$$ \tilde{\boldsymbol{X}}_{t}=\underbrace{[\boldsymbol{\Lambda}\quad-\boldsymbol{\Psi}\boldsymbol{\Lambda}]}_{\tilde{\boldsymbol{\Lambda}}}\underbrace{\left[\begin{array}{c}\boldsymbol{S}_{t}\\ \boldsymbol{S}_{t-1}\end{array}\right]}_{\tilde{\boldsymbol{S}}_{t}}+\boldsymbol{\nu}_{t},\qquad\boldsymbol{\nu}_{t}\sim\mathrm{i.i.d.}N(\mathbf{0},\mathbf{R}). $$

In a similar way, the transition equation (2.12) is also rewritten as

$$ \underbrace{\left[\begin{array}{c}\boldsymbol{S}_{t}\\ \boldsymbol{S}_{t-1}\end{array}\right]}_{\tilde{S}_{t}}=\underbrace{\left[\begin{array}{c c}\mathbf{G}(\boldsymbol{\theta})&\mathbf{O}\\ \mathbf{I}&\mathbf{O}\end{array}\right]}_{\tilde{\mathbf{G}}}\underbrace{\left[\begin{array}{c}\boldsymbol{S}_{t-1}\\ \boldsymbol{S}_{t-2}\end{array}\right]}_{\tilde{S}_{t-1}}+\underbrace{\left[\begin{array}{c}\mathbf{E}(\boldsymbol{\theta})\\ \mathbf{O}\end{array}\right]}_{\tilde{\mathbf{E}}}\boldsymbol{\varepsilon}_{t}, $$

where I is a $ N \times N $ identity matrix. The estimation method of the data-rich DSGE model is explained using the state-space model (2.17) and (2.18), and we estimated this model using the Bayesian Method via MCMC in Section 4. For convenience, we set the parameters of the measurement equation (2.17) as $ \Gamma = \{\Lambda, \Psi, R\} $ . And the Bayesian estimation of the parameters $ \Gamma $ follow Chib and Greenberg (1994), as described in Appendix A3.

## 3 The DSGE model with Two Financial Frictions in Corporate and Banking Sectors

In order to model the balance sheets of the corporate and banking sectors in a DSGE framework, we combined the essence of Bernanke, Gertler, and Gilchrist (hereafter, BGG) (1999), Gertler and Karadi (2011), and Gertler and Kiyotaki (2010). We adopted the stylized DSGE model based on CEE (2005) and Smets and Wouters (2003, 2007), which focused on the nominal rigidities of price level and wage as well as the quadratic adjustment cost of investment, and embedded the financial frictions of the corporate and banking sectors to it. This section is the highlight, modelling the frictions in our DSGE model. The rest of our model is described in Appendix A4.

### 3.1 Financial Friction in Corporate Sector

#### 3.1.1 Entrance and Exit of Entrepreneurs

Following BGG (1999), there is a continuum of entrepreneurs indexed by $ j \in [0,1] $ where each entrepreneur is risk-neutral and has a finite expected horizon. $ ^{5} $ Each entrepreneur faces an exogenous time-varying stochastic survival rate of $ \gamma_{t+1}^{E} $ from period t to $ t+1 $ , which is common across all entrepreneurs. $ ^{6} $

Between period t and $ t + 1 $ , after $ 1 - \gamma_{t+1}^{E} $ , a fraction of entrepreneurs will exit from the business, and exactly the same number of new entrepreneurs will enter the business, so the population of entrepreneurs in the economy remains the same (i.e., a fraction $ f^{E} $ of the total members of the household) from period t to $ t + 1 $ . Each entering entrepreneur will receive a “start-up” transfer from the household and the total “start-up” transfer from the household will be equal to the constant fraction $ \xi^{E} $ of aggregate net worth available in the corporate sector, $ n_{t}^{E} $ , i.e., $ \xi^{E} n_{t}^{E} $ . For $ 1 - \gamma_{t+1}^{E} $ , a fraction of entrepreneurs who happen to exit the business will first sell the capital they purchased during the last period and will retire all of their debts before their maturity. Then, they will transfer their remaining net