Due to computational costs, our analysis of this issue focuses on the two smaller models, FM and MSR, for which we can investigate rules that include all observed state variables. The

FM model contains eight such variables (the current values of the output gap and inflation rate, two lags of the output gap, three lags of the inflation rate, and the lagged interest rate) while the MSR model contains 20 observed state variables. Results from TAYMCM for rules with up to six parameters confirm the findings we obtain from the two smaller models.

As seen in the top panel of Figure 4, 8-parameter rules that respond to all observable state variables in the FM model provide only negligible improvements in output and inflation stability beyond the optimal 3-parameter rules. Although the inflation and output variances do not change noticeably, the response coefficients in the more complicated rules differ quite a bit from the response coefficients in comparable 3-parameter rules. For example, the more complicated rules respond much more aggressively to inflation in the current quarter than inflation in the preceding 3 quarters.

Because demand is disaggregated in the MSR model, additional gains in performance might be expected by augmenting the 3-parameter rule in equation (4) to include consumption, fixed investment, inventory investment, and government spending. We find noticeable, but admittedly still moderate, improvements in output and inflation stability when moving from 3 to 8-parameter rules that include lags of the output gap and inflation rate, and again when moving from 8 to 12 parameters that include current values of the individual components of aggregate demand. The lower panel of figure 4 shows the 3-parameter frontier and the 12-parameter frontier of the MSR model, while the 8-parameter frontier is omitted. As in the previous case, the coefficients of these complicated rules are quite different from simple rules, particularly the coefficients on quarterly inflation rates and the components of aggregate demand. Finally, although MSR contains other observed state variables, including these variables in the policy rules did not generate noticeable improvements in output and inflation stability beyond the 12-parameter frontier.

Due to computational costs, our analysis of this issue focuses on the two smaller models, FM and MSR, for which we can investigate rules that include all observed state variables. The FM model contains eight such variables (the current values of the output gap and inflation rate, two lags of the output gap, three lags of the inflation rate, and the lagged interest rate) while the MSR model contains 20 observed state variables. Results from TAYMCM for rules with up to six parameters confirm the findings we obtain from the two smaller models. As seen in the top panel of Figure 4, 8-parameter rules that respond to all observable state variables in the FM model provide only negligible improvements in