to government takeover. These financial institutions included Lehman Brothers, Merrill Lynch, Fannie Mae, Freddie Mac, Washington Mutual, Wachovia, Citi group, and AIG. However, the timings of the peaks of the corporate net-worth shock are not consistent and are divided into two periods, i.e., 2009Q1 in Cases A and B, and 2009Q2 in Cases C and D. Notice that the corporate net-worth shocks have peaks after the banking sector shocks hit its peaks, whatever the case.

## [Insert Table 5 around here]

We considered the accuracy of the estimation for the eight shocks using an average range of 90% to be a credible interval across all of the sample period, as shown in Table 6. If we observe that the 90% interval ranges are smaller, then we might think that the shocks are likely to be identified more precisely. Among the four cases, five average intervals of shocks out of eights are smaller in Cases C and D than in Cases A and B. These five shocks are (1) preference, (2) banking net worth, (3) labour supply, (4) government spending, and (5) monetary policy. In the two cases with time-varying volatility shocks, the intervals in the former three shocks are about half those of the other two cases with constant shocks. And those of government spending shocks shrank by one eighth to one tenth by adopting SV shocks. These statistics suggest that the constant volatilities of shocks might be misspecified and that the shocks follow time-varying volatilities. In particular, the volatilities are expected to change to larger values at the turning points of the business cycles, as shown later.

## [Insert Table 6 around here]

Figure 3 draws estimates of the time-varying volatilities of shocks for Cases C and D. Surprisingly, the seven shocks, minus the government spending shocks, are very similar in both cases. In Figure 3, the deep blue and the deep red solid lines denote the posterior means of Cases C and D, respectively. As seen from this figure, the six shocks, minus the preference and labour supply shocks, are very stable and level off between 1990Q1 and 2007Q3, while the preference and labour supply shocks might play an important role of the boom between 2003 and 2005. After August 2007, when the financial crisis of 2007 to 2009 began with the seizure in the banking system, precipitated by BNP Paribas announcing that it was ceasing activity in three hedge funds that specialized in US mortgage debt, the volatilities of both the banking and the corporate net-worth, investment, and TFP rapidly increased. Although our DSGE model is not thought to perfectly capture the macroeconomic fluctuations in the period of the Great Recession, the estimates show extraordinary sizes of the volatilities in this period.

## [Insert Figure 3 around here]

Table 7 indicates the average 90% intervals of the SV over the entire sample period in the two cases because of our verifying whether the data-rich approach contributes to the improvement of the estimates of the SV of the shocks. As seen from Table 7 as well as from Figure 3, there are no differences of means of the interval ranges between Cases C and D. However, it might be too hasty to conclude that the data-rich method does not improve the accuracy of the SV estimates. We would need to validate the further evidences in this question.

## [Insert Table 7 around here]