**2. Model**

the point of view of a DSGE model. In fact, according to Ireland [4], there are three sets of considerations that are premature for existing DSGE models. First, failures of financial institutions and liquidity drain should be endogenously described with other fundamental macroeconomic variables for producing economic insights. Second, most recessions have been associated with a rise in bankruptcies among banking and corporate sectors alike. And recessions have featured systematic problems in the banking and loan industry. And third, declines in housing prices and problems in the credit markets might have played an independent and causal role in the Great Recession's severity. Our study challenges to struggle with the former two exercises of Ireland [4], by identifying two different unobservable net-worth shocks of both banking and corporate sectors in a medium scale NK-DSGE model, into which two different financial frictions are newly embedded. And, we estimate time-varying volatility of these structural shocks in order to examine rapid changes of uncertainty and risk for financial crisis across financial markets and the economy

As advanced econometric tool, we adopt a data-rich environment to estimate a NK DSGE model following Smets and Wouters [5, 6] but adding above two financial frictions for the US economy. The advantage of incorporating a data-rich environment into a NK DSGE model is that we can more robustly identify two different net-worth shocks generated by two financial frictions because of decomposing comovements of model variables and idiosyncrasy of measurement errors from observable variables of big macroeconomic panel dataset. And this advantage is also useful to estimate a time-varying stochastic volatilities (SVs) of the structural shocks including financial shocks in the DSGE model and to estimate contributions of financial frictions on the real economy both during the Great Recession and after it, because this framework allows the structural shocks to relax

By adopting the data-rich environment and SV shocks, we will consider four alternative cases, based on the number of observation variables (11 vs. 40 observable variables) and the specification of the volatilities of the structural shocks (constant volatility vs. time-varying volatility). By comparing the four cases, we report the following three findings of empirical evidence in the Great Recession: (1) the net-worth shock of financial institution had gradually declined prior to a huge decrease of net-worth of corporate sector. (2) The net worth shock of nonfinancial firms played an important role during the Great Recession and after it, in terms of the data-rich NK DSGE model with the SV of structural shocks, unlike the standard NK DSGE model. (3) The Troubled Asset Relief Program (TARP) would have immediately worked to improve balance sheets of financial institutions, although it would not have stopped worsening those of the corporate sector for a while. These findings suggest that it is effective to strengthen the regulation, supervision and risk management of banks for preventing financial crisis. And they seem to support the Basel III framework developed by the Basel Committee in response to the global

As describing our estimation results, introducing structural SV shocks to a DSGE model has their credible interval narrower than half of the model with constant volatilities that indicates a realistic assumption of the time-varying structural shocks. And it is plausible that the uncertainty is trivial in ordinary times but it

The chapter is organized as follows. Section 2 illustrates two financial frictions of the New Keynesian model. Section 3 presents the estimation technique and data description. Sections 4 and 5 discuss the estimation results and interpretation of the Great Recession in terms of the New Keynesian model. Section 6 concludes

becomes to a huge size at the turning points of recessions.

as a whole.

the specifications thanks to big dataset.

*Financial Crises - A Selection of Readings*

financial crisis of 2007–2009.

the paper.

**34**

We adopt the stylized DSGE model, often referred to as the medium-scale New Keynesian (NK) model, following Christiano et al. [7] and Smets and Wouters [5, 6], which focused on the nominal rigidities of price level and wage as well as the quadratic adjustment cost of investment and habit formation of consumption as blue arrows shown in **Figure 1(a)**. In this NK model, it is generally assumed that

#### **Figure 1.**

*Our NK model. (a) Flowchart of economy. (b) Two financial frictions. Notes: Panel (a) shows the mediumscale NK model, following Christiano et al. [7] and Smets and Wouters [5, 6], which assume the nominal rigidities of price level and wage as well as the quadratic adjustment cost of investment and habit formation of consumption. Panel (b) shows two financial frictions in which the spread between lending rate R<sup>E</sup> <sup>t</sup> and deposit rate Rt is divided into two portions by introducing the risk-adjusted return for banks R<sup>F</sup> <sup>t</sup> in between, and which are modeled to reflect the two different relationship between the balance sheets of the corporate and banking sectors and the borrowers' agency costs against the lenders, respectively.*

there are six structural shocks, i.e., (1) preference shock, (2) labor supply shock in households, (3) total factor productivity (TFP) shock, (4) investment-specific technology shock in production function, (5) monetary policy shock and (6) government spending shock in the policy and government sectors.

log *σ*<sup>2</sup>

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

a vector of structural shocks. *σ*<sup>2</sup>

*Source of the Great Recession*

shown in **Figure 2**.

