Federal Reserve Bank of Dallas
Globalization and Monetary Policy InstituteWorking Paper No. 220
http://www.dallasfed.org/assets/documents/institute/wpapers/2014/0220.pdf

Japan’s Financial Crises and Lost Decades *Naohisa Hirakata
Bank of Japan
Nao SudoBank of Japan
Ikuo Takei
Bank of Japan
Kozo Ueda
Waseda University
December 2014
Abstract
In this paper we explore the role of financial intermediation malfunction in macroeconomic
fluctuations in Japan. To this end we estimate, using Japanese data, a financial accelerator
model in which the balance sheet conditions of entrepreneurs in a goods-producing sector
and those of a financial intermediary affect macroeconomic activity. We find that shocks tothe balance sheets of the two sectors have been quantitatively playing important role inmacroeconomic fluctuations by affecting lending rates and aggregate investments. Their
impacts are prominent in particular during financial crises. Shocks to the entrepreneurs
balance sheets have played a key role in lowering investment in the bubble burst during theearly 1990s and in the global financial crisis during the late 2000s. Shocks to the financial
intermediaries balance sheets have persistently lowered investment throughout the 1990s.
JEL codes: E31, E44, E52*

Naohisa Hirakata, Director, Financial System and Bank Examination Department, Bank of Japan. 2-1-1
Nihonbashi-Hongokucho Chuo-ku, Tokyo 103-8660 Japan. naohisa.hirakata@boj.or.jp. Nao Sudo,
Director, Financial System and Bank Examination Department, Bank of Japan 2-1-1 NihonbashiHongokucho Chuo-ku, Tokyo 103-8660 Japan. nao.sudou@boj.or.jp. Ikuo Takei, Financial System andBank Examination Department, Bank of Japan, 2-1-1 Nihonbashi-Hongokucho Chuo-ku, Tokyo 103-8660
Japan. Ikuo.takei@boj.or.jp. Kozo Ueda, Waseda University, 1-6-1 Nishiwaseda Shinjuku-ku, Tokyo 1698050, Japan. kozo.ueda@waseda.jp. The authors would like to thank Kosuke Aoki, Hitoshi Mio, Masashi
Saito, Tsutomu Watanabe, the participants at SWET and the staff of the Bank of Japan for their usefulcomments. The views in this paper are those of the authors and do not necessarily reflect the views of the
Bank of Japan, the Federal Reserve Bank of Dallas or the Federal Reserve System.

1

Introduction

Over the last twenty years, the Japanese economy has witnessed three large …nancial
crises. The …rst crisis is the burst of the asset price bubble in February 1991 followed
by a prolonged economic contraction. Stock and land prices that rose steadily from themid-1980s plummeted at that time. These developments in asset prices have not only
weakened aggregate demand through a negative wealth e¤ect but also hampered …nancial
intermediation functions as …rms used land as collateral for business loans and banks helda large amount of stock, leading to a further decline of macroeconomic activity (Bayoumi,2001).1 The second crisis emerged as a series of collapses of …nancial institutions during
the late 1990s. The crisis started with interbank market turmoil triggered by the default
of Sanyo Securities in November 1997 and resulted in collapses of large banks and security
companies such as Hokkaido Takushoku Bank and Yamaichi Securities. In most cases,
these defaulting …nancial institutions had over the years failed to improve their balance
sheets that had been impaired due to excessive investment in real estate or stocks during
the bubble boom period. The third crisis is the spillover e¤ect of the global recession in
the United States following the global …nancial market turmoil since the summer of 2007.
Though the crisis itself mainly originated from malfunctions of …nancial institutions in
the United States and Europe, its impact was propagated to Japan’s economy throughtrade relationship. The annual GDP growth rate in Japan in 2009 was -5.5 percent due
to the severe decline in real exports by 26.2 percent.
Despite the crisis episodes, there has been no agreement regarding how important…nancial intermediation has been to macroeconomic ‡uctuations in Japan. A pioneering
work by Hayashi and Prescott (2002), based on a simple growth model, showed thatmovements of total factor productivity (hereafter TFP), which are regarded as exogenous changes in the technology level in their model, explains the bulk of output decline
from the early 1990s onward.2 Braun and Shioji (2007) obtained a similar result based a
growth model in which two classes of technology, investment-speci…c technology and TFP,
drive macroeconomic ‡uctuations in Japan. From the perspective of a New Keynesianframework, Sugo and Ueda (2008) estimate a model that is close to the model of Smets
and Wouters (2005) using Japanese data and show that TFP shocks and investment adjustment cost shocks are the two important shocks that account for output ‡uctuationsin Japan. In contrast to these studies, several studies emphasize the importance of …nancial factors in accounting for macroeconomic ‡uctuations in Japan. Bayoumi (2001),
based on the vector autoregression model, argues that the failure of …nancial intermediation is the major explanation for economic stagnation during the 1990s. Hirose and1

Kwon (1998) argues that a fall in land prices caused by the contractionary monetary policy leads
to an economic downturn through the collateral e¤ect.
2
While Hayashi and Prescott (2002) argue that non-…nancial factor is important in explaining mostof the output growth slowdown during the lost decade, they admit that for 1996–1998, the performanceof the banking sector has played an exceptionally important role in economic activity in Japan.

2

Kurozumi (2010) estimate a New Keynesian model with investment-speci…c technology
shocks and show that investment-speci…c technology shocks have played a quantitatively
important role in investment ‡uctuations in Japan. They also argue that investmentspeci…c technology is related to the function of …nancial intermediation because the timeseries of estimated investment-speci…c technology shocks moves together with that of…rms’…nancial position index that is released from the Bank of Japan.3
In the present paper, we quantitatively study the roles of …nancial intermediation malfunction as well as technology growth slowdown in macroeconomic ‡uctuations in Japan.
To do this, we estimate a dynamic stochastic general equilibrium model developed by
Hirakata, Sudo, and Ueda (hereafter HSU, 2011) using Japanese data from the 1980s
to the 2010s. The model is built on a …nancial accelerator model of Bernanke, Gertler,
and Gilchrist (1999, hereafter BGG). It explicitly incorporates credit-constrained …nancial intermediaries (hereafter FIs) and credit-constrained entrepreneurs, both of whichraise external funds by making credit contracts. In the model, …nancial shocks, suchas an unexpected net worth shocks to FIs, a¤ect aggregate investment by changing thefunctioning of …nancial intermediation and by a¤ecting funding expenses that serve for
production inputs. By estimating the model using U.S. data, HSU (2011) show thata sizable portion of macroeconomic ‡uctuation in the United States is attributed to …nancial shocks that are shocks to net worth in the FI sector and the goods producing
sector.
By estimating the parameters of the HSU (2011) model using Japanese data, we
disentangle macroeconomic ‡uctuations in Japan into those that are attributed to …nancial shocks and those that are attributed to non-…nancial shocks including technology
shocks and preference shocks. Our data sample is from the 1980s to the 2010s, which
covers three …nancial crises. We extract time series of various types of shocks from thedata, including net worth shocks of FIs and entrepreneurs as well as TFP shocks, andinvestment adjustment cost shocks. We then study how and when net worth shocks have
hampered …nancial intermediation and dampened key macroeconomic variables, such as
GDP and investment.
We …nd that net worth shocks to FIs and entrepreneurs have been playing a quantitatively important role in macroeconomic ‡uctuations. These shocks impair the balance
sheets of these two sectors, increase the external …nance premium, and dampen aggregate
investment. Their impacts on investment are prominent particularly during the three…nancial crises. Net worth shocks to entrepreneurs have played the key role in lowering
investment during the periods of the bubble burst and the global …nancial crisis. Net
worth shocks to FIs have contributed to investment decline in the early 1990s and persistently lowered investment throughout the 1990s. It is important to note, however,that contribution of these two shocks is not the largest shocks among structural shocks
3

