Silviase/jgov_v1.4_full_ann huggingface dataset:
$$ \begin{array}{rcl}\bar{\mathbf{M}}_{k}&=&\mathbf{M}_{k,0}+\left(\boldsymbol{S}^{*\prime}\boldsymbol{S}^{*}\right)\\\bar{\mathbf{\Lambda}}_{k}&=&\bar{\mathbf{M}}_{k}^{-1}\bigg(\mathbf{M}_{k,0}\mathbf{\Lambda}_{k,0}+(\boldsymbol{S}^{*\prime}\boldsymbol{S}^{\prime})\hat{\mathbf{\Lambda}}_{k}\bigg)\\\bar{s}&=&s_{0}+s+(\lambda_{k,0}-\hat{\mathbf{\Lambda}}_{k})^{\prime}\bigg[\mathbf{M}_{k,0}^{-1}+(\boldsymbol{S}^{*\prime}\boldsymbol{S}^{*})^{-1}\bigg]^{-1}(\lambda_{k,0}-\hat{\mathbf{\Lambda}}_{k})\\\bar{\nu}&=&\nu_{0}+T\end{array} $$

and $ \Lambda_{k,0} $ , $ M_{k,0} $ , $ s_{0} $ , and $ \nu_{0} $ are parameters of the prior density.

We sample factor loading $ \Lambda_{k} $ and the variance of measurement error $ R_{kk} $ sequentially from

$$ \begin{aligned}R_{kk}|\Psi_{kk},\boldsymbol{S}^{T},\boldsymbol{\theta},\boldsymbol{X}^{T}\quad&\sim&IG(\bar{s},\bar{\nu})\\\mathbf{\Lambda}_{k}|R_{kk},\Psi_{kk},\boldsymbol{S}^{T},\boldsymbol{\theta},\boldsymbol{X}^{T}\quad&\sim&N(\bar{\mathbf{\Lambda}}_{k},R_{kk},\bar{\mathbf{M}}_{k}^{-1})\end{aligned} $$

Step 2. Sampling $\Psi_{kk}$ from conditional posterior distribution $p(\Psi_{kk}|\Lambda, R_{kk}, S^{T}, \theta, X^{T})$ for estimating equation of measurement errors

$$ \boldsymbol{e}_{k}=\boldsymbol{\Psi}_{k k}\boldsymbol{e}_{k,-1}+\boldsymbol{\nu}_{k}. $$

The conditional posterior density : $ p(\Psi_{kk}|\mathbf{\Lambda}, R_{kk}, S^{T}, \theta, X^{T}) $ is given as

$$ p(\Psi_{kk}|\boldsymbol{\Lambda}_{k},R_{kk},\boldsymbol{S}^{T},\boldsymbol{\theta},\boldsymbol{X}^{T})\propto p(\boldsymbol{X}_{k}^{T}|\boldsymbol{S}^{T},\boldsymbol{\Lambda}_{k},R_{kk},\boldsymbol{\Psi}_{kk},\boldsymbol{\theta})p(\boldsymbol{\Psi}_{kk}), $$

where $ p(\mathbf{X}_{k}^{T}|S^{T},\mathbf{\Lambda}_{k},R_{kk},\Psi_{kk},\boldsymbol{\theta}) $ is likelihood function and $ p(\Psi_{kk}) $ is prior density. Then, above likelihood function is proportional to the normal density such as

$$ p(\boldsymbol{X}_{k}^{T}|\boldsymbol{S}^{T},R_{kk},\Psi_{kk},\boldsymbol{\theta})\propto\exp\left[-\frac{1}{2R_{kk}}(\Psi_{kk}-\hat{\Psi}_{kk})^{\prime}\boldsymbol{e}_{k,-1}^{\prime}\boldsymbol{e}_{k,-1}(\Psi_{kk}-\hat{\Psi}_{kk})\right]. $$

And above prior density of coefficient of AR (1) errors $ \Psi_{kk} $ is also normal density but truncated at less than unity because dynamic of errors keep to be stationary. So, prior density is assumed to be such as

$$ p(\Psi_{k k})\quad\propto\quad\exp\left[-\frac{1}{2\sigma_{\Psi,0}^{2}}(\Psi_{k k}-\Psi_{0})^{2}\right]\times\mathbf{1}_{\{|\Psi_{k k}|<1\}}, $$

where $ 1_{\{|\Psi_{kk}|<1\}} $ denotes indicator function which is unity if $ |\Psi_{kk}|<1 $ , otherwise zero.

