### Regime-Switching Policy vs. Fixed Policy

Table 3 summarizes the results of 100,000 replications derived from policy functions for a regime-switching policy and a fixed-regime policy. Panels (a) and (b) represent the results of a mixed-regime policy and a fixed-regime policy differentiated by the absence and presence of the ZLB constraint, respectively. In the case of the absence of the ZLB (panel (a)), the MS Taylor rule indicates an MSLRE model, so that the mean of each variable is consistent with its steady-state value, i.e., zero, regardless of the forms of expectations. Furthermore, the standard deviation of each variable is the same for stochastic rational expectations and perfect foresight. These calibration results are consistent with the theoretical conjecture for the effect of the forms of expectations in an MSLRE model. In addition, the standard deviation is larger under a regime-switching policy than under a fixed monetary policy. This result suggests that a regime-switching policy induces the instability of business cycles, as pointed out by Davig and Leeper (2007). On the other hand, in the case of an economy subject to the ZLB, the effects of these two policies are completely different from the case of its absence. As seen in Table 3, as in Table2, we can also observe the negative values of the means far from steady states for all the variables, regardless of the form of the expectations. The means of the regime-switching policy are smaller than those of the fixed policy. The discrepancy in the standard deviations between the two policies is much smaller than in the case of no ZLB. There are non-negligible sizes in means and standard deviations between stochastic rational expectations and perfect foresight.

In Figures 10 (a) and (b), the artificial data of regime switching and fixed policies generated from Monte Carlo simulation are depicted by distinguishing them according to the presence or the absence of the ZLB, respectively. The same random seed is adopted in panels (a) and (b) to compare the effect of the ZLB constraint, so that the same structural shocks determine the endogenous variables in both graphs. A light shade indicates the passive regime. The fluctuations in the variables under the regime-switching policy (the solid line) have a bigger swing in the passive regime period than under the fixed policy (the dashed line) in the case of the absence of the ZLB, as in panel (a). In contrast, positive demand shocks make the reactions of these variables appear similar to those above, whereas negative big shocks cause big declines of these variables, regardless of the presence of policy regime changes. The size of the decline is larger in panel (b) than in panel (a); for example, period 80 through 90. Accordingly, the effects of negative shocks on an economy do not depend on whether the policy regime changes or remains fixed.

## The Impact of Mitigating the Uncertainty of Demand Shocks to an Economy

Here, let us consider some policy implications for recovering recessions under the ZLB. As seen above, the effect of the active policy regime is similar to that of the passive regime. As a simple case, a 20% reduction in the volatility of an aggregate demand shock is introduced into the model. Figure 11 shows that the