Next, we turn to discuss the leverage effects of the SV shocks. Table 11 summarizes the estimation results of the parameters in the SV model defined in eq.(2.2) through eq.(2.4) and used in Cases C and D. The leverage effect is represented by the sign of the correlation coefficient $ \rho_{\sigma} $ of each shock. If $ \rho_{\sigma} $ is negative, the shock has a leverage effect, which implies that the negative shock at the present period amplifies its volatility at the next period, and vice versa. Table 8 sums up the sign of the correlation coefficient $ \rho_{\sigma} $ of each shock in terms of the 90%-credible interval. The mark “-” indicates the negative of $ \rho_{\sigma} $ (leverage effect) at the 90%-credible degree of the posterior probability, while the mark “+” indicates the positive of $ \rho_{\sigma} $ (opposite to the leverage effect) in a similar way. The mark “0” implies that we do not judge the sign of $ \rho_{\sigma} $ nor the leverage effect of each shock because zero is within the 90% interval of $ \rho_{\sigma} $ . According to many financial empirical studies, the leverage effect is often observed in financial time series such as in stock prices. Our question is whether banking and corporate net-worth shocks have the leverage effect, which would imply that a decline of net-worth shocks leads to extending its volatility or its uncertainty in the next period. However, we did not observe leverage effects for these two shocks; instead we observe the opposite leverage effect of the corporate net-worth shock in Case C, as shown in Table 8. This result might be derived from either the number of observations, the specification of our DSGE model, or something else. To answer this question, we need to continue development of the econometric method as well as to select and to accumulate data.

## [Insert Table 8, 9, 10 and 11 around here]

Finally, we note the monetary policy in the period of the Great Recession, although we adopted a liner-type Taylor rule and estimated it for the sample period including QE1 (round 1 of quantitative easing by FRB, between 2008Q4 and 2010Q2) and QE2 (2010Q4 to 2011Q2). The monetary policy shocks in Figures 1 and 2 seem to have two big negative spikes after 2007. The first negative spike was observed at 2007Q4 when the BNP Paribas announcement impacted the global financial market. And the second one was observed at 2008Q3, immediately before the FRB conducted an unconventional monetary policy (QE1). In particular, the magnitudes of these two negative shocks are distinguished in the cases of time-varying volatility, as shown in Figure 2. Figure 3 also captures the rapid appreciation of these volatilities of policy shocks in the period between 2007Q4 and 2008Q3. Table 8 shows the monetary policy has the opposite leverage effect across all of the sample periods in Case D, even though FRB took tremendous monetary easing policies in the recession. That is, tightening the policy is likely to happen more boldly and without hesitation, while easing policy might be done more carefully, according to the results with the 90% credible degree of the posterior probability.

### 6.3 Historical Decompositions

To investigate the sources of the Great Recession, we focused on the historical decompositions of four observable variables: (1) the real GDP as an output gap, (2) the gross private domestic investment (fixed investment) as investment, (3) Moody's bond index (corporate Baa) as the corporate borrowing rate, (4) the commercial banks' leverage ratio as the bank leverage ratio, which is described in detail in the Data Appendix. Each of Figures 4 through 7 draws four decompositions of each observable variable based on the four cases for the periods between 2000Q1 and 2012Q2, and the light blue shade denotes the period of the Great Recession (2007Q3 to 2009Q2). To facilitate visualization and focus on the contributions of the two financial frictions, the technology and monetary policy shocks for the recession, we collected the remaining four miscellaneous shocks as one bundle in these figures.