**4.1 Structural shocks and their volatilities**

In Cases A and B estimating standard data structure with the 11 observable variables, the posterior mean (deep blue solid lines) and a 90% credible band (a light blue shade) of the eight structural shocks with constant and time-varying volatilities are drawn in **Figure 4(a)** and **(b)**, respectively. And, **Figure 5(a)** and **(b)** show those of the data rich structure with the 40 observable variables, say Cases C and D, respectively. By comparing estimations of the eight structural shocks of different cases, we observe the following two points. First, although a couple of estimated shocks such as TFP and monetary policy shocks looks very similar among four cases, others, especially labor supply and government spending shocks, have different shapes among the four cases despite using the same DSGE model. Second, every structural shocks with stochastic volatilities (Case B and D) become more volatile in recessions, i.e., 1990:Q2 through 91:Q1, 2001:Q2 through 01:Q3, 2007:Q4 through 08:Q2, and more stable in remaining periods than their counterparts (Case A and C), without regard to data structure used.

Next we consider about financial and nonfinancial net-worth shocks affected on balance sheets on both sectors as shown in the second and third row of **Figures 4** and **5**, respectively. Firstly, we can see deep trough at 2008:Q3 in the banking net-worth shocks (the third row) of all cases in these fours figures. In fact, in September and October 2008, major financial institutions such as Lehman Brothers, Merrill Lynch, Fannie Mae, Freddie Mac, Washington Mutual, Wachovia, Citi group, and AIG either failed, were acquired under duress, or were subject to government takeover. On the other hand, the huge troughs of the corporate networth shock might not coincide in all cases, and seem to split to two different periods, 2009:Q1 in constant volatility cases (Cases A and C), and 2009:Q2 in stochastic volatilities cases (Cases B and D). However it is worthy of notice that in every case, the corporate net-worth shocks have arrived at deep troughs after the banking sector shocks have experienced its huge drop.

#### **Figure 4.**

*Structural shocks of standard data structure. (a) Constant volatility: Case A. (b) Stochastic volatility: Case B. Notes: Case A and Case B are described in Table 1. Eight shocks in our DSGE model are explained in Section 2. Corporate Net Worth shock and Bank Net Worth are balance sheet shocks of nonfinancial and financial sectors described in Figure 1(b). TFP (total factor productivity), investment specific technology, and labor shock are belong to supply shocks, whereas preference of consumers, monetary policy, and government spending shocks belong to demand shocks. The deep blue lines and blue shaded area are posterior mean and 90% credible interval of structural shocks in Cases A and B, respectively.*

In order to measure the accuracy of the eight estimated shocks, we calculate an average range of 90% credible interval across all of the sample period as **Figures 4** and **5**. When the average of 90% interval of a shock of one case become smaller than those of another case, then we can regard that the shock of the case is more precisely identified than another case. Although we leave out the explanation of detail values, averages of five shocks, say (1) preference, (2) banking net worth, (3) labor supply, (4) government spending, and (5) monetary policy, are less in stochastic volatilities cases, B and D, than constant volatilities cases, A and C. In Cases B and D, the averages in the former three shocks are around half against those in Cases A and C. Furthermore, average of government spending shocks downscales by one eighth to one tenth. From these results, we infer that the time-varying volatilities of shocks might be more fit to data generation process which we cannot

observe. In addition, we expect that the SV shocks are likely to match for a rapid change of uncertainty and volatilities at the turning points of the Great Recession,

*Structural shocks of data rich environment. (a) Constant volatility: Case C. (b) Stochastic volatility: Case D. Notes: Case C and Case D are described in Table 1. Eight shocks in our DSGE model are explained in Section 2. Corporate Net Worth shock and Bank Net Worth are balance sheet shocks of nonfinancial and financial sectors described in Figure 1(b). TFP (total factor productivity), investment specific technology, and labor shock are belong to supply shocks, whereas preference of consumers, monetary policy, and government spending shocks belong to demand shocks. The deep blue lines and blue shaded area are posterior mean and 90% credible*

**Figure 6** shows the posterior means (deep blue lines) and 90% interval (light blue shade area) of the SVs of all eight shocks for standard data structure (Cases B) and data rich structure (Case D), as well as the posterior means of constant volatilities of the shocks (red dashed flat lines) in Case A and C. As these graphs, in ordinary period, say before the recession, a large part of the deep blue lines (Cases B and D) is under the red dashed lines (Cases A and C). Smoothing SVs of the six

rather than the constant volatilities cases, as shown later.