**Figure 2.**

*one matching relation between them.*

Matching between Model Variables and Obs.

*volatilities, respectively.*

*Setting of four cases.*

**Table 1.**

**37**

Types of econometrics framework Standard

*belongs to is described in the second column of the table.*

*of this table, while 40 observations of Cases C and D are all of the table including remains.*

**3.2 Setting of four cases**

*<sup>t</sup>* <sup>¼</sup> <sup>μ</sup> <sup>þ</sup> <sup>ϕ</sup> log *<sup>σ</sup>*<sup>2</sup>

where *Xt* and *St* are vectors of observable and model variables, respectively. *ε<sup>t</sup>* is

process such as the third equation, say the SV model. In the framework of the datarich environment, we make one to many matching relation between *St* and *Xt*, whereas a standard DSGE model takes one to one matching between them, as

Based on above econometric framework, we consider four *alternati*ve cases

vs. time-varying volatility) and on the number of observation variables, *Xt*, (11 vs. 40 observable variables) as summarized in **Table 1**. The first case (referred to as **Case A**) dealt with one of the standard DSGE models that used 11 observable variables in the measurement equation and the structural shocks with i.i.d. Normal distribution in the transition equation. The second case (**Case B**) was extended to SV shocks from Case A. The third case (**Case C**) extends to the data-rich approach

*Data-rich approach. Notes: In the data-rich environment (right panel), we make one to many matching relation between model variables and observations. And in a standard DSGE model (left panel), we take one to*

DSGE

Num. of Obs. **11 11 40 40**

Types of Struct. Shocks iid normal SV iid normal SV *Notes: The second row denotes types of econometrics framework as shown in Figure 2. The third and fourth rows stand for number of observations for estimation and relation between model variables and observations, respectively. The fifth row represents type of distribution of independent structural shocks. Abbreviation "iid" and "SV" denotes identical and independent distribution and stochastic*

*For the third row, contents of the observations are described in table of Appendix. 11 observations of Cases A and B are in the first 11 rows*

*For the forth row, "1 to 4" denotes matching one model variables with four observations. A model variable which each observation*

**Case A Case B Case C Case D**

**1 to 1 1 to 1 1 to 4 1 to 4**

Data-rich DSGE

Data-rich DSGE

Standard DSGE

based on the specification of the volatilities of the structural shocks, *σ*<sup>2</sup>

*<sup>t</sup>*�<sup>1</sup> <sup>þ</sup> *<sup>η</sup>t*, *<sup>η</sup>t*∽*N*ð Þ 0, 1 , (3)

*<sup>t</sup>* , (constant

*<sup>t</sup>* is time-varying variance following autoregressive

And, shown as two red arrows in **Figure 1(a)**, we additionally incorporate two different financial frictions in our NK model, since banks have two roles in generating two agency costs with asymmetric information between borrowers and lenders. One is as the lenders to the corporate sector and the other is as the borrowers from depositors. These two financial frictions are designed to reflect the two different relationship between the balance sheets of the corporate and banking sectors and the borrowers' agency costs against the lenders, respectively. The former friction between the bank and the corporate sectors was developed by Bernanke et al. [8], and estimated by Christensen and Dib [9] and Christiano et al. [10]. The latter friction between banks and depositors was proposed by Gertler and Karadi [11] and Gertler and Kiyotaki [12]. Recently, comparisons of both frictions have been studied by Villa [13] and Rannenberg [14] etc. Brumermeier et al. [15] summarized the recent development of these financial friction models of macroeconomics.

