Next, the nominal rigidities of the price level and the wage are examined. In our study, these rigidities are governed by a Calvo-type model and are explained in Appendix A4. The Calvo price $ \theta_{P} $ implies that the ratio of intermediate-goods firms face monopolistic competition and reconcile to maintain their price without optimally setting a new price. The value of $ \theta_{P} $ is theoretically a real number between 0 and 1. As can be seen from Table 4, the posterior mean of $ \theta_{P} $ in Case B is nearly half the size (0.37) of the other three cases as those have a relatively high normal rigidity (around 0.8), indicating that new prices are set at one-time per every five-quarter period. On the other hand, Calvo wage $ \theta_{W} $ (the ratio of workers facing monopolistic competition and reconciling to maintain their wage without optimally setting a new wage) is nearly 0.43 in Case B and those in other cases are between 0.5 and 0.6. These values imply that wages are reset with a frequency of around one time per half year.

Finally, Table 4 also reports the three parameters of a Taylor-type monetary policy rule, eq.(A24) described in Appendix A4. $ \rho^{R} $ denotes the size of the inertia of the policy interest rate, i.e., the federal fund rate. And, $ \mu^{\pi} $ and $ \mu^{Y} $ are Taylor coefficients in response to the inflation gap and the output gap, respectively. There are no big differences among the three parameters in the four cases. That is, $ \rho^{R} $ is between 0.63 and 0.67, $ \mu^{\pi} $ is between 2.8 and 3.0, and $ \mu^{Y} $ is tiny, such as from 0.006 to 0.010. These results imply that the central bankers' reactions for the inflation gap are aggressively implemented, while those for the output gap are not so. However, the volatilities of the monetary policy shocks are largely different among the four cases. We will see in Section 6.2 that time-varying volatilities of the monetary policy shocks rapidly increased in the period of the recession.

### 6.2 Structural Shocks and their Volatilities

Figure 1 shows the posterior mean and a 90% credible interval of the eight structural shocks in Cases A and B, which deal with models with constant volatility shocks, whereas Figure 2 shows those in Cases C and D, estimating models with time-varying volatility shocks. In panel (a) of each figure, the shocks of the model with the 11 observable variables are drawn with deep blue solid lines for posterior means and with a light blue shade for the 90% interval, while panel (b) shows the estimates of the shocks of the data-rich approach with deep red solid lines and with a light red shade in a similar way. In each panel, the lines and shadings of its counterpart are underlain because of their being compared to each other. Also Figure 3 depicts the posterior means and the 90% intervals of the time-varying volatility in Cases C and D. From Figures 1 and 2, two points are impressively observed. First, the fluctuation of each structural shock is different in the four cases based on the number of observable series and the specification of the shocks, despite using the same DSGE model. This induces different interpretations of economic analysis for the business cycle, despite adopting the same models. Second, the structural shocks (red shade) estimated from the data-rich approach seemed to fluctuate with bigger swings than those (blue shade) of the standard approach. In particular, the red shade is distinguished in the data-rich approach as covering almost the entire area of the blue shade in Case C in Figure 2, dealing with models with SV shocks.

## [Insert Figure 1 and 2 around here]

Next, we focus on the two structural shocks pertaining to the financial frictions in the banking and corporate sectors. In Table 5, the timings of the peaks of the two shocks are described for the four cases. At first, the banking net-worth shocks have exactly the same peak at 2008Q3 for all cases. In this period, i.e., September and October 2008, several major financial institutions either failed, were acquired under duress, or were subject