The coefficient values for optimal 3-parameter rules are shown in Figure 3. As the coefficients on inflation decrease, the standard deviation of inflation increases in all four models, as one would expect. The output gap coefficients vary noticeably less along the policy frontier. The output gap coefficient in MSR is close to unity along the whole policy frontier. In the FRB model, the output gap coefficient is smaller for rules corresponding to very high values of A, but is otherwise quite close to unity. The output gap coefficient in TAYMCM ranges between 0.6 and 1.5 along the policy frontier. Finally, the optimal output gap and inflation coefficients for the FM model are much smaller than for the other three models.

The key result to be noted from Figure 3 is that the 3-parameter policy frontiers of all four models are associated with rules in which the coefficient p on the lagged funds rate is very close to unity. In particular, the parameterp takes values in the range of {0.84, 0.95} for the FM model; {1.0, 1.1} for the MSR model; {0.96, 1.03} for the FRB model;16 and {0.94,0.98} for TAYMCM. Thus, the relatively poor performance of the estimated reaction function in the latter three models can be attributed mainly to the fact that the estimated value of p = 0.8 in equation (1) is substantially smaller than the optimal value of p for these models.

For three of the four models (MSR, FRB, and TAYMCM), the E-frontier for first-difference rules is virtually identical to the 3-parameter E-frontier; i.e., imposing the constraint p = 1 is essentially costless in these models. For the FM model, first-difference rules are associated with slightly higher output and inflation volatility compared with 3-parameter rules, as seen by comparing the dashed and solid lines in the upper-left panel of Figure 2.

The coefficient values for optimal 3-parameter rules are shown in Figure 3. As the coefficients on inflation decrease, the standard deviation of inflation increases in all four models, as one would expect. The output gap coefficients vary noticeably less along the policy frontier. The output gap coefficient in MSR is close to unity along the whole policy frontier. In the FRB model, the output gap coefficient is smaller for rules corresponding to very high values of A, but is otherwise quite close to unity. The output gap coefficient in TAYMCM ranges between 0.6 and 1.5 along the policy frontier. Finally, the optimal output gap and inflation coefficients for the FM model are much smaller than for the other three models.