To examine this feature more closely, we consider the class of first-difference rules, which are a special case of the 3-parameter rules described by the previous equation.

Finally, the lower-left panel of Figure 2 shows that stabilization performance improves substantially in the FRB model if the simple policy rule is expressed in terms of Tl(12) t rather than 7I(4) t; i.e., a three-year moving average of inflation instead of a one-year moving average. This feature differs across the four models: for the FM and MSR models, using a longer moving average of inflation (e.g., 7I(S) t or 7C(12) t) provides relatively small improvements in terms of output and inflation volatility, while Ti:(4) t works best in the TAYMCM model. Thus, in the remainder of the paper, we use TI(12) t in computing the frontiers of simple rules for the FRB model, but continue to use TT(4) t for the other three models.

Complicated Policy Rules. In the simple rules described by equations (4) and (5), the funds rate is adjusted in response to only three variables: the current output gap, a moving average of the inflation rate, and the lagged interest rate. In practice, of course, central banks use much more information in making policy decisions. Furthermore, optimal control theory suggests that a policy rule should respond to all available information about the state of economy, that is, to all the state variables of the specific economic model under consideration. Thus, we investigate the extent to which complicated rules that respond to expanded subsets of the state variables can generate substantially lower output and inflation volatility.

To examine this feature more closely, we consider the class of first-difference rules, which are a special case of the 3-parameter rules described by the previous equation. Finally, the lower-left panel of Figure 2 shows that stabilization performance improves substantially in the FRB model if the simple policy rule is expressed in terms of Tl(12) t rather than 7I(4) t; i.e., a three-year moving average of inflation instead of a one-year moving average. This feature differs across the four models: for the FM and MSR models, using a longer moving average of inflation (e.g., 7I(S) t or 7C(12) t) provides relatively small improvements in terms of output and inflation volatility, while Ti:(4) t works best in the TAYMCM model. Thus,