*interval of structural shocks in Case C and D.*

*Source of the Great Recession*

*DOI: http://dx.doi.org/10.5772/intechopen.90729*

**Figure 5.**

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#### **Figure 5.**

In order to measure the accuracy of the eight estimated shocks, we calculate

*Structural shocks of standard data structure. (a) Constant volatility: Case A. (b) Stochastic volatility: Case B. Notes: Case A and Case B are described in Table 1. Eight shocks in our DSGE model are explained in Section 2. Corporate Net Worth shock and Bank Net Worth are balance sheet shocks of nonfinancial and financial sectors described in Figure 1(b). TFP (total factor productivity), investment specific technology, and labor shock are belong to supply shocks, whereas preference of consumers, monetary policy, and government spending shocks belong to demand shocks. The deep blue lines and blue shaded area are posterior mean and 90% credible*

an average range of 90% credible interval across all of the sample period as **Figures 4** and **5**. When the average of 90% interval of a shock of one case become smaller than those of another case, then we can regard that the shock of the case is more precisely identified than another case. Although we leave out the explanation of detail values, averages of five shocks, say (1) preference, (2) banking net worth, (3) labor supply, (4) government spending, and (5) monetary policy, are less in stochastic volatilities cases, B and D, than constant volatilities cases, A and C. In Cases B and D, the averages in the former three shocks are around half against those in Cases A and C. Furthermore, average of government spending shocks downscales by one eighth to one tenth. From these results, we infer that the time-varying volatilities of shocks might be more fit to data generation process which we cannot

*interval of structural shocks in Cases A and B, respectively.*

*Financial Crises - A Selection of Readings*

**Figure 4.**

**40**

*Structural shocks of data rich environment. (a) Constant volatility: Case C. (b) Stochastic volatility: Case D. Notes: Case C and Case D are described in Table 1. Eight shocks in our DSGE model are explained in Section 2. Corporate Net Worth shock and Bank Net Worth are balance sheet shocks of nonfinancial and financial sectors described in Figure 1(b). TFP (total factor productivity), investment specific technology, and labor shock are belong to supply shocks, whereas preference of consumers, monetary policy, and government spending shocks belong to demand shocks. The deep blue lines and blue shaded area are posterior mean and 90% credible interval of structural shocks in Case C and D.*

observe. In addition, we expect that the SV shocks are likely to match for a rapid change of uncertainty and volatilities at the turning points of the Great Recession, rather than the constant volatilities cases, as shown later.

**Figure 6** shows the posterior means (deep blue lines) and 90% interval (light blue shade area) of the SVs of all eight shocks for standard data structure (Cases B) and data rich structure (Case D), as well as the posterior means of constant volatilities of the shocks (red dashed flat lines) in Case A and C. As these graphs, in ordinary period, say before the recession, a large part of the deep blue lines (Cases B and D) is under the red dashed lines (Cases A and C). Smoothing SVs of the six

#### **Figure 6.**

*Stochastic volatilities of structural shocks. (a) Stochastic volatility: Case B. (b) Stochastic volatility data rich: Case D. Notes: Case B and Case D are described in Table 1. Eight shocks in our DSGE model are explained in Section 2. Corporate Net Worth shock and Bank Net Worth are balance sheet shocks of nonfinancial and financial sectors described in Figure 1(b). TFP (total factor productivity), investment specific technology, and labor shock are belong to supply shocks, whereas preference of consumers, monetary policy, and government spending shocks belong to demand shocks. The deep blue lines and blue shaded area are posterior mean and 90% credible interval of stochastic volatility (SV) of Cases B and D, respectively. The red dashed lines denote the posterior means of constant volatilities shocks estimated in Case A and C, respectively. SV shocks are explained in Section 3.*

specialized in US mortgage debt at this moment.), the SVs of net-worth shocks of financial and nonfinancial sectors have rapidly jumped to ceil for both of Case B and D, as well as other shocks such as TFP, monetary policy, IST and labor supply shocks. And levels of these SVs (deep blue lines) exceed the red dashed flat lines

*Historical decomposition of output. (a) Constant volatility Case A. (b) Stochastic volatility Case B. (c) Constant volatility data rich Case C. (d) Stochastic volatility data rich Case D. Notes: Four Cases A, B, C and D are described in Table 1. Case A; 11 observable variables and constant volatility shocks. Case B: 11 observable variables and structural shocks with SV. Case C: 40 observable variables and constant volatility shocks. Case D: 40 observable variables and structural shocks with SVs. Eight shocks are explained in Section 2*

In this study, we would like to verify whether the data-rich approach contributes

to the accuracy of the estimated SVs, compared with standard data structure. **Figures 4(b)** and **5(b)** show averages of the 90% interval (light shade area) in Cases B does not look different from those of Case D. And, although **Figure 6** reports difference in sizes of the 90% intervals (light shade area) of the SVs over the entire sample period between Cases B and D, we do not find obvious improvement of 90% band by the data-rich approach in Case D. From only the three figures, we cannot yet include the data-rich environment improve the accuracy of the SVs

indicating estimation of constant volatilities as **Figure 6**.

**Figure 7.**

**43**

*and SV shocks are explained in Section 3.*

*Source of the Great Recession*

*DOI: http://dx.doi.org/10.5772/intechopen.90729*

estimates. This inquiry will be remained until further research.

shocks, but investment-specific technology (IST) shock and the labor supply shocks, look very similar in Cases B and D. And the SVs of the preference and labor supply shocks fluctuate with large amplitude during the period of the expansion between 2001:Q4 and 2007:Q4, and it indicates that they have played an important role of boom. Meanwhile, the SVs of the remaining shocks seem to be quiet and level off between 1990:Q1 and 2007:Q3. After August 2007, when the Great Recession began with the seizure in the banking system (in fact, BNP Paribas precipitated ceasing investment activity and was followed by three big hedge funds that