One other strand of literature includes Caballero, Hoshi, and Kashyap (2008). They consider thee¤ect of malfunction of the …nancial intermediary sector on the economy, in particular on productivity,
through zombie lending.

3

in accounting for investment and other macroeconomic variables. TFP shocks and investment adjustment cost shocks play a quantitatively larger role than these …nancial
shocks. Our result is therefore consistent with studies that stress the role of non-…nancial
factors such as Hayashi and Prescott (2006) and Ueda and Sugo (2008) though it is notinconsistent with studies that stress the role of …nancial factors such as Bayoumi (2001)
and Hirose and Kurozumi (2010).
In addition, we explore how investment adjustment cost shocks are related to net
worth shocks estimated in our model. As discussed by Justiniano, Primiceri, and Tambalotti (2008), the estimates of the New Keynesian model typically indicate that shocks
to investment adjustment cost play an important role in producing business cycles. Hirose and Kurozumi (2010) by estimating a New Keynesian model using Japanese dataalso document that most of the Japanese investment variations are accounted for bythese shocks. These shocks are considered to be related to the e¢ ciency of …nancial intermediation in Hirose and Kurozumi (2008) and Justiniano, Primiceri, and Tambalotti(2011). To see how investment adjustment cost shocks are related to …nancial factors,
we estimate alternative models that abstract from …nancial frictions and compare quantitative roles of estimated investment adjustment cost shocks in these models with thosein our baseline model. We …nd that quantitative impacts of the shocks to investment
adjustment cost are reduced when credit frictions are explicitly incorporated into themodel. Our results suggest that some portion of investment adjustment cost shocks estimated in Hirose and Kurozumi (2008) and Justiniano, Primiceri, and Tambalotti (2011)
may re‡ect shocks to …nancial intermediation.
The remainder of our paper is organized as follows. In Section 2, we brie‡y describe
the model. In Section 3, we explain the estimation procedure. In Section 4, we report
the estimation results. Section 5 contains discussion about our outcomes and comparison
with other existing works. Section 6 concludes.

2

The Model

Our model setting is the same as that used in HSU (2011). The economy consists of acredit market, a goods market, and ten types of agents: investors, FIs, entrepreneurs,a household, …nal goods producers, retailers, wholesalers, capital goods producers, thegovernment, and the monetary authority. The goods market is a standard one and theunique feature of the model comes from the credit market. In particular, the net worthsof FIs together with those of entrepreneurs play key roles in macroeconomic ‡uctuations
by a¤ecting the cost of external …nance that is realized in the credit market.
Since our settings for credit contracts are the same as those in HSU (2011), we do
not explain them in detail in the main text. Instead, we describe them in Appendix A.
We also describe the equilibrium conditions of our model in Appendix B.

4

2.1

The Credit Market

Overview of the two types of credit contracts
In each period, entrepreneurs conduct projects with size Q (st ) K (st ) ; where Q (st )is the price of capital and K (st ) is capital. Entrepreneurs own net worth, N E (st ) <Q (st ) K (st ) ; and borrow funds, Q (st ) K (st ) N E (st ) ; from the FIs through credit
contracts, which we call the FE contracts. The FIs also own net worth, N F (st ) <Q (st ) K (st ) N E (st ) ; and borrow funds, Q (st ) K (st ) N F (st ) N E (st ) ; from investors
through credit contracts which we call the IF contracts. In both credit contracts, agency
problems arise from asymmetric information between borrower and lender. Borrowersof the FE and IF contracts, which are the entrepreneurs and the FIs, are subject toidiosyncratic productivity shocks, which we denote by ! E (st+1 ) and ! F (st+1 ) : Lendersof the contracts, which are the FIs and investors, cannot observe the realizations ofthese shocks without paying monitoring costs. Under this setting, similar to credit
contracts in BGG (1999), both the FE and IF contracts are formulated as one-period debt
contracts with costly state veri…cation. That is, in these contracts, there are cuto¤ values
for the realization of idiosyncratic productivity shocks, which we denote as ! E (st+1 )and ! F (st+1 ), such that borrowers declare defaults when the realization of idiosyncratic
productivity shocks ! E (st+1 ) and ! F (st+1 ) are smaller than the cuto¤ values ! E (st )and ! F (st ) and repay interest rates Z E (st+1 ) and Z F (st+1 ) otherwise. When borrowersof credit contracts default, lenders take all of the earnings of the defaulting borrowers.
The FIs are monopolistic suppliers of external funds to entrepreneurs. Taking thecredit market imperfections described above as given, the FIs choose clauses of the twocredit contracts, including cuto¤ values ! E (st ) and ! F (st ), so as to maximize their
expected pro…ts. The detail of the FIs’maximization problem is shown in Appendix A.
As a result of the FIs’pro…t maximization, for a given riskless rate of the economy
R (st ) ; the external …nance premium Et RE (st+1 ) =R (st ) is expressed byinverse of the share of pro…t going to the investors in the IF contractz

Et RE (st+1 )=R (st )}|N E (st )N (s );Q (st ) K (st ) Q (st ) K (st )
F

F

!

F

t

{
1

inverse of the share of pro…t going to the FIs in the FE contract

z

E

!

