INTEREST-RATE RULES: Consequences of Simple Policy Rules 2

The first column of Table 1 serves as a key for Figures 1, 2 and 3, where the consequences of these rules for the variability of output, inflation, interest rates and long-run price-level forecasts are plotted. The first of these figures has a certain similarity to the policy frontier shown in Taylor (1979), in that rules that have smaller standard deviations of inflation tend to involve larger standard deviations of output and vice versa. The only rules that appear to be “dominated” in this plot are the rules with labels in the series C* and Д. These are simple “Taylor Rules” that make the funds rate a function only of current inflation and output, and they respond much more strongly to output fluctuations than does our optimal rule in that family (labeled F0).

The rules in families C{ and Di are worse than the Bi rules because they induce a higher standard deviation of inflation without reducing the standard deviation of output. Interestingly, the rule Fo, which is the best rule of this type in terms of minimizing our utility-based loss measure, is something of an outlier as well in that it involves more variability of both inflation and output relative to other rules in the set. From the point of view solely of the criteria plotted in this figure, historical policy seems to be slightly worse than the rules described by Д, but not significantly so.
Figure 2 paints a different picture, one that involves pure dominance relations and no trade-offs. Once again, the rules C* and Д are particularly bad, in that they now also involve a high standard deviation of the funds rate. Among the remaining rules, those with a lower standard deviation of inflation tend to have lower standard deviations of the funds rate so they allow average inflation to be lower as well. Thus, the best rules in this plot are the rules Ei which, as we shall see below, also minimize L + 7Г*2 among rules that are as simple as these. These involve both low standard deviations of inflation and interest rates, while the other rules perform worse on both dimensions. When coupled with the results of Figure 1, we see that – leaving aside Ci and Д – the rules we consider here have the property that those that reduce the standard deviation of output tend to raise the standard deviation of inflation and interest rates simultaneously.
Figure 3 shows the implications of these rules for the variance of inflation and the variance in the innovation of the forecast of the long-run price-level. We see in this Figure that the specific rules we consider rank equally along these two dimensions. The price-level rules G{ and the Ei rules have both the lowest variance of inflation and the smallest innovations in the long run price level. That the price-level rules have low variances in the long-run price level is not surprising, since they ensure the price level is stationary. What is perhaps more surprising is that the best of the rules that respond to deviations of the inflation rate from target have this property as well.