## 6 Empirical Results

In this section, we report the results of our estimation and especially focus on the estimates of several key structural parameters, those of the SV shocks, and historical decompositions of four principal model variables: (1) output, (2) investment, (3) bank leverage and (4) borrowing rate, playing a significant role in the recession and the financial crisis of 2007-2008. Then, we discuss and remark on the sources of the recession in light of the data-rich approach. $ ^{15} $ Our estimation results are constructed from 300,000 draws of the hybrid MCMC algorithm as posterior distributions of interest for every case. $ ^{16} $

### 6.1 Key Structural Parameters

The estimates of the structural parameters of Cases A and B are summarized in Table 9, and those of Cases C and D are expressed in Table 10. Table 11 notes the estimates of the parameters of the SV models concerning the eight structural shocks. Because the New-Keynesian DSGE model with the two financial frictions was estimated, we focused on interpreting the seven key structural parameters, i.e., two financial frictions, two nominal rigidities, and three monetary policy parameters. Table 4 shows the collection of the parameters of the four cases for ease in comparing with one another. The parenthesis in the table indicates the 90% credible interval of the posterior distribution of the structural parameters.

## [Insert Table 4 around here]

First of all, we considered two estimated parameters involved in the financial friction of the corporate sector; $ \kappa $ and $ \varphi $ . $ \kappa $ denotes the elasticity of the quadratic adjustment cost of investment in eq.(A20), as described in Appendix A4, while $ \varphi $ is the elasticity of the external financial premium in eq.(3.7). According to Table 4, the posterior mean of $ \kappa $ in Case B (the data-rich approach with constant-volatility shocks) is around 0.88, whereas those in the rest of the cases are between 0.56 and 0.63. The large elasticity, $ \kappa $ , in Case B implies that the corporate net worth shock more strongly amplifies the fluctuation of business cycles via the channel of adjustment of the capital asset price (Tobin's marginal q). On the other hand, the posterior means of $ \varphi $ are less than 0.03 in Cases A and B (models with constant volatility shocks), whereas those on the counterpart cases with SV shocks are nearly 0.04. Because the elasticity of the external financial premium, $ \varphi $ , which reflects the size of the agency costs in the corporate sector, is the coefficient of the logarithm of the corporate leverage ratio for explaining the aggregated level of external financial premium $ s_{t} $ as shown in eq.(3.7), the relatively large size of $ \varphi $ in Cases C and D, incorporating the effect of the SV shocks into the DSGE models, suggests that variation of the leverage ratio in the corporate sector is likely to be more influential in enlarging the external financial premium and to lead to a more severe decline of investment than would the results of Cases A and B with structural shocks following normal i.i.d. Notice that there are no parameters concerning the financial friction in the banking sector of our model, following Gertler and Kiyotaki (2010) and Gertler and Kradi (2011), so we cannot show the comparison among the cases in the banking sector. Instead, structural shock pertaining to banking net-worth will be compared among the cases in the following subsection.