E

}|
N E (st )Q (st ) K (st ){1ratio of the debt to the size of the capital investmentz}|
N F (st )1
Q (st ) K (st )F n F s t ; nE s t ;with5

N E (st )Q (st ) K (st ){(1)expected return from defaulting FIs
F

!

F

s

z
}|
{
t+1
F
F
G ! s

t+1

expected return from nondefaulting FIs

z

Z 1}|

+ ! F st+1

dF F ! F! F (st+1 ){expected monitoring cost paid by investors

z

F

}|
{
GF ! F st+1

(2)

expected return from defaulting entrepreneurs
E

z
}|
{
GE ! E st+1

! E st+1

expected return from nondefaulting entrepreneurs+z! E st+1

Z 1}|

dF E ! E! E (st+1 ){expected monitoring cost paid by FIs

z

E

}|
{
GE ! E st+1

(3)twhere nFt (st ) and nEt (s ) are the ratios of net worth to aggregate capital in the two
sectors, ! F (st+1 ) and ! E (st+1 ) are the cuto¤ value for the FIs’ idiosyncratic shock! F (st+1 ) in the IF contract and the cuto¤ value for the entrepreneurial idiosyncratic
shock ! E (st+1 ) in the FE contract. Equation (1) is a key equation that links the net
worth of the borrowing sectors to the external …nance premium. The external …nancepremium is determined by three components: the share of pro…t in the IF contract goingto the investors, the share of pro…t in the FE contract going to the FIs, and the ratioof total debt to aggregate capital. Lower pro…t shares going to the lenders cause ahigher external …nance premium through the …rst two terms of equation (1) : Otherwise,
the participation constraints of investors would not be met and …nancial intermediation
fails. A higher ratio of the debt results in higher external costs, since it raises the default
probability of the IF contracts and investors require higher returns from the IF contracts
to satisfy their participation constraint. The presence of the …rst two channels suggeststhat not only the sum of both net worths but also the distribution of the two net worths
matters in determining the external …nance premium. See Appendix B for the explicit
forms of GF ! F (st+1 ) and GE ! E (st+1 ) .

Borrowing rates The two credit borrowing rates, namely, the entrepreneurial borrowing rate and the FIs’ borrowing rate, are given by the FE and the IF contracts,
respectively. The entrepreneurial borrowing rate, denoted by Z E (st+1 ) ; is given as the6contractual interest rate that nondefaulting entrepreneurs repay to the FIs:
! E (st+1 ) RE (st+1 ) Q (st ) K (st ):Q (st ) K (st ) N E (st )Z E st+1(4)

Similarly, the FIs’borrowing rate, denoted by Z F (st+1 ) ; is given by the contractualinterest rate that nondefaulting FIs repay to the investors. That isZFs! F (st+1 ) E ! E (st+1 ) RE (st+1 ) Q (st ) K (st ):Q (st ) K (st ) N F (st ) N E (st )

t+1

(5)

Dynamic behavior of net worth The main sources of net worth accumulation of the
FI and the goods-producing sector are the earnings from the credit contracts discussed
above. In addition, there are two other sources of earnings that serve for the net worth
accumulation. First, FIs and entrepreneurs inelastically supply a unit of labor to thegoods producers and receive in return labor incomes that are depicted by WF (st ) andWE (st ) ; respectively.4 Second, the net worths of the two sectors are subject to exogenous
disturbances "NF (st+1 ) and "NE (st+1 ). The aggregate net worths of the FIs and theentrepreneurs then evolve according to equations below:
N F st+1 =F

V F st + W F st + "NF st+1 ;(6)

N E st+1 =E

V E st + W E st + "NE st+1 ;

(7)

with
V F st1

F! F st+1

V E st1

E! E st+1

E! E st+1

RE st+1 Q st K st ;RE st+1 Q st K st :

where
F

!F s

t+1

Z 1

! F (st+1 )

E

!E s

t+1

Z 1

!F s

t+1

dF (! E ) +Z !F (st+1 )! E dFE (! E ) and

0

!E s

t+1

dF (! E ) +! E (st+1 )Z !E (st+1 )! E dFE (! E ) :0

Note that each FI and entrepreneur in the goods-producing sector survives to thenext period with probability F and E ; and those who are in business in period t andttfail to survive in period t + 1 consume (1E ) VE (s ) and (1F ) VF (s ) ; respectively.
4

See BGG (1999), Christiano, Motto, and Rostagno (2008) and HSU (2011) for the technical reason
for introducing inelastic labor supply from the FIs and the entrepreneurs.

7

The exogenous net worth disturbances represented by "NF (st ) and "NE (st ) are i.i.d. andorthogonal to the earnings from the credit contracts. These shocks capture an “asset
bubble,”“irrational exuberance,”or an “innovation in the e¢ ciency of credit contracts,”
hitting the FI sector or the goods-producing sector.5

2.2

The Rest of the Economy

Household A representative household is in…nitely lived and maximizes the following
utility function:
8
9
1
1
<
t+l 1+ =
X
H s
t+l
B t+l
t+l
max
E
exp(e
(s
))
log
C
s
;
(8)
t
:
;
C(st );H(st );D(st )
1+ 1
l=0

subject to

C st + D st

W st H st + R st D st 1 +st

T st ;

where C (st ) is …nal goods consumption, H (st ) is hours worked, D (st ) is real deposits
held by the investors, W (st ) is the real wage measured by the …nal goods; R (st ) is
the real risk-free return from the deposit D (st ) between time t and t + 1; (st ) is thedividend received from the ownership of retailers, and T (st ) is a lump-sum transfer.
2 (0; 1) ; ; and are the subjective discount factor, the elasticity of leisure, and theutility weight on leisure, respectively. eB (st ) is a preference shock with mean one thatprovides the stochastic variation in the discount factor.
Final goods producer The …nal goods Y (st ) are composites of a continuum of retail goods Y (h; st ) : The …nal goods producer purchases retail goods in the competitivemarket and sells the output to a household and capital producers at price P (st ). P (st )is the aggregate price of the …nal goods. The production technology of the …nal goods
is given by
Y s

t

=

Z 1

Y h; st

1

1

dh

;

(9)

:

(10)

0

where > 1: The corresponding price index is given by
P s

t

=

Z 1

1

P h; s

t 1

1

dh

0

5

The similar shocks that a¤ect the net worth of goods producers are considered in existing studies
including Gilchrist and Leahy (2002), Christiano, Motto and Rostagno (2003, 2008) and Nolan andThoenissen (2009).