The conditional posterior density is proportional to a product of above two normal densities, and represented as

$$ \begin{align*}p(\Psi_{kk}|R_{kk},\boldsymbol{S}^{T},\boldsymbol{\theta},\boldsymbol{X}^{T})\quad&\propto\quad\exp\left[-\frac{1}{2R_{kk}}(\Psi_{kk}-\hat{\Psi}_{kk})^{\prime}\boldsymbol{e}_{k,-1}^{\prime}\boldsymbol{e}_{k,-1}(\Psi_{kk}-\hat{\Psi}_{kk})\right]\\&\times\quad\exp\left[-\frac{1}{2\sigma_{\Psi,0}^{2}}(\Psi_{kk}-\Psi_{0})^{2}\right]\times\mathbf{1}_{\{|\Psi_{kk}|<1\}}.\end{align*} $$
$$ c_{t}+b_{t}=\frac{R_{t-1}}{\pi_{t}}b_{t-1}-\tau_{t}+\Xi_{t}^{d i v}+\Xi_{t}^{E}+\Xi_{t}^{F}. $$

Consumption and Deposit Decision The first-order conditions (hereafter, FOCs) of the household with respect to $ c_{t} $ and $ b_{t} $ as follows;

$$ \zeta_{t}^{H}=\chi_{t}^{c}\left(c_{t}-h c_{t-1}\right)^{-\sigma^{c}} $$

$$ \zeta_{t}^{H}=\beta E_{t}\zeta_{t+1}^{H}\frac{R_{t}}{\pi_{t+1}}. $$

where $ \zeta_{t}^{H} $ is Lagrangian multiplier associated with the budget constraint. (A.16) is the FOC of consumption which equates the marginal utility of consumption to the shadow price of the final goods. (A.17) is the FOC of deposit decision.

Wage Setting Decision by Workers Following Erceg, Henderson, and Levin (2000) (hereafter, EHL), each worker indexed by $ x \in [0,1] $ supplies differentiated labor input, $ l_{t}(x) $ , monopolistically and sells this service to the labor union who is perfectly competitive. $ ^{22} $ Each worker sets his nominal wage according to Calvo style sticky price setting where fraction $ \theta^{w} $ of the entire workers cannot freely adjust the wages at their discretion. For fraction $ \theta^{w} $ of workers, the partial indexation of the nominal wage is assumed. $ ^{23} $ Due to the perfect risk-sharing assumed in the model, each worker maximizes the objective function (A.14) by choosing the amount of individual labor supply, $ l_{t}(x) $ , while taking the amount of consumption, $ c_{t} $ , as given. Under this setting, $ (1 - \theta^{w}) $ fraction of workers maximize their objective function by setting the nominal wage, $ \widetilde{W}_{t} $ , such that

$$ E_{t}\sum_{i=0}^{\infty}\beta^{i}(\theta^{w})^{i}\left[\frac{\widetilde{W}_{t}}{P_{t+i}}\left(\frac{P_{t-1+i}}{P_{t-1}}\right)^{\iota^{w}}\chi_{t+i}^{c}\left(c_{t+i}-h c_{t+i-1}\right)^{-\sigma^{c}}-(1+\psi^{w})\chi_{t+i}^{c}\chi_{t+i}^{L}\left(l_{t+i}(x)\right)^{\sigma^{L}}\right]l_{t+i}(x)=0. $$

The law of motion of the aggregate wage index can be shown to be as follows,

$$ W_{t}^{-1/\psi^{w}}=\theta^{w}\left[W_{t-1}\left(\frac{W_{t-1}}{W_{t-2}}\right)^{\iota^{w}}\right]^{-1/\psi^{w}}+(1-\theta^{w})\widetilde{W}_{t}^{-1/\psi^{w}}. $$

Finally, the real wage index in the economy is defined as $ w_{t} \equiv W_{t}/P_{t} $ .

