We start by considering 3-parameter rules in which the federal funds rate rt is determined as a linear function of the current output gap, j>t, the four-quarter average inflation rate, TT(4)t, and the lagged funds rate, rM :

where r* is the equilibrium real rate, and 7C* is the inflation target (assumed to be constant throughout this paper).

The solid lines in Figure 2 depict the 3-parameter E-frontier of each model. As expected, the frontier is convex to the origin, with truncated vertical and horizontal asymptotes as the objective function in equation (3) switches from a concern only for inflation stabilization (A = 0) toward one concerned only with output stabilization (A = 1). Each panel of Figure 2 also indicates the relative performance of the estimated rule, denoted by the letter “E.” Because the estimated rule generates the same amount of funds rate volatility as the 3-parameter E-frontier of each model, comparison of the estimated rule to the policy frontier is straightforward. The estimated rule performs appreciably worse than the optimal 3-parameter rules for MSR, FRB, and TAYMCM, despite the fact that the estimated rule incorporates an additional variable (the lagged output gap). As discussed below, the optimal value of p for these three models is substantially higher than the estimated value of p in equation (1).

We start by considering 3-parameter rules in which the federal funds rate rt is determined as a linear function of the current output gap, j>t, the four-quarter average inflation rate, TT(4)t, and the lagged funds rate, rM : where r* is the equilibrium real rate, and 7C* is the inflation target (assumed to be constant throughout this paper). The solid lines in Figure 2 depict the 3-parameter E-frontier of each model. As expected, the frontier is convex to the origin, with truncated vertical and horizontal asymptotes as the objective function in equation (3) switches from a concern only for inflation stabilization (A = 0) toward one concerned only with output stabilization (A = 1). Each panel of Figure 2 also