8

Retailers The retailers h 2 [0; 1] are populated over a unit interval, each producing
di¤erentiated retail goods Y (h; st ) ; with production technology:
Y h; st = y h; st ;(11)

where y (h; st ) for h 2 [0; 1] are the wholesale goods used for producing the retail goods
Y (h; st ) by retailer h 2 [0; 1] : The retailers are price takers in the input market andchoose their inputs taking the input price 1=X (st ) as given. However, they are monopolistic suppliers in their output market and set their prices to maximize pro…ts.
Consequently, the retailer h faces a downward-sloping demand curve:
P (h; st )P (st )

Y h; st =Y st :

Retailers are subject to nominal rigidity. They can change prices in a given period
only with probability (1) ; following Calvo (1983). Retailers who cannot reoptimize
their price in period t; say h = h; set their prices according toP h; st =

st 1

1

p

p

P h; st 1 ;where (st 1 ) denotes the gross rate of in‡ation in period t 1, that is, (st 1 ) =P (st 1 ) =P (st 2 ) : denotes a steady-state in‡ation rate, and p 2 [0; 1] is a parameterthat governs the size of price indexation. Denoting the price set by the active retailers
by P (h; st ) and the demand curve the active retailer faces in period t + l by Y h; st+l ,retailer h’s optimization problem with respect to its product price P (h; st ) is written
in the following way:
1
X

Et

st+l

l=0

where

(1

p

)l

l 1
Y

p

st+k

k=0

P st+lX (st+l )!

!

h; st Y h; st+lP

Y h; st+l!

= 0;

st+l is given by
st+l =t+l

C (st )C (st+l ):Using equations (9) ; (10) ; and (11) ; the …nal goods Y (st ) produced in period t are
expressed with the wholesale goods produced in period t as the following equation:
"Z
#
Z 1
1
t
P
(h;
s
)
t
dh Y st :y st =
y h; st dh =
t)
P
(s
0
0
9

Moreover, because of stickiness in the retail goods price, the aggregate price index
for …nal goods P (st ) evolves according to the following law of motion:
P st

1

= (1

h; st

)P

1

st 1

+

p

1

p

P st 1

1:

Wholesalers The wholesalers produce wholesale goods y (st ) and sell them to theretailers with the relative price 1=X (st ) : They hire three types of labor inputs, H (st ) ;H F (st ) ; and H E (st ) ; and capital K (st 1 ) : These labor inputs are supplied by thehousehold, the FIs, and the entrepreneurs for wages W (st ) ; W F (st ) ; and W E (st ) ;respectively. Capital is supplied by the entrepreneurs with the rental price RE (st ) : At
the end of each period, the capital is sold back to the entrepreneurs at price Q (st ) : The
maximization problem for the wholesaler is given bymaxy(st );K(st 1 );H(st );H F (st );H E (st )1y st + Q st K st 1 (1)
t
Xt (s )
R E st Q st 1 K st 1
W st H st
W F st H F st

W E st H E st ;subject toy st = A exp eA st

K st 1

H st

(1

F

E )(1

)

H F stF (1)

H E st

E (1

)

;
(12)
where A exp eA (st ) denotes the level of technology of wholesale production and 2(0; 1], ; F and E are the depreciation rate of capital goods, the capital share, theshare of the FIs’labor inputs and the share of entrepreneurial labor inputs, respectively.
Capital goods producers The capital goods producers own the technology that converts …nal goods to capital goods. In each period, the capital goods producers purchaseI (st ) amounts of …nal goods from the …nal goods producers. In addition, they purchaseK (st 1 ) (1) of used capital goods from the entrepreneurs at price Q (st ). They thenproduce new capital goods K (st ) ; using the technology FI ; and sell them in the competitive market at price Q (st ) : Consequently, the capital goods producer’s problem is
to maximize the following pro…t function:

max
t
I(s )

1
X

Et

st+l

Q st+l1

FI I st+l ; I st+l 1

l=0

where FI is de…ned as follows:
10

I st+l

I st+l;(13)

FI I st+l ; I st+l 1!2

exp(eI (st ))I st+l
I (st+l 1 )

2

1

(14)

:

Note that is a parameter that is associated with investment technology with an adjustment cost, where eI (st ) is the shock to the adjustment cost.6 Here, the developmentof the total capital available at period t is described as
K st = 1

FI I st ; I st 1

) K st 1 :I st + (1(15)

Government The government collects a lump-sum tax from the household T (st ) andspends G (st ). A budget balance is maintained for each period t: Thus, we have
G st exp eG (st ) = T st ;(16)

where eG (st ) is the stochastic component of government spending.
Monetary authority In our baseline model, the monetary authority sets the nominalinterest rate Rn (st ) according to a standard Taylor rule with inertia:y log

Y (st )
Y

where is the autoregressive parameter of the policy rate,and

Rn st = Rn st 1 + (1)

st ) +((st ) and the output gap log

on the in‡ation rate of …nal goods+ eR st ;(17)

y are the policy weight
Y (st )Y

; respectively,

and eR (st ) is the shock to the monetary policy rule. Because the monetary authority
determines the nominal interest rate, the real interest rate in the economy is given by
the following Fisher equation:
R st

Et

Rn (st )(st+1 )

(18):

Resource constraint The resource constraint for …nal goods is written as
Y st = C st + I st + G st exp eG (st )+E

G E ! E st

R E st Q st 1 K st 1+

F

G F ! F st

R F stQ st 1 K st 1

+ C F st + C E st :N E st 1(19)

6Equation (13) does not include a term for the purchase of the used capital K st 1 from theentrepreneurs at the end of the period. This is because we assume, following BGG (1999), that the priceof old capital that the entrepreneurs sell to the capital goods producers, which we denote as Q (st ) ; isclose to the price of the newly produced capital Q (st ) around the steady state.

