.4 A Welfare-Based Quadratic Objective . 63 2.4.1 The Case of an Efficient Steady State . 64 2.4.2 The Case of Small Steady-State Distortions . 69 2.4.3 The Case of Large Steady-State Distortions . 71 2.5 Second-Order Conditions for Optimality . 74 2.6 When is Price Stability Optimal? . 76 3 Generalizations of the Basic Model . 79 3.1 Alternative Models of Price Adjustment . 79 3.1.1 Structural Inflation Inertia . 81 3.1.2 Sticky Information . 88 3.2 Which Price Index to Stabilize? . 92 ∗Prepared for the new (2010) volumes of the Handbook of Monetary Economics, edited by Ben- jamin M. Friedman and Michael Woodford. I would like to thank Ozge Akinci, Ryan Chahrour, V.V. Chari, Marc Giannoni and Ivan Werning for comments, Luminita Stevens for research assistance, and the National Science Foundation for research support under grant SES-0820438. 3.2.1 Sectoral Heterogeneity and Asymmetric Disturbances . 93 3.2.2 Sticky Wages as Well as Prices . 107 4 Research Agenda . 111 This chapter reviews the theory of optimal monetary stabilization policy in New Keynesian models, with particular emphasis on developments since the treatment of this topic in Woodford (2003). The primary emphasis of the chapter is on methods of analysis that are useful in this area, rather than on final conclusions about the ideal conduct of policy (that are obviously model-dependent, and hence dependent on the stand that one might take on many issues that remain controversial), and on general themes that have been found to be important under a range of possible model specifications.1 With regard to methodology, some of the central themes of this review will be the application of the method of Ramsey policy analysis to the problem of the optimal conduct of monetary policy, and the connection that can be established between utility maximization and linear-quadratic policy problems of the sort often considered in the central banking literature. With regard to the structure of a desirable decision framework for monetary policy deliberations, some of the central themes will be the importance of commitment for a superior stabilization outcome, and more generally, the importance of advance signals about the future conduct of policy; the advantages of history-dependent policies over purely forward- looking approaches; and the usefulness of a target criterion as a way of characterizing a central bank's policy commitment. In this chapter, the question of monetary stabilization policy | i.e., the proper monetary policy response to the various types of disturbances to which an economy may be subject | is somewhat artificially distinguished from the question of the optimal long-run inflation target, which is the topic of another chapter (Schmitt- Groh´eand Uribe, 2010). This does not mean (except in section 1) that I simply take as given the desirability of stabilizing inflation around a long-run target that has been determined elsewhere; the kind of utility-based analysis of optimal policy expounded in section 2 has implications for the optimal long-run inflation rate as much as for the optimal response to disturbances, though it is the latter issue that is the focus of the discussion here. (The question of the optimal long-run inflation target is not entirely independent of the way in which one expects that policy should respond to shocks, either.) It is nonetheless reasonable to consider the two aspects of optimal policy in separate chapters, insofar as the aspects of the structure of the economy that are of greatest significance for the answer to one question are not entirely the same as those that matter most for the other. For example, the consequences of inflation for 1Practical lessons of the modern literature on monetary stabilization policy are developed in more detail in the chapters by Taylor and Williams (2010) and by Svensson (2010) in this Handbook. 1 people's incentive to economize on cash balances by conducting transactions in less convenient ways has been a central issue in the scholarly literature on the optimal long-run inflation target, and so must be discussed in detail by Schmitt-Groh´eand Uribe (2010), whereas this particular type of friction has not played a central role in discussions of optimal monetary stabilization policy, and is abstracted from entirely in this chapter.2 Monetary stabilization policy is also analyzed here under the assumption (made explicit in the welfare-based analysis introduced in section 2) that a non-distorting source of government revenue exists, so that stabilization policy can be considered in abstraction from the state of the government's budget and from the choice of fiscal policy. This is again a respect in which the scope of the present chapter has been deliberately restricted, because the question of the interaction between optimal mone- tary stabilization policy and optimal state-contingent tax policy is treated in another chapter of the Handbook, by Canzoneri et al. (2010). While the \special" case in which lump-sum taxation is possible might seem of little practical interest, I believe that an understanding of the principles of optimal monetary stabilization policy in the simpler setting considered in this chapter provides an important starting point for understanding the more complex problems considered in the literature reviewed by Canzoneri et al. (2010).3 In section 1, I introduce a number of central methodological issues and key themes of the theory of optimal stabilization policy, in the context of a familiar textbook ex- ample, in which the central bank's objective is assumed to be the minimization of a conventional quadratic objective (sometimes identified with “flexible inflation tar- geting"), subject to the constraints implied by certain log-linear structural equations (sometimes called \the basic New Keynesian model"). In section 2, I then consider the connection between this kind of analysis and expected-utility-maximizing policy 2This does not mean that transactions frictions that result in a demand for money have no consequences for optimal stabilization policy; see e.g., Woodford (2003, chap. 6, sec. 4.1) or Khan et al. (2003) for treatment of this issue. This is one of many possible extensions of the basic analysis presented here that are not taken up in this chapter, for reasons of space. 3From a practical standpoint, it is important not only to understand optimal monetary policy in an economy where only distorting sources of government revenue exist, but taxes are adjusted optimally, as in the literature reviewed by Canzoneri et al. (2010), but also when fiscal policy is sub-optimal owing to practical and/or political constraints. Benigno and Woodford (2007) offer a preliminary analysis of this less-explored topic. 2 in a New Keynesian model with explicit microfoundations. Methods that are useful in analyzing Ramsey policy and in characterizing the optimal policy commitment in microfounded models are illustrated in section 2 in the context of a relatively simple model that yields policy recommendations that are closely related to the conclusions obtained in section 1, so that the results of section 2 can be viewed as providing welfare-theoretic foundations for the more conventional analysis in section 1. How- ever, once the association of these results with very specific assumptions about the model of the economy has been made, an obvious question is the extent to which sim- ilar conclusions would be obtained under alternative assumptions. Section 3 shows how similar methods can be used to provide a welfare-based analysis of optimal policy in several alternative classes of models, that introduce a variety of complications that are often present in empirical DSGE models of the monetary transmission mechanism. Section 4 concludes with a much briefer discussion of other important directions in which the analysis of optimal monetary stabilization policy can or should be extended. 1 Optimal Policy in a Canonical New Keynesian Model In this section, I illustrate a number of fundamental insights from the literature on the optimal conduct of monetary policy, in the context of a simple but extremely influential example. In particular, this section shows how taking account of the way in which the effects of monetary policy depend on expectations regarding the future conduct of policy affects the problem of policy design. The general issues that arise as a result of forward-looking private-sector behavior can be illustrated in the context of a simple model in which the structural relations that determine inflation and output under given policy on the part of the central bank involve expectations regarding future inflation and output, for reasons that are not discussed until section 2. Here I shall simply take as given both the form of the model structural relations and the assumed objectives of stabilization policy, to illustrate the complications that arise as a result from forward-looking behavior, especially (in this section) the dependence of the aggregate-supply tradeoff at a point in time on the expected rate of inflation. I shall offer comments along the way about the extent to which the issues that arise in the analysis of this example are ones that occur in broader classes of stabilization 3 policy problems as well.
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