Finally, optimal control theory suggests that the optimal policy rule should take into account all available information, including lagged values of the output gap and inflation rate.

A rule with a high value of p implicitly makes the current interest rate depend on the complete history of output and inflation, albeit in a very restricted way. Thus, the lagged funds rate may be serving as a simple proxy that permits additional information to be included in a suboptimal level rule. We test this explanation by computing frontiers for rules that include all observable state variables, and then checking whether these complicated rules are characterized by smaller lagged funds rate coefficients. Because of the high computational cost in conducting this experiment, we focus on the small models, FM and MSR. The policy frontiers associated with complicated rules for these models have already been shown in Figure 4. Here we simply note that rules which include all observed state variables call for somewhat smaller coefficients on the lagged funds rate. In the FM model, the range of values of p along the frontier is almost identical for the case of three-parameter rules as for rules that respond to all observable state variables, while in the MSR model, the range of values of p decline from [1.0,1.1] to [0.91,0.99] for rules that respond to all observed state variables.

Finally, optimal control theory suggests that the optimal policy rule should take into account all available information, including lagged values of the output gap and inflation rate. A rule with a high value of p implicitly makes the current interest rate depend on the complete history of output and inflation, albeit in a very restricted way. Thus, the lagged funds rate may be serving as a simple proxy that permits additional information to be included in a suboptimal level rule. We test this explanation by computing frontiers for rules that include all observable state variables, and then checking whether these complicated rules are characterized by smaller lagged funds rate coefficients. Because of the high computational cost in conducting this experiment,