11Note that the fourth and the …fth terms on the right-hand side of the equation correspondto the monitoring costs incurred by the FIs and investors, respectively. The last two terms
are the FIs’and entrepreneurs’consumption.
Law of motion for exogenous variables There are …ve equations for the shockprocesses, eA (st ) ; eI (st ), eB (st ) ; eG (st ) ; and eR (st ) ; following processes as below:
eA st =AAe

st 1 + "A st ;(20)

eI st =

IIe

st 1 + "I st ;(21)

eB st =

eB st 1 + "

st ;

(22)

eG st =

GGe

st 1 + "G st ;(23)

eR st =

RRe

st 1 + "R st ;(24)

where A ; I ; B ; G ; and R 2 (0; 1) are autoregressive roots of the exogenous variables
and "A (st ) ; "I (st ) ; "B (st ) ; "G (st ) ; and "R (st ) are innovations that are mutually independent, serially uncorrelated, and normally distributed with mean zero and variances222; 2G ; and 2R , respectively.
A; I ;

2.3

Equilibrium Condition

An equilibrium consists of a set of prices, fP (h; st ) for h 2 [0; 1] ; P (st ); X(st ); R (st ) ;RF (st ) ; RE (st ) ; W (st ) ; W F (st ) ; W E (st ) ; Q (st ) ; RF (st+1 ) ; RE (st+1 ) ; Z F (st+1 ) ;
F
E
t 1
F
t 1
t+1 1
Z E (st+1 )g1)gt=0 ; f! E (st+1 )g1
t=0 , and the allocations f! (st=0 ; fN (s )gt=0 ; fN (s )gt=0
ffy(h; st )); Y (h; st ) for h 2 [0; 1] ; Y (st ) ; C (st ) ; D (st ) ; I (st ) ; K (st ) ; H (st ) ; H F (st ) ;
n
t
t
t 1
H E (st )gg1
t=0 ; for a given government policy fR (s ) ; G (s ) ; T (s )gt=0 , realization ofEF
exogenous variables f"A (st ) ; eB (st ); eG (st ); eI (st ); "R (st ) ; "N (st ) ; "N (st )g1
t=0 andF
E
initial conditions N 1 ; N 1 ; K 1 such that for all t and h:(1) a household maximizes its utility given the prices;(2) the FIs maximize their pro…ts given the prices;(3) the entrepreneurs maximize their pro…ts given the prices;(4) the …nal goods producers maximize their pro…ts given the prices;(5) the retail goods producers maximize their pro…ts given the prices;(6) the wholesale goods producers maximize their pro…ts given the prices;(7) the capital goods producers maximize their pro…ts given the prices;(8) the government budget constraint holds; and(9) markets clear.
12

3

Data and Estimation Strategy

Following Christensen and Dib (2008) and HSU (2011), we set some of the parameters
to the values used in the existing studies. These include the quarterly discount factor ;the labor supply elasticity ; the capital share ; the quarterly depreciation rate ; andthe steady-state share of government expenditure in total output G=Y . See Table 1 forthe values of these parameters.
In addition, we calibrate six parameters for the credit contracts: the lenders’monitoring cost in the IF contract F , the lenders’monitoring cost in the FE contract E ;the standard error of the idiosyncratic productivity shock in the FI sector F , the standard error of the idiosyncratic productivity shock in the entrepreneurial sector E , thesurvival rate of FIs F ; and the survival rate of entrepreneurs E , so that the following
six equilibrium conditions are met at the steady state:(1) the risk spread, RE

R; is 200 basis points annually;(2) the ratio of net worth held by FIs to the aggregate capital, N F =QK, is 0.1, ahistorical average in the Japanese economy;(3) the ratio of net worth held by entrepreneurs to the aggregate capital, N E =QK, is0.5, a historical average in the Japanese economy;(4) the annualized failure rate of FIs is 3%;(5) the annualized failure rate of entrepreneurs is 3%; and(6) the ratio of the spread between the FIs’ borrowing rate and the entrepreneurial
borrowing rate, Z E Z F ; to the spread between the entrepreneurial borrowing
rate and the riskless rate, Z F R; is 186/32, the value taken from a historical
average.
We estimate the rest of parameters of the model using a Bayesian method. Estimatedparameters are the frequency of price adjustment ; the degree of price indexation p , aparameter that controls the capital adjustment cost ; the coe¢ cients of the policy rule;and y ; the autoregressive parameters of the shock process A ; I ; B ; G ; and R ,the variances of these shocks 2A ; 2I ; 2B ; 2G ; and 2R ; and the variances of the shocks
to net worth 2NF and 2NE : To calculate the posterior distribution and to evaluate themarginal likelihood of the model, the Metropolis-Hastings algorithm is employed. To dothis, a sample of 200,000 draws was created, neglecting the …rst 100,000 draws.

13

3.1

Data

Our dataset includes seven time series for the Japanese economy: the growth rate of realGDP, the growth rate of real consumption, the growth rate of real investment, the log
di¤erence of the GDP de‡ator, the call rate, and the growth rates of real net worth of thebanking sector and the entrepreneurial sector.7;8 In estimating the model, we demean
these variables, assuming that the mean of each variable in the model coincides with thatin the data, following CMR (2008). Following Sugo and Ueda (2008), the variables otherthan the GDP de‡ator and the call rate are demeaned with a trend break in 1991Q2.
Our dataset covers the period from 1981Q1 to 2013Q4.9 All data series used for
estimation are shown in Figure 1. The shaded areas are recessions which start at thepeak of business cycles and end at the trough. The reference dates are speci…ed by the
Economic and Social Research Institute of the Japanese government.

3.2

Prior Distribution of the Parameters

Table 2 shows the prior distributions of parameters. The adjustment cost parameter forinvestment is normally distributed with a mean of 4.0 and a standard error of 1.5;
the Calvo probability is beta distributed with a mean of 0.5 and a standard error of
0.15; the degree of indexation to past in‡ation p is beta distributed with a mean of 0.5
and a standard error of 0.2; the policy weight on the lagged policy rate is normally
distributed with a mean of 0.75 and a standard error of 0.1; the policy weight on in‡ation
is normally distributed with a mean of 1.5 and a standard error of 0.125; and thepolicy weight on the output gap y is normally distributed with a mean of 0.125 and astandard error of 0.05.
The priors on the autoregressive parameters A ; I ; B ; G ; and R are beta distributed with a mean of 0.5 and a standard deviation of 0.2. The variances of theinnovations in exogenous variables 2A ; 2I ; 2 ; 2G ; 2NF , 2NE ; and 2R are assumed tofollow an inverse-gamma distribution with a mean of 0.01 and a standard deviation of 2.
7

The …rst …ve variables are expressed in per capita terms. The two net worth series are de‡ated by
the GDP de‡ator.
8
The two net worth series are constructed based on the ‡ow of funds accounts.
9
While existing studies such as Sugo and Ueda (2008) and Hirose and Kurozumi (2010) estimate their
Dynamic Stochastic General Equilibrium models using only the periods where the nominal interest rate
has been well above zero, our sample includes the periods where it has been close to zero. The reason wetake this approach is that the goal of the current paper is to study the role of …nancial intermediation
malfunction throughout the 1990s and 2000s, which covers the three …nancial crises. We con…rmedthat our parameter estimates and impulse response of key macroeconomic variables to structural shocks
hardly change when we instead use the sample periods until 1995Q4.