In our NK model with the financial frictions, the spread between lending rate RE t and deposit rate Rt is divided into two portions by introducing the risk-adjusted return for banks R<sup>F</sup> <sup>t</sup> in between, as shown in **Figure 1(b)**. The positive corporate net-worth shock shrinks the difference between R<sup>E</sup> <sup>t</sup> and R<sup>F</sup> <sup>t</sup> by enlarging the liability of the corporate sector, while the positive bank's net-worth shock shortens the difference between R<sup>F</sup> <sup>t</sup> and Rt by expanding the liability of the bank sector. Most of DSGE studies adopt independent assumptions of structural shocks, since they are set up originally but not accessional from others and the relaxation of this assumption is involved in difficulty to identify shocks. Following them, it is plausible to assume that these two shocks are independent from one other, since our purpose is to identify different impacts of balance sheet channels of financial and nonfinancial firms on the recessions by measuring sizes of the both financial frictions through the both net-worth shocks of the balance sheets in the these firms.

Decomposing the effects of the two financial frictions on macroeconomic fluctuations might be important for finding out the origin of the Great Recession as well as measuring the degree of damage to the US economy. More detail explanation of this model is described in Iiboshi et al. [16].

## **3. Estimation methods and data**

#### **3.1 Econometric methods**

To estimate our NK DSGE model, we adopt two econometric approaches. One is the data-rich approach proposed by Boivin and Giannoni [17], whose method followed by Shorfheide et al. [18], Nishiyama et al. [19] and Iiboshi et al. [20]. The other is to incorporate SV structural shocks in the DSGE model that was proposed by Justiniano and Primiceri [21]. They focused on the Great Moderation using a NK DSGE model with structural shocks with SV framework.

This econometric framework such as the data-rich approach with SV structural shocks can be described as

$$X\_t = \Lambda \mathbb{S}\_t + \mathbf{e}\_t,\tag{1}$$

$$\mathbf{S}\_{t} = \Gamma(\boldsymbol{\Theta})\mathbf{S}\_{t-1} + \boldsymbol{\varepsilon}\_{t}, \quad \boldsymbol{\varepsilon}\_{t} \sim \mathcal{N}(\mathbf{0}, \sigma\_{\ \ \boldsymbol{\varepsilon}}^{2}), \tag{2}$$

*Source of the Great Recession DOI: http://dx.doi.org/10.5772/intechopen.90729*

$$
\log \sigma\_t^2 = \mu + \phi \log \sigma\_{t-1}^2 + \eta\_t, \quad \eta\_t \sim N(0, 1), \tag{3}
$$

where *Xt* and *St* are vectors of observable and model variables, respectively. *ε<sup>t</sup>* is a vector of structural shocks. *σ*<sup>2</sup> *<sup>t</sup>* is time-varying variance following autoregressive process such as the third equation, say the SV model. In the framework of the datarich environment, we make one to many matching relation between *St* and *Xt*, whereas a standard DSGE model takes one to one matching between them, as shown in **Figure 2**.

#### **3.2 Setting of four cases**

there are six structural shocks, i.e., (1) preference shock, (2) labor supply shock in households, (3) total factor productivity (TFP) shock, (4) investment-specific technology shock in production function, (5) monetary policy shock and (6) gov-

And, shown as two red arrows in **Figure 1(a)**, we additionally incorporate two different financial frictions in our NK model, since banks have two roles in generating two agency costs with asymmetric information between borrowers and lenders. One is as the lenders to the corporate sector and the other is as the borrowers from depositors. These two financial frictions are designed to reflect the two different relationship between the balance sheets of the corporate and banking sectors and the borrowers' agency costs against the lenders, respectively. The former friction

between the bank and the corporate sectors was developed by Bernanke et al. [8], and estimated by Christensen and Dib [9] and Christiano et al. [10]. The latter friction between banks and depositors was proposed by Gertler and Karadi [11] and Gertler and Kiyotaki [12]. Recently, comparisons of both frictions have been studied by Villa [13] and Rannenberg [14] etc. Brumermeier et al. [15] summarized the recent devel-

