As can be seen from the above equation, the idiosyncratic factor pertaining to banker m is averaged away and, thus, the realization of the risk-adjusted return of the banking sector (i.e., $ \overline{r}_{t+1}^{F} $ ) only depends on the aggregate factors in the economy. Now, by using (3.22), the aggregate net worth transition equation becomes

$$ n_{t+1}^{F}=\gamma_{t+1}^{F}\left[\left(\overline{{r}}_{t+1}^{F}-r_{t+1}\right)\phi_{t}+r_{t+1}\right]n_{t}^{F}+\xi^{F}n_{t}^{F}. $$

### 3.3 Incorporation of the two Frictions within the DSGE model

To incorporate the two financial frictions into a stylized DSGE model, we used twelve constraints and FOC equations, which consist of five and seven equations derived in the corporate and banking sectors, respectively. $ ^{9} $ The five equations representing the financial friction in the corporate sector are (i) the balance sheet statement of the corporate sector (3.2), (ii) the capital demand function (3.6), (iii) the external financial premium (3.7), (iv) the realized gross return from the capital investment (3.11), and (v) the aggregate net worth transition equation of the corporate sector (3.12). On the other hand, the seven equations expressing the financial friction in the banking sector are (vi) the balance sheet statement of the banking sector (3.13), (vii) the dynamics of the weight on the lending volume for the value of the banking business, $ \nu_{t} $ , (3.18), (viii) the dynamics of the weight on the bank's net worth for the value of the banking business, $ \eta_{t} $ , (3.19), (ix) the definition of the threshold, $ \phi_{t} $ , ([3.20}), (x) the banker's leverage ratio constraint (3.22), (xi) the relationship between the corporate nominal borrowing rate, and the risk-adjusted nominal lending rate of the banking sector (3.24), and (xii) the aggregate net worth transition equation of the banking sector (3.25).

To complete our model, we employed the CEE (2005)-type medium scale DSGE model described in Appendix A4 with the equations above, as well as the structural shocks. We set the following eight structural shocks, each of them having a specific economic interpretation; i.e., (1) TFP shock, (2) preference shock, (3) labour-supply shock, (4) investment specific technology shock, (5) government spending shock, (6) monetary policy shock, (7) corporate net-worth shock, and (8) bank net-worth shock. With the exception of the monetary policy shock, all of the structural shocks are assumed to follow AR(1) stochastic processes. We devoted the following two shocks out of the eight to identifying the fundamental factors causing the financial crisis. Corporate net-worth shock $ \varepsilon_{t}^{E} $ was inserted into the AR(1) process of the survival rate of the corporate sector $ \gamma_{t}^{E} $ , which is a component of equation (3.12), while the bank net worth shock $ \varepsilon_{t}^{F} $ is put into the AR(1) process of the survival rate of the banking sector $ \gamma_{t}^{F} $ , which is that of the equation (3.25). The two shocks are given as follows:

$$ \begin{aligned}Corporate net worth shock&:\quad\hat{\gamma}_{t}^{E}=\rho^{E}\hat{\gamma}_{t-1}^{E}+\varepsilon_{t}^{E},\\ Bank net worth shock&:\quad\hat{\gamma}_{t}^{F}=\rho^{F}\hat{\gamma}_{t-1}^{F}+\varepsilon_{t}^{F},\end{aligned} $$

where $ \rho $ is for the AR(1) coefficients for respective structural shocks. Both shocks indicating stochastic survival rate for entrepreneurs and bankers at the micro-level can be interpreted as net-worth shocks for the corporate and banking sectors at the aggregate level,