14

4

Estimation Results

In this section, we show the estimated parameter values and distilled structural shocks.
In addition, we examine the model-generated time series of credit spreads. While credit
spreads play the key role in transmitting the FIs’shocks to the real activities in the model,
because of the data limitation, we do not make use of the spread data in estimating
the model. By comparing the model-generated series with a number of actual …nancial
stress indicators, we show how well our model captures the developments of credit market
conditions during the lost decade(s).

4.1Parameter Estimates

Table 2 reports the estimated values of the structural parameters and the standard
deviations of the shocks. For the investment adjustment cost, we obtain = 8:67. Thisvalue falls between the estimates of 0.65 (Meier and Muller, 2006) and 32.1 (Ireland,2003) reported in the existing studies for the U.S. economy. Our estimates of the degreeof nominal price rigidity, the frequency of price adjustment and the degree of priceindexation, are = 0:606 and p = 0:074, respectively. These values, in particular thelatter, are smaller than the …ndings in Meier and Muller (2006). The estimated monetary
policy rule exhibits an active response to current in‡ation= 1:48; with inertia of theinterest rate = 0:845; and a mild reaction to the current output y = 0:024.
Shocks to government expenditure and preference are particularly persistent with
AR(1) coe¢ cients of 0.87 and 0.91, respectively, compared with other shocks. The
standard deviation of the entrepreneurial net worth shocks is 0.335, being the largest
among the shocks. Comparing these estimates with those for the U.S. data reported
in HSU (2011), the value is larger than that of the United States, which is 0.179. The
estimate of the standard deviation of the FIs’net worth shocks is almost double that of
the United States, which is 0.041.

4.2

Identi…ed Shocks to Net WorthWe identify time series of seven structural shocks, "A (st ) ; eB (st ); eG (st ); eI (st ); "R (st ) ;EF"N (st ) ; and "N (st ) ; from 1981Q1 to 2013Q4 based on the estimation. The identi…ed
FEshocks to the FI’s net worth and the entrepreneurial net worth "N (st ) and "N (st ) aredisplayed in Figure 2a. Similarly to Figure 1, the shaded areas are recessions in Japanesebusiness cycles. Realized values of the two …nancial shocks are negatively related tobusiness cycles: values of the two shocks typically fall below zero during recessions,suggesting that they are contributing to economic downturns. Net worth shocks toentrepreneurs have a large negative value for several years after the asset bubble burst
in the early 1990s, during the early 2000s after the dot-com boom ended, and during thelate 2000s when the global …nancial crisis took place. Net worth shocks to the FIs have15continuously shown negative values since the asset bubble burst from the early 1990s to
the 2000s.
We compare the time series of net worth shocks estimated for Japan’s economy withthose estimated for the U.S. economy. Figure 2b displays identi…ed time series of net
worth shocks in the United States that are taken from HSU (2011) as well as thosein Japan. Note that in HSU (2011) we estimate the same model as the model in thecurrent paper using time series of the U.S. macroeconomic variables. During the global…nancial crisis, the United States witnessed a large negative net worth shock to both
entrepreneurs and FIs. In contrast, Japan witnessed a large negative net worth shock
only to entrepreneurs and only a moderate negative shock to FIs. This observation
demonstrates that Japanese FIs hardly su¤ered from the global …nancial crisis, though
the Japanese economy was severely dampened due to net worth shocks to entrepreneurs.

4.3

Checking the Estimation Results

Following Nolan and Thoenissen (2009), we check the reasonableness of our estimation
results by making use of actual time series of an indicator of external …nance premium
Z E R: Note that since we do not employ an external …nance premium in estimating
model parameters and shocks, we can assess the validity of our estimation results bycomparing indicators and the model-generated external …nance premium. As discussed
in De Graeve (2008), however, the data series of the external …nance premium that
corresponds to the model’s external …nance premium is often di¢ cult to observe, andthis is why we did not use the data for estimation. To this end, we compare timeseries data of four indicators of the external …nance premium with the time series of theexternal …nance premium Z E (st ) R (st ) generated from our model. The four indicators
include two market spreads: the spread between bank lending rates on contracted shortterm loans and short-term government bond rates and the spread between bank lending
rates on newly contracted short-term loans and short-term government bond rates, andtwo di¤usion indices, the Financial Position Di¤usion Index and the Lending Attitudeof Financial Institutions Di¤usion Index. The index series are of the Tankan (ShortTerm Economic Survey of Enterprises in Japan) released from the Bank of Japan. They
indicate the strain that non-…nancial …rms face in raising external funds from …nancial
institutions.10
Table 3 presents cross-correlation coe¢ cients between those four measures and themodel-generated series Z E (st ) R (st ) for a one-year range of leads and lags that arecomputed from the sample period from 1981 to 2013.11 The model-generated series
10

The Financial Position Di¤usion Index is constructed from the number of …rms that report “Easy”
minus the number of …rms that report “Tight.” The Lending Attitude Di¤usion Index is constructedfrom the number of …rms that report “Accommodative”minus the number of …rms that report “Severe.”
11
Correlation coe¢ cients regarding the second measure are computed from the data series from 1993
onward because of the data availability of the series.

16

positively correlates with the …rst, third, and forth indicators in a statistically signi…cantmanner, indicating that our estimated model well captures developments in cost that areassociated with external funding or those of demand for funding of non-…nancial …rms
in Japan. Though the model generated series displays a weaker statistical relationshipwith the second indicator, the coe¢ cients are positive in most leads and lags.

5

Financial Factors in Japanese Business Cycles

In this section, we study the role of net worth shocks to the FI and entrepreneurial sector
in generating macroeconomic dynamics in the Japanese economy. We …rst describe theimpacts of net worth shocks on the macroeconomy and discuss how they di¤er from theimpacts of other shocks. We then examine the relative signi…cance of net worth shocks
in accounting for variations in key macroeconomic variables.