#### A.4.2 Capital Production Sector

Capital producers are identical, perfectly competitive, and risk neutral. They purchase $ i_{t}^{k} $ units of final goods from the retailer, convert them to $ i_{t}^{k} $ units of capital goods, and combine them with existing capital stock, $ (1 - \delta)k_{t} $ , to produce new capital stock, $ k_{t+1} $ . Capital producers will, then, sell off new capital stock to entrepreneurs in a perfectly competitive manner. Capital producers have linear production technology in converting final goods to capital goods. In addition, they will incur quadratic investment adjustment cost when
they change the production capacity of capital goods from previous period. Each capital producer maximizes the expected discounted cash flow with respect to $ i_{t}^{k} $ . $ {}^{24} $ The FOC is given by

$$ q_{t}=\frac{1}{A_{t}^{k}}\left[1+\kappa\left(\frac{i_{t}^{k}}{i_{t-1}^{k}}-1\right)\frac{i_{t}^{k}}{i_{t-1}^{k}}+\frac{\kappa}{2}\left(\frac{i_{t}^{k}}{i_{t-1}^{k}}-1\right)^{2}\right]-\beta\frac{\kappa}{A_{t+1}^{k}}\left(\frac{i_{t+1}^{k}}{i_{t}^{k}}-1\right)\left(\frac{i_{t+1}^{k}}{i_{t}^{k}}\right)^{2}. $$

where $ A_{t}^{k} $ is the investment-specific technology shock common across all capital producers and $ \kappa $ is the investment adjustment cost parameter. Finally, aggregate capital accumulation equation is given by

$$ k_{t+1}=i_{t}^{k}+(1-\delta)k_{t}. $$

#### A.4.3 Retailing Sector

Retailers $ z \in [0,1] $ purchase intermediate goods from the entrepreneur at perfectly competitive price and resale them monopolistically in the retail market. $ ^{25} $ We assume Calvo type sticky price setting for the retailer where, for any given period t, fraction $ \theta^{p} $ of the entire retailers cannot freely revise their prices. Further, $ \theta^{p} $ fraction of the retailers who did not receive a 'signal of price change' will partially index their nominal prices to lagged inflation rate of price index. $ ^{26} $ Under this setting, for $ (1 - \theta^{p}) $ fraction of the retailers who received a 'price changing signal' at period t, they maximize their expected discounted sum of profits by setting the nominal price, $ \tilde{p}_{t} $ , such that

$$ E_{t}\sum_{i=0}^{\infty}\beta^{i}(\theta^{p})^{i}\left[\frac{\widetilde{p}_{t}}{P_{t+i}}\left(\frac{P_{t-1+i}}{P_{t-1}}\right)^{\iota^{p}}-\left(\frac{\epsilon}{\epsilon-1}\right)p_{t+i}^{m c}\right]y_{t+i}(z)=0. $$

From the definition of aggregate price index, the law of motion of $ P_{t} $ can be shown to be as follow,

$$ \left(P_{t}\right)^{1-\epsilon}=\theta^{p}\left[P_{t-1}\left(\frac{P_{t-1}}{P_{t-2}}\right)^{\iota^{p}}\right]^{1-\epsilon}+(1-\theta^{p})\tilde{p}_{t}^{1-\epsilon}. $$

#### A.4.4 The Rest of the Economy

In closing the model, we describe the rest of the model structure here. The central bank is assumed to follow a standard Taylor-type monetary policy rule,

$$ \hat{R}_{t}=\rho^{R}\hat{R}_{t-1}+\left(1-\rho^{R}\right)\left[\mu^{\pi}\hat{\pi}_{t}+\mu^{y}\hat{Y}_{t}\right]+\varepsilon_{t}^{R} $$

$$ E_{t}\sum_{i=0}^{\infty}\beta^{i}\left\{q_{t+i}i_{t+i}^{k}-\frac{1}{A_{t+i}^{k}}\left[i_{t+i}^{k}+\frac{\kappa}{2}\left(\frac{i_{t+i}^{k}}{i_{t+i-1}^{k}}-1\right)^{2}i_{t+i}^{k}\right]\right\} $$
where $ \rho^{R} $ controls the magnitude of interest smoothing, $ \mu^{\pi} $ is Taylor coefficient in response to inflation gap, $ \mu^{y} $ is Taylor coefficient in response to output gap, and $ \varepsilon_{t}^{R} $ is i.i.d. monetary policy shock.