In our NK model with the financial frictions, the spread between lending rate RE

<sup>t</sup> in between, as shown in **Figure 1(b)**. The positive corporate

<sup>t</sup> and R<sup>F</sup>

<sup>t</sup> and Rt by expanding the liability of the bank sector. Most of

and deposit rate Rt is divided into two portions by introducing the risk-adjusted

of the corporate sector, while the positive bank's net-worth shock shortens the

DSGE studies adopt independent assumptions of structural shocks, since they are set up originally but not accessional from others and the relaxation of this assumption is involved in difficulty to identify shocks. Following them, it is plausible to assume that these two shocks are independent from one other, since our purpose is to identify different impacts of balance sheet channels of financial and nonfinancial firms on the recessions by measuring sizes of the both financial frictions through

Decomposing the effects of the two financial frictions on macroeconomic fluctuations might be important for finding out the origin of the Great Recession as well as measuring the degree of damage to the US economy. More detail explanation of

To estimate our NK DSGE model, we adopt two econometric approaches. One is

This econometric framework such as the data-rich approach with SV structural

*St* <sup>¼</sup> Γ θð Þ*St*�<sup>1</sup> <sup>þ</sup> *<sup>ε</sup>t*, *<sup>ε</sup><sup>t</sup>* � *<sup>N</sup>* 0, *<sup>σ</sup>*<sup>2</sup>

*Xt* ¼ Λ*St* þ *et*, (1)

*t*

, (2)

the data-rich approach proposed by Boivin and Giannoni [17], whose method followed by Shorfheide et al. [18], Nishiyama et al. [19] and Iiboshi et al. [20]. The other is to incorporate SV structural shocks in the DSGE model that was proposed by Justiniano and Primiceri [21]. They focused on the Great Moderation using a NK

DSGE model with structural shocks with SV framework.

t

<sup>t</sup> by enlarging the liability

ernment spending shock in the policy and government sectors.

*Financial Crises - A Selection of Readings*

opment of these financial friction models of macroeconomics.

the both net-worth shocks of the balance sheets in the these firms.

net-worth shock shrinks the difference between R<sup>E</sup>

this model is described in Iiboshi et al. [16].

**3. Estimation methods and data**

**3.1 Econometric methods**

shocks can be described as

**36**

return for banks R<sup>F</sup>

difference between R<sup>F</sup>

Based on above econometric framework, we consider four *alternati*ve cases based on the specification of the volatilities of the structural shocks, *σ*<sup>2</sup> *<sup>t</sup>* , (constant vs. time-varying volatility) and on the number of observation variables, *Xt*, (11 vs. 40 observable variables) as summarized in **Table 1**. The first case (referred to as **Case A**) dealt with one of the standard DSGE models that used 11 observable variables in the measurement equation and the structural shocks with i.i.d. Normal distribution in the transition equation. The second case (**Case B**) was extended to SV shocks from Case A. The third case (**Case C**) extends to the data-rich approach

#### **Figure 2.**

*Data-rich approach. Notes: In the data-rich environment (right panel), we make one to many matching relation between model variables and observations. And in a standard DSGE model (left panel), we take one to one matching relation between them.*


*Notes: The second row denotes types of econometrics framework as shown in Figure 2. The third and fourth rows stand for number of observations for estimation and relation between model variables and observations, respectively. The fifth row represents type of distribution of independent structural shocks. Abbreviation "iid" and "SV" denotes identical and independent distribution and stochastic volatilities, respectively.*

*For the third row, contents of the observations are described in table of Appendix. 11 observations of Cases A and B are in the first 11 rows of this table, while 40 observations of Cases C and D are all of the table including remains.*

*For the forth row, "1 to 4" denotes matching one model variables with four observations. A model variable which each observation belongs to is described in the second column of the table.*

#### **Table 1.** *Setting of four cases.*

with i.i.d shocks, including 40 observable variables, which indicate more or less four observable variables corresponding to one specified model variable. And the fourth case (**Case D**) extends to the data-rich approach with SV shocks from Case C.

