### Rules for Monetary Policy

Mark Thoma points out to Greg Mankiw and myself that Michael Woodford is the real "state of the art" on the problem of what the central bank should try to stabilize.

Woodford speaks:

Rules for Monetary Policy: 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.) 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. 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 (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 -- 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. 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.

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 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 Gali and Mark Gertler.

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. This provides a theoretical basis for seeking to stabilize an appropriately defined measure of "core" inflation rather than an equally weighted price index.... [I]f wages are sticky as are goods prices, as implied by many empirical DSGE models, then instability in the rate of growth of a broad index of nominal wages results in distortions similar to those created by variations in goods price inflation. If wages are staggered in accordance with the Calvo specification, then the welfare-theoretic loss function includes a term proportional to the squared rate of goods price inflation and another term proportional to the squared rate of wage inflation each period. In this case, optimal policy involves a tradeoff between inflation stabilization, nominal wage growth stabilization, and output-gap stabilization, as first shown by Chris Erceg, Dale Henderson, and Andy Levin....

My research has emphasized that, when choosing a policy to best serve the goal of stabilization, it is crucial to take account of the effects of the policy's systematic component on people's expectations.... [W]hen one takes account of forward-looking behavior, it can be desirable for a central bank to only gradually adjust its operating target for overnight interest rates when underlying fundamentals change, rather than jumping immediately to a new level that depends only on current conditions. This kind of policy inertia -- often argued to characterize actual central bank behavior, but frequently assumed to indicate a failure of central bankers to fully optimize -- can reduce the amplitude of the swings in short-term interest rates required to stabilize inflation and real activity in response to real disturbances. It allows market participants to anticipate that the movements in short rates that occur will be more persistent, resulting in a larger effect on long rates and other asset prices, which are what matter for the effect of policy on aggregate demand....

The criteria used by inflation-forecast targeting central banks, such as the Bank of England (which seeks to ensure that CPI inflation is always projected to reach its target level of 2 percent per year at a horizon two to three years in the future), are an example of commitments... represent the closest approximation to the ideal of rule-based policymaking yet observed.... In the case of a canonical "New Keynesian" model, with an aggregate-supply relation of the kind implied by flexible wages and Calvo-style staggered pricing, the optimal target criterion is a "flexible inflation target," under which short-run departures of the inflation rate from a constant long-run target level should vary inversely with the projected growth in the output gap....

[I]f the likelihood of a price revision increases with the time since the last revision, then... temporary increases in inflation should not be immediately reversed.... [O]ne important conclusion from my study of this topic is that an optimal target criterion almost surely will not be focused so exclusively on projected outcomes two or more years in the future, as are the criteria that currently are used at the leading inflation-targeting central banks, at least according to their official rhetoric...

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