ESRI Discussion Paper Series No.313
Sources of the Great Recession:
A Bayesian Approach of a Data-Rich DSGE model with Time-Varying Volatility Shocks

Hirokuni Iiboshi
Professor, Department of Business Administration Graduate School of Social Sciences Tokyo Metropolitan University
Tatsuyoshi Matsumae
Research Fellow, Economic and Social Research Institute, Government of Japan
Shin-Ichi Nishiyama
Associate Professor, Graduate School of Economics and Management Tohoku University


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 data-rich 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 net-worth shock gradually spread before the corporate net worth shock burst ; (2) the data-rich 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 time-varying 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, Data-rich approach, Bayesian estimation, financial friction, stochastic volatility, leverage effect. JEL Classification: E32, E37, C32, C53.

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  2. page1
  3. page2
    1 Introduction
  4. page4
    2 Data Rich Approach with Stochastic Volatility Shocks
    1. page4
      2.1 Stochastic Volatility with Leverage in DSGE models
    2. page5
      2.2 Data Rich DSGE Models
      1. page5
        2.2.1 Significance of Data Rich DSGE models
      2. page6
        2.2.2 Dynamic Factor Model (DFM)
      3. page7
        2.2.3 Data-Rich DSGE Model
    3. page8
      2.3 Data Rich DSGE models with Stochastic Volatility
      1. page8
        2.3.1 Stochastic Volatility in a Data-Rich DSGE models
      2. page9
        2.3.2 Transformation into Estimated State Space Model
  5. page10
    3 The DSGE model with Two Financial Frictions in Corporate and Banking Sectors
    1. page10
      3.1 Financial Friction in Corporate Sector
      1. page10
        3.1.1 Entrance and Exit of Entrepreneurs
      2. page11
        3.1.2 Individual Entrepreneur’s Problem
      3. page12
        3.1.3 Debt Contract
      4. page12
        3.1.4 Aggregation
    2. page13
      3.2 Financial Friction in Banking Sector
      1. page13
        3.2.1 Entrance and Exit of Bankers
      2. page14
        3.2.2 Individual Banker’s Problem
      3. page15
        3.2.3 Aggregation
    3. page16
      3.3 Incorporation of the two Frictions within the DSGE model
  6. page17
    4 Method of Estimation
  7. page19
    5 Preliminary Settings and Data Description
    1. page19
      5.1 Specifications of Four Alternative Cases
    2. page20
      5.2 Calibrations and Priors of Parameters
    3. page20
      5.3 Data Description
  8. page22
    6 Empirical Results
    1. page22
      6.1 Key Structural Parameters
    2. page23
      6.2 Structural Shocks and their Volatilities
    3. page25
      6.3 Historical Decompositions
    4. page27
      6.4 Observations and Interpretation
  9. page28
    7 Conclusion
  10. page29
    A Appendix
    1. page29
      A.1 Sampling Stochastic Volatility with Leverage
      1. page29
        Step 1: Draw the structural shocks
      2. page29
        Step 2: Draw the stochastic volatilites
      3. page30
        Step 3: Draw the indicators of the mixture approximation
      4. page31
        Step 4: Draw the coefficients
    2. page31
      A.2 Simulation Smoother of Model Variable
      1. page31
        Step 1: Kalman filter for state space model is implemented.
      2. page32
        Step 2: Generate values
      3. page32
        Step 3: Smoothing of structural shocks
      4. page32
        Step 4: Generate model variables
    3. page32
      A.3 Sampling of Parameters Set
      1. page33
        Step 1. Sampling
      2. page34
        Step 2. Sampling
    4. page35
      A.4 The Remaining Framework of the DSGE model
      1. page35
        A.4.1 Household Sector
      2. page36
        A.4.2 Capital Production Sector
      3. page37
        A.4.3 Retailing Sector
      4. page37
        A.4.4 The Rest of the Economy
      5. page38
        A.4.5 Structural Shocks in the Model
  11. page38
  12. Data Appendix
    1. Table 1: Specifications of Four Alternative Cases
    2. Table 2: Calibrated Parameters and Key Steady States
    3. Table 3: Prior Settings of Structural Parameters
    4. Table 4: Posterior Estimates of Key Structural Parameters
    5. Table 5: Timings of Peaks of the Financial Shocks
    6. Table 6: Average Ranges of 90% Credible Interval of Structural Shocks over the entire sample peiods
    7. Table 7: Average Ranges of 90% Credible Interval of Stochastic Volatilities in the entire sample peiods
    8. Table 8: Leverage Effect of Structural Shocks: Correlation between the Sign of Shock and its Volatility
    9. Table 9: Posterior Estimates: Case A and Case B
    10. Table 10: Posterior Estimates: Case C and Case D
    11. Table 11: Posterior Estimates of Parameters of SVs: Case C and Case D
      1. (a) Case A (Blue)
      2. (b) Case B (Red)
    12. Figure 1: Structural Shocks with i.i.d. Normal in Cases A and B
      1. (a) Case C (Blue)
      2. (b) Case D
    13. Figure 2: Structural Shocks with SV in Cases C and D
      1. (a) Case C (Blue)
      2. (b) Case D (Red)
    14. Figure 3: Stochastic Volatilities of Structural Shocks in Cases C and D
      1. (a) Case A (b) Case B
      2. (c) Case C (d) Case D
    15. Figure 4: Historical Decomposition of Real GDP
      1. (a) Case A (b) Case B
      2. (c) Case C (d) Case D
    16. Figure 5: Historical Decomposition of Gross Private Domestic Investment
      1. (a) Case A (b) Case B
      2. (c) Case C (d) Case D
    17. Figure 6: Historical Decomposition of Moody’s Bond Index (Corporate Baa)
      1. (a) Case A (b) Case B
      2. (c) Case C (d) Case D
    18. Figure 7: Historical Decomposition of Commercial Bank Leverage Ratio
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