To measure the external finance premium, we employed the charge-off rates for all

In Cases C and D, to activate the data rich environment, we populate an additional 29 series composed of 18 series of key macroeconomics and 11 series of the banking sector into the existing 11 series in Cases A and B. In **Figure 3(a)**, three different loan charge-off rates based on different institutions are selected as external finance premium. And Panel (c), we take the inverse of the commonly-used ratio, i.e., bank asset over bank equity as the leverage ratio. As shown in this figure, we can find comovements of 11 observations among four kinds of model variables related to the banking sector. In the data rich framework, these comovements are made full use as the model variables, and idiosyncrasy of an observation apart from

Before discussing and remaking the source of Great Recession, we firstly report estimation results, especially focusing on estimations of eight structural shocks by smoothing technique and historical decompositions of four key model variables, (a) output, (b) investment, (c) bank leverage ratio, and (d) borrowing rate, based on the four cases. Those estimations must be significant clue for figuring it out.

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

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

banks' credits and issuer loans, measured as an annualized percentage of uncollectible loans. The two leverage ratios were calculated as their total asset

its comovement is turned out as its measurement error in a DSGE model.

divided by their net worth, respectively.

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

*Source of the Great Recession*

**4.1 Structural shocks and their volatilities**

A and C), without regard to data structure used.

banking sector shocks have experienced its huge drop.

**39**

**4. Empirical results**

#### **3.3 Data description**

By adopting the data-rich approach, we can adopt a relatively large and quarterly panel dataset with 40 observable variables. (More detail explanation of the observations is in the section, Appendix, in the end of the chapter.) In order to focus on the period of Great Moderation after 1984, we estimate between 1985:Q2 and 2012:Q2 including the Great Recession (Dec. 2007–Jun. 2009) and after it, since avoiding the period of the instable monetary policy regime, especially around the end of the 1970s and the early 1980s, say Hyper Inflation, directed by chairmen of the FRB, P. Volcker and A. Greenspan.

The contents of 40 observations are described in **Appendix** in the end of this chapter. Here, we mention about how to assort them based on the four cases. In Cases A and B, we looked at the following 11 series: (1) output, (2) consumption, (3) investment, (4) inflation, (5) real wage, (6) labor input, (7) the nominal interest rate, (8) the nominal corporate borrowing rate, (9) the external finance premium, (10) the corporate leverage ratio, and (11) the bank leverage ratio. The first seven series are following Smets and Wouters [5, 6]. The four remaining financial observable variables were selected for matching the model variables corresponding to the two financial frictions. The entrepreneur's nominal borrowing rate is the yield on Moody's Baa-rated corporate bonds detrended by the Hodrick-Prescott filter.

#### **Figure 3.**

*Observed financial data for identifying two financial shocks. (a) External finance premium. (b) Corporate leverage ratio. (c) Bank leverage ratio. (d) Borrowing rate. Notes: Four panels show 11 series involved in both the financial and nonfinancial sectors corresponding to the four model variables of the two financial frictions, respectively. These observations are used to identify the two financial shocks. For more detail description, see Appendix in the end of chapter.*

#### *Source of the Great Recession DOI: http://dx.doi.org/10.5772/intechopen.90729*

To measure the external finance premium, we employed the charge-off rates for all banks' credits and issuer loans, measured as an annualized percentage of uncollectible loans. The two leverage ratios were calculated as their total asset divided by their net worth, respectively.

In Cases C and D, to activate the data rich environment, we populate an additional 29 series composed of 18 series of key macroeconomics and 11 series of the banking sector into the existing 11 series in Cases A and B. In **Figure 3(a)**, three different loan charge-off rates based on different institutions are selected as external finance premium. And Panel (c), we take the inverse of the commonly-used ratio, i.e., bank asset over bank equity as the leverage ratio. As shown in this figure, we can find comovements of 11 observations among four kinds of model variables related to the banking sector. In the data rich framework, these comovements are made full use as the model variables, and idiosyncrasy of an observation apart from its comovement is turned out as its measurement error in a DSGE model.