The government budget constraint is simply specified as

$$ g_{t}=\tau_{t}. $$

The government expenditure, $ g_{t} $ , is financed solely by lump-sum tax, $ \tau_{t} $ . In our model, we simply assume that the government expenditure to follow stochastic AR(1) process.

Finally, the market clearing condition for final goods is given as follow,

$$ Y_{t}=c_{t}+i_{t}^{k}+g_{t}. $$

#### A.4.5 Structural Shocks in the Model

There are eight structural shocks in the model, each of them having a specific economic interpretation as below. Except for monetary policy shock, all of the structural shocks are assumed to follow AR(1) stochastic processes where $ \rho $ is for the AR(1) coefficients for respective structural shocks.

TFP shock : $\hat{A}_{t} = \rho^{A} \hat{A}_{t-1} + \varepsilon_{t}^{A}$

Preference shock : $\hat{\chi}_{t}^{c} = \rho^{c}\hat{\chi}_{t-1}^{c} + \varepsilon_{t}^{c}$

Labor supply shock : $ \hat{\chi}_{t}^{L} = \rho^{L}\hat{\chi}_{t-1}^{L} + \varepsilon_{t}^{L} $

Investment specific technology shock : $\hat{A}_{t}^{K} = \rho^{K} \hat{A}_{t-1}^{K} + \varepsilon_{t}^{K}$

Government spending shock : $ \hat{g}_{t} = \rho^{G}\hat{g}_{t-1} + \varepsilon_{t}^{G} $

Monetary policy shock : $ \varepsilon_{t}^{R} $

$$ Corporate net worth shock\quad:\quad\hat{\gamma}_{t}^{E}=\rho^{E}\hat{\gamma}_{t-1}^{E}+\varepsilon_{t}^{E} $$

$$ \mathbf{Bank net worth shock}\quad:\quad\hat{\gamma}_{t}^{F}=\rho^{F}\hat{\gamma}_{t-1}^{F}+\varepsilon_{t}^{F} $$

Notice that each stochastic disturbance $ \varepsilon_{t} $ including monetary policy shock is assumed to follow time varying volatility using SV model as mentioned in Section 2.

## References

[1] Adrian, T and Shin, H. S. (2010) "Liquidity and leverage," Journal of Financial Intermediation, vol. 19(3), 418-437.

[2] Adrian, T., Colla, P. and Shin, H. S. (2012) “Which Financial Frictions? Parsing the Evidence from the Financial Crisis of 2007-09,” Federal Reserve Bank of New York Staff Reports, No. 528.

[3] Albert, J. H. and Chib, S. (1993) "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics; Jan1993, Vol. 11 Issue 1, p1-15, 15p

[4] Bauwens, L., Lubrano, M. and Richard, J.-F. (1999) Bayesian Inference in Dynamic Econometric Models, Oxford University Press.

[5] Bernanke, B.S., Gertler, M. and Gilchrist, S. (1999) “The Financial Accelerator in a Quantitative Business Cycles Framework,” In: Taylor, J.B. and Woodford, M. (eds.) Handbook of Macroeconomics, vol. 1C, p 1341-1393, North-Holland.
[6] Boivin, J. and Giannoni, M. (2006) “DSGE Models in a Data-Rich Environment,” Manuscript, HEC Montreal and Columbia University.

[7] Carlstrom, C. T. and Fuerst, T. S. (1997) “Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis, American Economic Review, 87, 893-910.

[8] Carter, C. and Kohn, R. (1994) “On Gibbs Sampling for State Space Models,” Biometrika, 81(3), pp. 541-553.

[9] Chib, S. (2001) “Markov Chain Monte Carlo Methods: Computation and Inference,” Handbook of Econometrics, Vol 5, pp.3569-3649.

[10] Chib, S. and Greenberg, E. (1994) “Bayes Inference in Regression Models with ARMA $ (p,q) $ Errors,” Journal of Econometrics, 64, pp.183-206.

[11] Christensen, I. and Dib, A. (2008) “The Financial Accelerator in an Estimated New Keynesian Model,” Review of Economic Dynamics, 11, 155-178.

[12] Cristiano, L.J., M. Eichenbaum, and C. Evans (2005) “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary policy,” Journal of Political Economy, 113, 1-45.