5.1

Impulse Responses

Figure 3 shows the impulse responses of key macroeconomic variables to shock to FIs’
net worth, and entrepreneurial net worth, productivity, and investment adjustment cost
FE
"N (st ), "N (st ) ; "A (st ) ; and "I (st ) : We normalize the size of the shocks to be one
standard deviation. We give positive shocks to the investment adjustment cost andnegative shocks to the other three variables.
The net worth shocks to the FIs and entrepreneurs are those that arise as innovations
to equations (6) and (7), respectively. At the impact, they in‡uence the terms of credit
contracts Z F (st+1 ) and Z E (st+1 ) and they are propagated to the rest of the economy bychanging volume of …nancial intermediation. For instance, when the balance sheets of FIs
are impaired by a negative net worth shock, investors require a higher expected return
Z F (st+1 ) in their credit contracts with the FIs because the borrower FIs are now lesscreditworthy than otherwise. The increase in the FIs’borrowing rate is translated to theentrepreneurial borrowing rate as shown in the panel (8). With a higher cost of borrowing
external funds, the entrepreneurs purchase less capital goods K (st ) from capital goods
producers. This results in a lower capital input supply, dampening investment andGDP. In‡ation falls, re‡ecting the weakened aggregate demand. The decline in demandfor capital goods K (st ) causes the second-round e¤ect on the endogenous developmentsin the net worths of FI’s and those of entrepreneurs by a¤ecting the capital goods priceQ (st ) : That is, a reduced value of capital goods price, shown in the panel (3), hampers
the net worth accumulation of the two sectors since the retained earnings in the these
sectors decrease following equations (6) and (7). The deteriorated net worths result in
the further rise in borrowing rates, dampening investment and GDP further.
In response to a negative shock to productivity in the wholesaler’s production function (12) ; because less output is produced from the same amount of production inputs,
investment and output are reduced. In‡ation increases as the real marginal cost of the17wholesaler increases. The increase in in‡ation leads the central bank to raise the nominal interest rate according to the Taylor rule (17), having a contractionary e¤ect on
output. Similarly to the consequence of net worth shocks, a decline in aggregate investment demand lowers the capital goods price Q (st ) : Consequently, as shown in the panels(5) and (6), the …nancial accelerator e¤ect emerges through endogenous deterioration of
net worth in both the FI and entrepreneurial sectors. Impaired balance sheets in these
sectors reinforce the adverse e¤ects of the productivity shock on the aggregate economy.
In response to a positive shock to the investment adjustment cost (14) ; the capital
goods price Q (st ) increases, while the other types of shocks lower it. This is because otherthings being equal capital goods producers need to purchase more …nal goods to produce
the same amount of capital goods K (st ). Since capital goods become more expensive
than otherwise, capital input supply is reduced, resulting in a lower aggregate investment
and GDP. Although the increase in the capital goods price helps the accumulation of
net worth in the FI and entrepreneurial sectors as shown in the panels (5) and (6) andreduces the entrepreneurial borrowing rate, this favorable e¤ect is dominated by theadverse e¤ect due to the increase in the capital goods price.

5.2

Historical Decomposition

Using the time series of structural shocks that are extracted from the estimation above,
we next evaluate how shocks to the net worth of FIs and entrepreneurs a¤ected macroeconomic ‡uctuations in Japan over the last thirty years. Figure 4 plots historical decompositions of ‡uctuations in investment, GDP, and in‡ation into structural shocks.
This …gure suggests that shocks to the net worth of entrepreneurs have contributed
substantially to the declines in investment during the period of the …rst crisis in the early
1990s and during the period of the third crisis in the late 2000s. As illustrated in Figure
3, negative entrepreneurial net worth shocks cause …nancial intermediation malfunction
by increasing entrepreneurs’borrowing rates and reducing the amount of funds that areintermediated from households to entrepreneurs, leading to economic downturn. It isseen that the net worth shocks also contributed to a decline in investment during therecession that started from November 2000 as the boom in IT industry ended. The GDP
and in‡ation rate have been dampened by the shocks as well particularly during the…rst and the third crises. In contrast to ‡uctuations in investment, ‡uctuations in thesevariables are more a¤ected by TFP shocks.
Compared with entrepreneurial net worth shocks, the e¤ects on ‡uctuations in investment of net worth shocks to the FIs have been relatively minor. In particular, thecontribution of these shocks to investment decline during the third crisis was negligible.
This observation is consistent with the view that the origin of the current global …nancial crisis is the deterioration of the balance sheets of U.S. banks rather than those ofJapanese banks. The FIs’net worth shocks, however, have been continuously dampening investment since the burst of the asset price bubble, and the impact of these shocks
18

has been sizable throughout the 1990s. As documented by Hoshi and Kashyap (2010),
Japanese banks have been su¤ering from non-performing loan problems and recorded
loan losses of about 13 trillion yen in 1996, 1998, and 1999, and their balance sheets
were severely impaired. Our estimation results show that the impaired balance sheetsof the FIs have dampened …nancial intermediation and reduced loan supply to …rms,
which is consistent with the documentation. The adverse e¤ects of the shocks have been
gradually diminishing since early 2000. This timing is consistent with the time the Financial Revival Program was launched by the Japanese Financial Service Agency led
by Heizo Takenaka and when the Japanese government started to increase pressure onlarge Japanese banks to strengthen their capital conditions. The shocks also have been
contributing to lower GDP and in‡ation throughout the 1990s.
Shocks to the investment adjustment cost have been an important driver of investment
declines during periods other than the three …nancial crisis periods. For instance, during
the recession that started in June 1985 and during the period of moderate economic
slowdown around the mid-2000s, these shocks were the key determinant of ‡uctuationsin investment.
Table 4 computes the average contribution of each shock in accounting for threemacroeconomic variables over the full sample period, the 1990s, and the late 1990s. It isseen that the quantitatively most important shocks in explaining investment ‡uctuations
are shocks to the investment adjustment cost. The net worth shocks to entrepreneurs
are the second most important shocks. The contribution to investment ‡uctuations of
net worth shocks to the FIs is small for the full sample basis, though it is relatively large
for the late 1990s.

6

Financial Friction and Investment Adjustment Cost

In addition, we explore how the investment adjustment cost shocks are related to thenet worth shocks estimated in our model. As discussed by Justiniano, Primiceri, andTambalotti (2008), the estimates of the New Keynesian model typically indicate thatshocks to investment adjustment cost play an important role in producing business cycles.
Christensen and Dib (2008) also report that more than 90% of investment variations
originate in the shocks to investment e¢ ciency in the U.S. economy. Hirose and Kurozumi(2010) by estimating a New Keynesian model using Japanese data also document thatmost of the Japanese investment variations are accounted for by these shocks. These
shocks are considered to be related to the e¢ ciency of …nancial intermediation in Hirose
and Kurozumi (2008) and Justiniano, Primiceri, and Tambalotti (2011).
To see how investment adjustment cost shocks are related to …nancial factors, weestimate models that abstract from …nancial frictions and compare the role of estimatedinvestment adjustment cost shocks in these models with that in the current model.
The alternative models are the BGG model and the Non-FA (non-…nancial-accelerator)
model. In the BGG model, entrepreneurs are credit constrained but FIs are not. In the19Non-FA model, no credit market imperfection prevails in the economy. To illustrate therole that shocks to the FIs’net worth play, we estimate the BGG model and the Non-FAmodel along with the benchmark model by a Bayesian method.
Table 5 reports the variance decompositions of investment under the three models.
Under the Non-FA model, a bulk of the variations comes from the shocks to investment
adjustment cost "It , accounting for 94% of the investment variations. When shocks
originating in the credit market are incorporated, the contribution of the shocks toinvestment adjustment cost decreases. The estimated contribution of "It is 77% and64%, respectively, in the BGG model and the benchmark model. On the other hand,under the two models, a signi…cant portion of investment variation is attributed to theFEand "N
contributions of shocks originating in the credit market, "N
t . The contributiontEunder the benchmark model is larger than under the BGG model. This is becauseof "Nt
the ampli…cation and propagation mechanism is increased under the benchmark model.

