Rules for monetary policy.

• Author: Woodford, Michael
• Position: Research Summaries

Much of my recent research has sought to use economic analysis to determine the consequences of alternative rules for the conduct of monetary policy, and to formulate rules that will be desirable from the standpoint of individual welfare. Interest in the study of monetary rules has increased over the past decade, for reasons having to do with progress in central banking and progress in macroeconomic theory. On the one hand, many central banks--most notably, but not only, the "inflation targeting" banks--have increasingly come to organize their policy deliberations around an attempt to conform to specific targets or objectives, sometimes explicit quantitative targets. Moreover, central banks worldwide have increased the degree to which they discuss their decisions with financial market participants and the general public, and this too has increased the importance that the banks assign to having a clear framework to guide their deliberations. At the same time, the development of a new generation of quantitative macroeconomic models--that can be estimated using macroeconomic time series and have optimizing foundations that allow an explicit evaluation of outcomes in terms of individual welfare--has allowed modern macroeconomic analysis to be brought to bear on the evaluation of stabilization policies, in the context of models with sufficient claim to quantitative realism to be of interest to policymaking institutions. My own work has sought to extend the analysis of optimal monetary policy rules in directions that bring the theoretical literature into closer contact with the practical concerns of modern central bankers. (1)

Inflation Stabilization and Welfare

One goal of my research has been to clarify which kinds of macroeconomic stabilization objectives best serve economic welfare. Grounding the objectives of policy in consumer welfare has a number of advantages: one avoids the arbitrariness otherwise attendant upon the choice of a particular definition of "price stability" "full employment" or other conventional objectives. And, it also makes possible a natural integration of the theory of optimal monetary policy with the theory of optimal taxation. Yet it is not immediately obvious what the conventional goals of monetary stabilization policy--especially the nearly universal emphasis that central banks place on maintaining a low and stable inflation rate--have to do with consumer welfare; after all, the arguments of household utility functions generally are assumed to be the quantities of various goods and services, but not their prices. Nonetheless, I have shown that in familiar classes of sticky-price dynamic stochastic general equilibrium (DSGE) models--models that incorporate key elements of the current generation of empirical models of the monetary transmission mechanism, and even some relatively small complete macro models--it is possible to show that the expected utility of the representative household varies inversely with the expected discounted value of a quadratic loss function, the arguments of which are measures of price and wage inflation on the one hand and measures of real activity relative to a (time-varying) target level of activity on the other. (2) Thus, it makes sense to rank alternative monetary policies according to how well they stabilize (an appropriate measure of) inflation on the one hand, and how well they stabilize (an appropriate measure of) the output gap on the other. The theory clarifies both the appropriate definition of these stabilization objectives, and the appropriate relative weights to assign to them when a choice must be made between them.

The answer obtained depends, of course, on the structure of the economy. (3) In particular, inflation variability reduces welfare because of the presence of nominal rigidities; the precise nature of these rigidities determines the appropriate form of the inflation-stabilization objective. For example, if wages are flexible (or there are efficient contracts in the labor market), and price adjustments are staggered in the way assumed in the popular specification proposed by Guillermo Calvo (4) (with an equal probability of any given price being revised in any time period), then inflation variation results in distortions caused by the misalignment of prices that are adjusted at different times. The resulting welfare losses are proportional to the expected discounted sum of squared deviations of the inflation rate from zero. Other assumptions about the timing of price adjustments also imply that inflation variations reduce welfare, but with a different form of loss function, and thus a different ranking of equilibria in which prices are not completely constant. For example, if the probability of adjustment of an individual price is increasing in the time since that price was last reviewed--a specification that is both intuitively plausible and more consistent than the simple Calvo specification with empirical models of inflation dynamics (5)--then welfare losses are proportional to a discounted sum of squared deviations of the current inflation rate from a moving average of recent past inflation rates, rather than deviations from zero. (6) The goal of policy then should be to keep inflation from differing too greatly from the current "inertial" rate of inflation, which implies that inflation should not be reduced too abruptly if it has been allowed to exceed its optimal long-run level. (7) A similar conclusion is obtained if prices are assumed to be automatically indexed to a lagged price index, as in the well-known empirical model of Christiano, Eichenbaum, and Evans (8) and related studies, or if some prices are adjusted in accordance with a backward-looking "rule of thumb" as proposed in the empirical model of inflation dynamics of Jordi Gall and Mark Gertler. (9)

The theory also provides important insights into the question of which price index or indexes it is more important to stabilize. Again, the answer depends on the nature of the nominal rigidities. If prices are adjusted more frequently in some sectors of the economy than in others, then the welfare-theoretic loss function puts more weight on variations in prices in the sectors where prices are stickier, as first shown by Kosuke Aoki. (10) This...