[13] Del Negro, M. and Schorfheide, F. (2010) “Bayesian Macroeconomics,” In: Geweke, J., Koop, G. and van Dijk, H. (eds.) Oxford Handbook of Bayesian Econometrics, Oxford university press.

[14] Durbin, J., and S. J. Koopman (2001), Time Series Analysis by State Space Models, Oxford: Oxford University Press.

[15] de Jong, P., and Shephard, N. (1995) “The simulation smoother for time series,” Biometrika, 82, pp.339-350.

[16] Gertler, M. and Kiyotaki, N. (2010) “Financial Intermediation and Credit Policy in Business Cycle Analysis,” Handbook of Monetary Economics, in Friedman, B. M. and Woodford, M. (eds.), 3, 547-599.

[17] Gertler, M. and Karadi, P. (2011) “A Model of Unconventional Monetary Policy,” Journal of Monetary Economics. 58, 17-34.

[18] Ireland, P.N. (2011) “A New Keynesian Perspective on the Great Recession,” Journal of Money, Credit and Banking, 43 (1) 31-54.

[19] Iiboshi, H. (2012) “Measuring the Effects of Monetary Policy: A DSGE-DFM Approach,” ESRI discussion paper.

[20] Iiboshi, H., T. Matsumae, R. Namba, and Nishiyama, S.-I. (2012) "Estimating a DSGE model for Japan in a Data-Rich Environment," mimeo.

[21] Justiniao, A. and Primiceri, G. (2008) “The Time-Varying Volatility of Macroeconomic Fluctuations,” American Economic Review, 98 (3), 604-641.

[22] Kim, C.-J. and Nelson, C. (1999) State-Space Models with Regime Switching, MIT Press.

[23] Kim, S., Shephard, N. and Chib, S. (1998) “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,” Review of Economic Studies, 65, 361-393.
[24] Kryshko, M. (2011) "Data-Rich DSGE and Dynamic Factor Models," IMF Working Paper No. 11/216.

[25] Liu, Z., Waggoner, D. F. and Zha, T. (2009) “Asymmetrics Expectation Effects of Regime Shifts in Monetary Policy,” Reviews of Economic Dynamics, vol.12, p284-303.

[26] Liu, Z., Waggoner, D. F. and Zha, T. (2011) “Sources of Macroeconomic Fluctuations: A Regime-Switching DSGE Approach,” Quantitative Economics, vol.2, p251-301.

[27] Matsumae. T., H. Iiboshi, R. Namba, and S.-I. Nishiyama, (2011) “An Application of Hybrid MCMC and Simulation Smoother in Estimating a DSGE Model with Measurement Errors,” Journal of the Japanese Statistical Society, 41-J (1), 83-121 (in Japanese).

[28] Nishiyama, Iiboshi, Matsumae and Namba (2011) "How Bad was Lehman Shock? Estimating a DSGE model with Firm and Bank Balance Sheets in a Data-Rich Environment," mimeo.

[29] Neal, P. and Robert, G.O. (2008) “Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities,” Methodology and Computing in Applied Probability, 10, 277-297.

[30] Omori, Y., Chib S., Shephard, N., and Nakajima, J. (2007) “Stochastic Volatility with Leverage: Fast and Efficient Likelihood Inference,” Journal of Econometrics, 140, 425-449

[31] Robet, G.O., Gelman, A. and Gilks, W. (1997) "Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithm," Annals of Applied Probability, 7, 110-120.

[32] Schorfheide, F. (2005) “Learning and Monetary Policy Shifts,” Reviews of Economic Dynamics, vol.8, p392-419.

[33] Shorfheide, F., Sill, K., and Kryshko, M. (2010) “DSGE model-based forecasting of non-modelled variables,” International Journal of Forecasting 26, 348-373.

[34] Sims, C. (2002) “Solving Linear Rational Expectations Models,” Computational Economics, 20, 1-20.

[35] Smets, F. and R. Wouters (2003) "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, 1 (5), 1123-1175.

[36] Smets, F. and R. Wouters (2007) “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,” American Economic Review, vol. 97(3), pages 586-606.

[37] Stock, J. and Watson, M. (2002a) “Forecasting using principal components from a large number of predictors,” Journal of American Statistical Association, 97, p1167-1179.

