ESRI Discussion Paper Series No.313
Sources of the Great Recession：
A Bayesian Approach of a DataRich DSGE model with TimeVarying Volatility Shocks
Abstract
In order to investigate sources of the Great Recession (Dec. 2007 to Jun. 2009) of the US economy in the latter portion of the first decade of the 2000s, we modified the standard New Keynesian dynamic stochastic general equilibrium (DSGE) model by embedding financial frictions in both the banking and the corporate sectors. Furthermore, the structural shocks in the model are assumed to possess stochastic volatility (SV) with a leverage effect. Then, we estimated the model using a datarich estimation method and utilized up to 40 macroeconomic time series in the estimation. In light of a DSGE model, we suggest the following three empirical evidences in the Great Recession:(1) the negative bank networth shock gradually spread before the corporate net worth shock burst ; (2) the datarich approach and the structural shocks with SV found the contribution of the corporate net worth shock to a substantial portion of the macroeconomic fluctuations after the Great Recession, which is unlike the standard DSGE model; and (3) the Troubled Asset Relief Program (TARP) would work to bail out financial institutions, whereas balance sheets in the corporate sector would still not have stopped deteriorating. Incorporating timevarying volatilities of shocks into the DSGE model makes their credible bands narrower than half of the constant volatilities, which result implies that it is a realistic assumption based on the dynamics of the structural shocks. It is plausible that tiny volatilities (or uncertainty) in ordinary times change to an extraordinary magnitude at the turning points of business cycles. Keywords: New Keynesian DSGE model, Datarich approach, Bayesian estimation, financial friction, stochastic volatility, leverage effect. JEL Classification: E32, E37, C32, C53.
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page1Abstract

page21 Introduction

page42 Data Rich Approach with Stochastic Volatility Shocks

page42.1 Stochastic Volatility with Leverage in DSGE models

page52.2 Data Rich DSGE Models

page52.2.1 Significance of Data Rich DSGE models

page62.2.2 Dynamic Factor Model (DFM)

page72.2.3 DataRich DSGE Model


page82.3 Data Rich DSGE models with Stochastic Volatility

page82.3.1 Stochastic Volatility in a DataRich DSGE models

page92.3.2 Transformation into Estimated State Space Model



page103 The DSGE model with Two Financial Frictions in Corporate and Banking Sectors

page103.1 Financial Friction in Corporate Sector

page103.1.1 Entrance and Exit of Entrepreneurs

page113.1.2 Individual Entrepreneur’s Problem

page123.1.3 Debt Contract

page123.1.4 Aggregation


page133.2 Financial Friction in Banking Sector

page133.2.1 Entrance and Exit of Bankers

page143.2.2 Individual Banker’s Problem

page153.2.3 Aggregation


page163.3 Incorporation of the two Frictions within the DSGE model


page174 Method of Estimation

page195 Preliminary Settings and Data Description

page195.1 Specifications of Four Alternative Cases

page205.2 Calibrations and Priors of Parameters

page205.3 Data Description


page226 Empirical Results

page226.1 Key Structural Parameters

page236.2 Structural Shocks and their Volatilities

page256.3 Historical Decompositions

page276.4 Observations and Interpretation


page287 Conclusion

page29A Appendix

page29A.1 Sampling Stochastic Volatility with Leverage

page29Step 1: Draw the structural shocks

page29Step 2: Draw the stochastic volatilites

page30Step 3: Draw the indicators of the mixture approximation

page31Step 4: Draw the coefficients


page31A.2 Simulation Smoother of Model Variable

page31Step 1: Kalman filter for state space model is implemented.

page32Step 2: Generate values

page32Step 3: Smoothing of structural shocks

page32Step 4: Generate model variables


page32A.3 Sampling of Parameters Set

page33Step 1. Sampling

page34Step 2. Sampling


page35A.4 The Remaining Framework of the DSGE model

page35A.4.1 Household Sector

page36A.4.2 Capital Production Sector

page37A.4.3 Retailing Sector

page37A.4.4 The Rest of the Economy

page38A.4.5 Structural Shocks in the Model



page38References

Data Appendix

Table 1: Specifications of Four Alternative Cases

Table 2: Calibrated Parameters and Key Steady States

Table 3: Prior Settings of Structural Parameters

Table 4: Posterior Estimates of Key Structural Parameters

Table 5: Timings of Peaks of the Financial Shocks

Table 6: Average Ranges of 90% Credible Interval of Structural Shocks over the entire sample peiods

Table 7: Average Ranges of 90% Credible Interval of Stochastic Volatilities in the entire sample peiods

Table 8: Leverage Effect of Structural Shocks: Correlation between the Sign of Shock and its Volatility

Table 9: Posterior Estimates: Case A and Case B

Table 10: Posterior Estimates: Case C and Case D

Table 11: Posterior Estimates of Parameters of SVs: Case C and Case D

(a) Case A (Blue)

(b) Case B (Red)


Figure 1: Structural Shocks with i.i.d. Normal in Cases A and B

(a) Case C (Blue)

(b) Case D


Figure 2: Structural Shocks with SV in Cases C and D

(a) Case C (Blue)

(b) Case D (Red)


Figure 3: Stochastic Volatilities of Structural Shocks in Cases C and D

(a) Case A (b) Case B

(c) Case C (d) Case D


Figure 4: Historical Decomposition of Real GDP

(a) Case A (b) Case B

(c) Case C (d) Case D


Figure 5: Historical Decomposition of Gross Private Domestic Investment

(a) Case A (b) Case B

(c) Case C (d) Case D


Figure 6: Historical Decomposition of Moody’s Bond Index (Corporate Baa)

(a) Case A (b) Case B

(c) Case C (d) Case D


Figure 7: Historical Decomposition of Commercial Bank Leverage Ratio
