The evolution of research on monetary policy over the past two decades has been dramatic. The 1980's through the mid-1990's were dominated by work building on the insights of Kydland and Prescott, employing the notion of dynamic consistency to offer a theory of monetary policy, one in which discretionary policy by central banks led to socially costly inflation. Researchers studied the nature of the time inconsistency of monetary policy and developed solutions, ranging from appointing conservatives, to developing incentive contracts, to imposing inflation targets. Whether central bankers learned, in the words of Ben McCallum, to "just do it," or the nature of the incentives they faced changed, inflation was reduced in the industrialized economies during the 1980's and early 1990's. In the low-inflation environment since, central banks have, in the eyes of many monetary economists, changed from a source of (often) politically induced inflation to maximizers of social welfare. This shift has opened new and productive collaborations between academic economists and central bank economists interested in issues of monetary policy design. Much of this work builds on the basic foundations provided by the marriage of dynamic stochastic general equilibrium models, with their emphasis on optimizing behavior by economic agents and careful attention to budget constraints and equilibrium conditions, with simple models of price stickiness. Early contributors to these foundations include Yun (1996), Goodfriend and King (1997), and Rotemberg and Woodford (1997). The resulting framework for macroeconomic analysis, in its simplest form, boils down to an expectational IS curve, an inflation adjustment equation, and a specification of monetary policy in terms of either an objective function or a rule for setting the nominal rate of interest.

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The recent worldwide economic crisis has brought renewed attention to the question of the usefulness of government spending as a way of stimulating aggregate economic activity and employment during a slump. Interest in fiscal stimulus as an option has been greatly increased by the fact that in many countries, by the end of 2008, the short-term nominal interest rate used as the main operating target for monetary policy had reached zero-or at any rate, some very low value regarded as an effective lower bound by the central bank in question-so that further interest rate cuts were no longer available to stave off spiraling unemployment and fears of economic collapse. Increases in government spending were at least a dimension on which it was possible for governments to do more-but how effective should this be expected to be as a remedy?Much public discussion of this issue has been based on old-fashioned models (both Keynesian and anti-Keynesian) that take little account of the role of intertemporal optimization and expectations in the determination of aggregate economic activity. This paper, instead, reviews the implications for this question of the kind of New Keynesian dynamic stochastic general equilibrium (DSGE) models that are now commonly used in monetary policy analysis. It focuses on one specific question of current interest: the determinants of the size of the effect on aggregate output of an increase in government purchases, or what has been known since John Maynard Keynes (1936) as the government expenditure "multiplier." * Department of Economics, Columbia University, 420 West 118th Street, New York, NY 10027 (e-mail: michael.woodford@columbia.edu). I would like to thank Marco Bassetto, Pierpaolo Benigno, Sergio de Ferra, Gauti Eggertsson, Marty Eichenbaum, Bob Gordon, Bob Hall, John Taylor, and Volker Wieland for helpful discussions, Dmitriy Sergeyev and Luminita Stevens for research assistance, and the National Science Foundation for research support under grant SES-0820438.† To comment on this article in the online discussion forum, or to view additional materials, visit the article page at http://www.aeaweb.org/articles.php?doi=10.1257/mac.3.1.1.

This paper considers the desirability of the observed tendency of central banks to adjust interest rates only gradually in response to changes in economic conditions. It shows, in the context of a simple model of optimizing private-sector behavior, that such inertial policy can be optimal. The reason is that small but persistent changes in short-term interest rates in response to shocks allow a larger effect of monetary policy on long rates and hence upon aggregate demand, for a given degree of overall interest-rate variability. The paper also considers two ways of achieving the desirable degree of inertia in the equilibrium responses to shocks. One is by assignment of a loss function that penalizes squared interest-rate changes (despite the fact that interest-rate changes do not affect the true social objective) to a central bank that is then expected to use discretion in the pursuit of the goal. The second is through commitment to an explicit instrument rule, a generalization of the "Taylor rule" in which the funds rate is an increasing function of the lagged funds rate, as in estimated Fed reaction functions.

This paper seeks to evaluate monetary policy rules that generalize the rule proposed by Taylor (1993). In particular, we consider rules in which the Fed sets the federal funds rate as a function of the history of inflation, output, and the federal funds rate itself. Even though this is not part of Taylor's original formulation, we introduce the possibility that the federal funds rate depends on the history of the funds rate itself in order to allow for interest rate smoothing of the kind that appears to be an important feature of current Fed policy. We also consider the character of optimal policy, that is, the policy that maximizes the utility of the representative agent, assuming unlimited information about the exogenous disturbances to the economy. We then compare optimal policy in this unrestricted sense with the best rule of the generalized Taylor family. We evaluate these rules under the assumption that interest rate, inflation, and output determination in the U.S. economy can be compactly represented by the small structural model whose parameters we estimate in Rotemberg and Woodford (1997). This is a rational expectations model derived from explicit intertemporal optimization, in which firms are unable to change their prices every period, and in which purchases are determined somewhat in advance of when they actually take place. In evaluating different monetary rules we use two approaches. The first approach is simply to compute the welfare of the

The paper considers the determinacy of the equilibrium price level in the cash-in-advance monetary economy of Stokey (1983, 1987), in the case of deterministic "fundamentals". The possibilities both of a multiplicity of perfect foresight equilibria and of "sunspot equilibria" are considered. Two types of monetary policy regimes are considered and compared, one in which the money supply grows at a given exogenous rate (that may be positive or negative), and one in which the nominal interest rate on one-period government debt is pegged at a given non-negative level. In the case of constant money growth rate regimes, it is shown that one can easily have both indeterminacy of perfect foresight equilibrium and existence of sunspot equilibria; indeed, in the case of negative rates of money growth (as called for by Friedman (1969)), both types of indeterminacy necessarily occur. On the other hand, sufficient conditions for uniqueness of equilibrium (and non-existence of equilibria other than a deterministic steady state) are also given, and a class of cases is identified in which a sufficiently high rate of money growth guarantees this. Thus there may be a conflict between the aims of choosing a rate of money growth that results in a high level of welfare in the steady state equilibrium and choosing a rate that makes this steady state the unique equilibrium.) In the case of the interest rate pegging regimes, sufficient conditions are given for uniqueness of equilibrium (and impossibility of sunspot equilibria), and it is shown that these necessarily hold in the case of any low enough nominal interest rate. Thus the nominal interest rate peg allows simultaneous achievement of price level determinacy and a high level of welfare in the unique (steady state) equilibrium.In this paper I consider the consequences of alternative choices of the monetary policy regime for the determinacy of the rational expectations equilibrium value of money, and in particular for the existence or not of "sunspot" equilibria, i.e., rational * This paper represents a revision of Woodford (1988). I would like to thank

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