Next, we consider the argument that interest rate rules with a high degree of interest rate smoothing reduce overall variability by generating secondary cycles, e.g., overshooting of output. Figure 8 shows the stark contrast in the dynamic response of output to a demand shock under a level rule versus a 3-parameter rule with interest rate smoothing. Each rule corresponds to the policy frontier associated with the same level of interest volatility as that resulting from the estimated rule in equation (1).

In FM, the demand shock is a positive shock of one standard deviation to the IS curve. In MSR, the composite demand shock is the sum of one-standard-deviation shocks to consumption, fixed investment, inventory investment, and government spending. In both models, the smoothing rules substantially dampen the response of output in the first few quarters compared to the level rules and subsequently push output below potential for some time. Because the spending equations in both FM and MSR are forward-looking, these expected future movements in output, prices, and short-term interest rates play a role in dampening the initial impact of the aggregate demand shock. Of course, given the objective of minimizing the variance of output and inflation, there is a tradeoff between reducing the peak and increasing the extent of overshooting. Nevertheless, in both models overshooting resulting from policy with large values of p is preferred to a monotone reversion to equilibrium values; for example, the interest rate smoothing rule reduces the standard deviation of output by 15 percent in FM and by nearly 40 percent in MSR, compared with the level rule.

Next, we consider the argument that interest rate rules with a high degree of interest rate smoothing reduce overall variability by generating secondary cycles, e.g., overshooting of output. Figure 8 shows the stark contrast in the dynamic response of output to a demand shock under a level rule versus a 3-parameter rule with interest rate smoothing. Each rule corresponds to the policy frontier associated with the same level of interest volatility as that resulting from the estimated rule in equation (1). In FM, the demand shock is a positive shock of one standard deviation to the IS curve. In MSR, the composite demand shock is the sum of one-standard-deviation shocks to consumption, fixed investment, inventory investment, and government spending. In