[38] Stock, J. and Watson, M. (2002b) “Macroeconomic Forecasting using diffusion Indexes,” Journal of Business and Economic Statistics, 20(2), p147-162.

[39] Stock, J. and Watson, M. (2006) “Forecasting with many predictors,” In: Elliott, G., Granger, C.W.J. and Timmermann (eds.), A. Handbook of Economic Forecasting, Vol.1, p515-554.
[40] Stock, J. and Watson, M. (2010) “Dynamic Factor Models,” In: Clements, M. P. and Hendry, D. F. (eds.) Oxford Handbook of Economic Forecasting, Oxford University Press.

[41] Woodford, Michael (2009). "Convergence in Macroeconomics: Elements of the New Synthesis". American Economic Journal: Macroeconomics 1 (1): 267–79. doi:10.1257/mac.1.1.267.
Table 1: Specifications of Four Alternative Cases

Case A	Case B	Case C	Case D
Number of Observations	11	40	11	40
Model Variable to Obs.	1 to 1	1 to 4	1 to 1	1 to 4
Structural Shock	i.i.d. Normal	i.i.d. Normal	SV with Leverage	SV with Leverage

Note: Item Number of Observation in the first column denotes the number of data indicators used for estimating the model of each case. Item Model Variable to Obs denote the ratio what number of observations per one model variable are adopted. In the case of a standard DSGE model, we adopt one to one matching between model variables and observations. In data rich approach, one to many matching are adopted between model variables and observations. Item Structural Shock denotes specification of stochastic process of shocks. SV is abbreviation of stochastic volatility.

Table 2: Calibrated Parameters and Key Steady States

Calibrated Param.	Description	Value	Source
β	Discount factor	0.995	Our setting
δ	Depreciation rate	0.025	Christensen and Dib (2008)
α	Capital share	0.33	Gertler and Kiyotaki (2010)
γSS	Survival rate of entrepreneur in steady state	0.972	Christensen and Dib (2008)
γSS	Survival rate of banker in steady state	0.972	Gertler and Kiyotaki (2010)
λ	Bank's participation constraint parameter	0.383	Gertler and Kiyotaki (2010)
ψw	Wage markup	0.05	Smets and Wouters (2003)
ε	Elasticity Substitution of intermediate goods	11	Our setting
ξE	New entrepreneur entry rate	0.003	Our setting
ξF	New banker entry rate	0.003	Gertler and Kiyotaki (2010)
Key Steady State	Description	Value
mcSS	Steady state marginal cost	ε−1	-
SS	Steady state external financial premium	1.0075	Christensen and Dib (2008)
rrSS	Steady state corp. borrowing rate (real, QPR)	1.0152	From data (1980Q1-2010Q2)
rrSS	Steady state bank lending rate (real, QPR, ex-premium)	rrSS/SS	-
rrSS	Steady state real interest	1/β	-
νSS	Steady state Nu	(1−γSS)β(rrSS−rrSS)	-
ηSS	Steady state Eta	(1/β−γSS)	-
LevSS	Steady state leverage ratio of banker	1−γSS	-
KSS/NSS	Steady state leverage ratio of entrepreneur	1.919	From data (1980Q1-2010Q2)
KSS/YSS	Steady state capital/output ratio	αmcSS	-
ISs/YSS	Steady state investment/output ratio	δKSS/YSS	-
GSS/YSS	Steady state government expenditure/output ratio	0.2	Gertler and Kiyotaki (2010)
CSS/YSS	Steady state consumption/output ratio	1−ISs/YSS−GSS/YSS	-
Table 3: Prior Settings of Structural Parameters

