INTEREST-RATE RULES: The Welfare Loss from Price-Level Instability 4

For some Л > 0, assumed in many analyses of optimal monetary policy (e.g., Taylor (1979), Bean (1983)). Our utility-based derivation, however, allows us to assign a specific numerical weight to the relative importance of stabilization of output around У5, as opposed to inflation stabilization. It also clarifies the kinds of stabilization that are important. Because of the lags involved in pricing, it turns out to be desirable to reduce the variability of both expected inflation and unexpected inflation. Moreover, the variability of unexpected inflation deserves somewhat greater weight, unlike what the ad hoc loss function above would imply.

The analysis also makes it clear that it is the variability of quarter-to-quarter inflation, rather than some longer-horizon average rate of inflation, or the deviation of the price level from some deterministic or stochastic trend path, that is most closely related to the welfare losses due to price-level instability. Finally, it makes it clear that it is the variability of Y — Y5, rather than the variability of deviations of output from trend or the variability of output growth, that matters for welfare. Specifically, it is the variability of the part of Y — Ys that is forecast able two quarters earlier that policy should seek to minimize.

It is worth noting that all three of the terms in (1.33) are directly related, in different ways, to inflation variability. For the analysis of optimal policy below, it is helpful to rewrite L so that it depends only on the stochastic process for the relative price variable X. We show in the Appendix that the model’s structural equations imply that (1.33) may be rewritten in the form
both necessary and sufficient for achievement of the minimum value of L = 0. This means that, even though our proposed welfare criterion (1.30) assigns ultimate importance only to the efficiency of the level of real activity in each sector of the economy, it in fact justifies giving complete priority to inflation stabilization as opposed to output stabilization.

Given the model, one can compute the value of L as well as that of its components for any rule that sets the interest rate as a function of the history of inflation and output in such a way that there is a unique stationary equilibrium. But this still leaves open the question of whether there is a trade-off between stabilizing the economy by reducing L and keeping a low steady state level of inflation. As suggested by Summers (1991), the requirement that nominal interest rates must always be positive implies that a low average rate of inflation is inconsistent with a great deal of stabilization. The reason is that a low average rate of inflation implies that the average interest rate is low, and this means that the interest rate cannot be too variable. At the same time, keeping the variability of interest rates low weakens the government’s ability to reduce L by having the interest rate respond to shocks. To see this, it is worth displaying the relation between interest rates and X implied by our model.