INTEREST-RATE RULES: Consequences of Simple Policy Rules 4

Another fact that is apparent from the table is that the ranking of different rules according the value achieved for L is essentially the same as their ranking in terms of the variability of inflation. Thus our utility-based welfare criterion L+7T*2 leads to conclusions that are similar to those that would be reached by giving some weight to the reduction of both the variability of inflation and the variability of the funds rate. In both these respects, the rules labeled Ei: Giy and I are better than the others. We turn now to a more systematic exploration of the consequences of parameter variations, in order to clarify why this is so.

Simple “Taylor Rules”

Taylor (1993) and the related rule Do considered by Henderson and McKibbin (1993) belong to this family. Our aim here is to highlight the trade-offs involved in choice between having interest rates respond to output and having interest rates respond to inflation.

In the case of simple Taylor rules of the form (2.1) with a constrained to be positive, our loss criterion L + 7Г*2 reaches a minimum when a equals 2.88 and b equals 0.02. The consequences of this rule for our loss measures is displayed in Table 1, where the rule is designated Fq. As one might guess, this rule (which places essentially all of the weight on inflation variations rather than output variations) allows much greater variations in output relative to trend than do rules Co and D0. However, according to our model, it leads to less variability of output relative to its natural level, which is what matters for our loss measure.

It also results in significantly less variability of inflation, and noticeably less variability of the funds rate. (It is actually the latter difference that is most significant for our loss measure, because of the reduction in the average inflation rate 7r* that it allows.) The ultimate result is a reduction in deadweight loss by a factor of three, relative to the other proposals. However, our model and our loss measure imply that this rule would not represent an improvement upon historical U.S. policy in the Volcker-Greenspan period. To do better we must not simply vary the weights on inflation and output, but consider at least slightly more sophisticated rules.
Before turning to other families of rules, it is worth noting that the welfare criterion L + 7Г*2 reaches an even lower value, according to our model, if we allow a and b to be negative in (2.1). The optimum then involves a equal to —1 and b equal to —1.3. The idea that negative values of a and b are acceptable may be surprising. For this reason, Figure 4 displays both the region where equilibrium is determinate as well as a contour plot of L + 7Г*2 as we vary a and b.

The equilibrium is not unstable for any of these parameter values (i.e., a stationary equilibrium always exists), but equilibrium is indeterminate in the shaded region. Indeterminacy arises, for example, when b is zero and a is small and positive. This indeterminacy implies, among other things, that inflation can vary simply as a result of changes in expectations. A “sunspot” can lead inflation at t to rise, for example.