subsection, we estimate the model in the periods when the nominal interest rate does not bind zero and check the robustness of our results.

Figure 4-3 (a) shows the nominal interest rate from 1980Q2 to 2012Q4. While the Bank of Japan (BoJ) adopted the zero-interest-rate policy (with quantity easing policy) after March 2001, the BoJ has already derived a short-term nominal interest rate (uncollateral overnight call rate) to 0.15% at February 1999. Therefore, we estimate the model in the following sub-sample periods: 1980Q2-2001Q1 and 1980Q2-1998Q4.

Table 6 shows posterior means and 90% credible intervals in full sample and two subsample periods. We can see almost all parameters are surprisingly robust even if we include or exclude zero interest rate periods. Posterior means of EC and PPC, $ \nu_{g} $ and $ \alpha_{g} $ , without including zero interest rate periods are also in 90% credible intervals of full sample. Thus, IRFs for fiscal stimuli are almost all the same as those of full sample and our results do not necessarily rely on the reduction of crowding out effects in zero interest rate periods.

This robustness of estimated parameters under including zero interest rate periods is consistent with Hirose and Inoue (forthcoming), who investigate estimation bias when zero interest rate periods are included via the following Monte Carlo experiments: Given true distributions of parameters, data including zero interest rate are artificially generated by a new Keynesian model. Then, they estimate parameters without corresponding to zero interest rate periods and check the estimation bias. As a result, they find the robustness of estimated parameters, which might support our results.

However, Table 6 also shows contradictionary results with Hirose and Inoue (forthcoming). We find reductions of almost all estimated shock volatilities when zero interest rate periods are included. In contrast, Hirose and Inoue (forthcoming) report an upward bias on the estimated volatility of the monetary policy.

Binding at zero lower bound of nominal interest rate indicates deviations from the monetary policy rule, and deviations are regarded as monetary policy shocks. Thus, including zero interest rate periods will bring upward estimation bias for the volatility of monetary policy shock. This interpretation, however, is appropriate if the central bank keeps the monetary policy rule strictly in positive interest rate periods, which is a crucial assumption of Hirose and Inoue (forthcoming) in generating artificial data.

Figure 4-3 (b) shows a scatter plot between inflation (annual rate, horizontal axis) and nominal interest rate (annual rate, vertical axis). We can make two observations: First, deviations from the monetary policy rule seem to be high even in positive interest rate periods. Second, the variance of inflation seems to become smaller after 2001Q2. That is, there might be a possibility that the central bank does not strictly keep the Taylor rule in positive interest rate periods. The volatile variations of inflation in positive interest rate periods are captured as relatively higher volatility of the monetary policy shock. Therefore, estimating parameters including data after 2001Q2 when variations of inflation become relatively moderate might reduce volatility of the monetary policy shock even if the monetary authority keeps nominal interest rate at zero. The reason: our results show the decline of variance of monetary policy shock when zero interest rate periods are included.