Figure 5 compares the frontiers using current and lagged variables. The imposition of lagged variables in the rule imposes tiny costs in terms of stabilization in the FM and FRB models, and relatively small costs in the MSR and TAYMCM models. The characteristics of well-performing rules are also essentially unchanged. Evidently, a one-quarter information lag does not inhibit effective inflation and output stabilization in the models we consider here.

The reason for these small costs is that inflation and output are highly persistent in all four models and thus lagged inflation and output gaps are good proxies for the current ones.

Still, the first-order autocorrelations are less than unity and the main differences between the models arise from the differences in output persistence across models. For the MSR and TAYMCM models, which display relatively low output persistence (first-order autocorrelation under first-difference rules of about 0.75 and 0.5, respectively), the cost of using lagged output gaps is larger than for the FM and FRB models with relatively high output persistence (0.95 and 0.85 first-order autocorrelations under first-difference rules, respectively). In the case of inflation, any effects on performance due to the use of lagged variables is further dampened by the fact that frontier rules depend on four- to twelve-quarter moving averages of inflation.

The marginal impact of the current inflation rate is thus relatively small, so the shift in timing has little effect on the stabilization properties of frontier rules.

Figure 5 compares the frontiers using current and lagged variables. The imposition of lagged variables in the rule imposes tiny costs in terms of stabilization in the FM and FRB models, and relatively small costs in the MSR and TAYMCM models. The characteristics of well-performing rules are also essentially unchanged. Evidently, a one-quarter information lag does not inhibit effective inflation and output stabilization in the models we consider here. The reason for these small costs is that inflation and output are highly persistent in all four models and thus lagged inflation and output gaps are good proxies for the current ones. Still, the first-order autocorrelations are less than unity and the main differences between the models arise from the differences