Structural Parameters

Parameter	Description	Density	Prior Mean	Prior SE
$ \kappa $	Investment adjustment cost	Gamma	1.000	0.500
h	Habit formation	Beta	0.500	0.250
$ \sigma^{C} $	IES of consumption	Gamma	1.500	0.500
$ \sigma^{L} $	Inverse Frisch elasticity of labor supply	Gamma	1.500	0.500
$ \varphi $	Elasticity of premium to leverage ratio	Inv. Gamma	0.050	4.000
$ \iota_{P} $	Price indexation	Beta	0.500	0.100
$ \iota_{W} $	Wage indexation	Beta	0.500	0.250
$ \theta_{P} $	Calvo parameter for goods pricing	Beta	0.500	0.250
$ \theta_{W} $	Calvo parameter for wage setting	Beta	0.500	0.250
$ \rho_{R} $	Moneatory policy persist. param.	Beta	0.500	0.250
$ \mu_{\pi} $	Taylor coefficient for inflation	Gamma	1.500	0.500
$ \mu_{Y} $	Taylor coefficient for output gap	Gamma	0.500	0.250
Persistence Parameters for Structural Shocks
Parameter	Description	Density	Prior Mean	Prior SE
$ \rho_{A} $	Persistent parameter for TFP shock	Beta	0.500	0.250
$ \rho_{C} $	Persistent parameter for preference shock	Beta	0.500	0.250
$ \rho_{K} $	Persistent parameter for investment tech. shock	Beta	0.500	0.250
$ \rho_{E} $	Persistent parameter for entrepreneur net worth shock	Beta	0.500	0.250
$ \rho_{F} $	Persistent parameter for banking sector net worth shock	Beta	0.500	0.250
$ \rho_{G} $	Persistent parameter for government expenditure shock	Beta	0.500	0.250
$ \rho_{L} $	Persistent parameter for labor supply shock	Beta	0.500	0.250
Standard Errors for Structural Shocks
Parameter	Description	Density	Prior Mean	Prior SE
$ e_{A} $	SE of TFP shock	Inv. Gamma	0.707	4.000
$ e_{C} $	SE of preference shock	Inv. Gamma	0.707	4.000
$ e_{E} $	SE of entrepreneur net worth shock	Inv. Gamma	0.707	4.000
$ e_{F} $	SE of banking sector net worth shock	Inv. Gamma	0.707	4.000
$ e_{G} $	SE of government expenditure shock	Inv. Gamma	0.707	4.000
$ e_{K} $	SE of investment specific technology shock	Inv. Gamma	1.000	4.000
$ e_{L} $	SE of labor supply shock	Inv. Gamma	0.707	4.000
$ e_{R} $	SE or monetary policy shock	Inv. Gamma	0.224	4.000
Table 4: Posterior Estimates of Key Structural Parameters

Parameters	Case A	Case B	Case C	Case D
Parameters for Financial Friction in Corporate Section
$ \kappa $	0.614[0.547, 0.689]	0.877[0.818, 0.938]	0.564[0.498, 0.632]	0.562[0.470, 0.661]
$ \varphi $	0.027[0.024, 0.030]	0.025[0.023, 0.026]	0.039[0.032, 0.045]	0.041[0.036, 0.046]
Parameters for Nominal Rigidities
$ \theta_{P} $	0.854[0.811, 0.895]	0.374[0.305, 0.440]	0.804[0.763, 0.846]	0.760[0.697, 0.822]
$ \theta_{W} $	0.589[0.531, 0.649]	0.428[0.351, 0.500]	0.623[0.544, 0.703]	0.516[0.452, 0.580]
Parameters for Monetary Policy Rule
$ \rho_{R} $	0.670[0.581, 0.758]	0.643[0.582, 0.707]	0.653[0.605, 0.698]	0.632[0.590, 0.675]
$ \mu_{\pi} $	2.805[2.767, 2.842]	2.820[2.790, 2.848]	2.989[2.979, 2.998]	2.986[2.977, 2.995]
$ \mu_{Y} $	0.006[0.000, 0.014]	0.010[0.000, 0.020]	0.006[0.000, 0.013]	0.008[0.000, 0.018]

Note: The parenthesis in the table indicates 90% credible interval of structural parameters. 300,000 iterations are implemented using algorithm of MH within Gibbs described in Section 4. We sample one draw out of every 10 replicates and discard first 10,000 samples. The remaining 20,000 samples are used for calculating moments of the posterior distributions.

Table 5: Timings of Peaks of the Financial Shocks

Structural Shock
Case A	Case B	Case C	Case D
Corp. Net Worth	2009Q1	2009Q1	2009Q2	2009Q2
Bank Net Worth	2008Q3	2008Q3	2008Q3	2008Q3
Stochastic Volatilities
Case A	Case B	Case C	Case D
Corp. Net Worth	-	-	2009Q2	2009Q2
Bank Net Worth	-	-	2009Q3	2009Q3