7

Conclusion

In this paper, we have assessed the roles of …nancial shocks in accounting for macroeconomic ‡uctuations in Japan particularly during the periods when …nancial crises havetaken place. To this end, we have borrowed a version of …nancial accelerator model
developed by Hirakata, Sudo, and Ueda (2011). In this model, unexpected shocks to thenet worths of FIs and entrepreneurs a¤ect macroeconomic ‡uctuations by a¤ecting theterms of credit contracts and external …nance premiums that are relevant to the volume
of aggregate investment. We have estimated the model using Japanese data from the
1980s to the 2010s to obtain model parameters and underlying structural shocks. Using
the estimation results, we have decomposed ‡uctuations of macroeconomic variables into
those attributed to …nancial shocks and those attributed to non-…nancial shocks.
We have found that the two …nancial shocks, shocks to the net worths of FIs andentrepreneurs, are both important sources of macroeconomic ‡uctuation. These shocks
impair the balance sheets of the two sectors, increase the external …nance premium, anddampen aggregate investment. Their impacts on investment are prominent particularly
during the three …nancial crises. Net worth shocks to entrepreneurs have played the
key role in lowering investment during the periods of the bubble burst and the global…nancial crisis. Net worth shocks to FIs have contributed to investment decline in theearly 1990s and persistently lowered investment throughout the 1990s.
In addition, our result suggests that the shocks to investment adjustment cost thatare emphasized in the existing studies may be capturing shocks to the …nancial sector.
The comparison with other models that abstract from credit-constrained banks, creditconstrained entrepreneurs, or both, illustrates that investment variations explained by
the shocks to capital adjustment cost are reduced drastically by inclusion of the credit
market imperfection.
Finally, let us propose three important directions for future research. The …rst is20

to incorporate the zero lower bound of nominal interest rates and/or unconventionalmonetary policy. The second direction is to embed the stochastic trend in the current
model to explain a kinked decline in GDP growth rates since the burst of the bubble.
Third, another model for …nancial shocks is possible. Speci…cally, riskiness shocks rather
than net worth shocks have attracted attention following the work of Christiano, Motto,
and Rostagno (2014).

21

A

Credit Contracts

In this appendix, we discuss how the contents of the two credit contracts are determinedby the pro…t maximization problem of the FIs. We …rst explain how the FIs earn pro…tfrom the credit contracts and then explain the participation constraints of the otherparticipants in the credit contracts.
In each period t; the expected net pro…t of an FI from the credit contracts is expressedby:X

share of FIs earnings received by FI

z
1

st+1

st+1

F

}|
{
! F st+1

RF st+1

Qt st K st

N E st;(25)

where (st+1 ) is a probability weight for state st+1 : Here, the expected return on theloans to entrepreneurs, RF (st+1 ) is given by:zshare of entrepreneurial earnings received by FI
E

!

E

s

}|

t+1

RF st+1

E

G

E

!

E

s

Q st K st

t+1{

RE st+1 Q st K st

N E stfor 8st+1 :(26)

This equation indicates that the two credit contracts determine the FIs’pro…ts. In the
FE contract, the FIs receive a portion of what entrepreneurs earn from their projects astheir gross pro…t. In the IF contract, the FIs receive a portion of what they receive fromthe FE contract as their net pro…t and pay the rest to investors.
There is a participation constraint in each of the credit contracts. In the FE contract,the entrepreneurs’expected return is set to equal the return from their alternative option.
We assume that without participating in the FE contract, entrepreneurs can purchasecapital goods with their own net worth N E (st ) : Note that the expected return fromthis option equals RE (st+1 ) N E (st ). Therefore the FE contract is agreed upon theentrepreneurs only when the following inequality is expected to hold:share of entrepreneurial earnings kept by the entrepreneur

z
1

E

}|
{
! E st+1

RE st+1 Q st K st

RE st+1 N E st for 8st+1 :(27)

We next consider a participation constraint of the investors in the IF contract. We
assume that there is a risk-free rate of return in the economy R (st ) and that investors
22

may alternatively invest in this asset. Consequently, for investors to join the IF contract,
the loans to the FIs must equal the opportunity cost of lending. That is:zshare of FIs’earnings received by the investorsF! F st+1}|

F

GF ! F st+1

R st

Q st K st{

RF st+1

Q st K st

N F stN E stN E st(28):

The FI maximizes its expected pro…t (25) by optimally choosing the variables ! F (st+1 ) ;! E (st+1 ) ; and K (st ) ; subject to the entrepreneurial participation constraint (27) andthe investors’participation constraint (28). Combining the …rst-order conditions yields
the following equation:
X
F
E
0=
st+1
! F st+1
1
st+1 RE st+1
st+1
0F

! F (st+1 ) F t+1 E t+1 Ess
Rt+1 st+1
0F (st+1 )0F! F (st+1 )R(st )
0F (st+1 )F
0E
1! F (st+1 )(st+1 )
E+
! E st+1
10E! E (st+1 )

+

+

0F

! F (st+1 )0F (st+1 )(st+1 ) 0E (st+1 )10E! E (st+1 )RE st+1

FE! E st+1

RE st+1

Using equations (26) and (28), we obtain equation (1) in the text.

23

)

:

(29)

B

Equilibrium Conditions of the Benchmark ModelIn this appendix, we describe the equilibrium system of our benchmark model. We
express it in …ve blocks of equations.
(1) Household’s Problem and Resource Constraint
1= Et
C (st )

exp eB (st+1

W st = H st

Rt = Et

)

1

1
Rt ;
C (st+1 )(30)

C st ;

(31)

;

(32)

Rtn
t+1

Y st = C st + I st + G st exp eG (st )
+

E

E
st
GE
t !

R E st Q st 1 K st 1+

F

GFt ! F st

R F stQ st 1 K st 1

N E st 1+ C F st + C E st ;

(33)

with:
C F st

1

F

1

C E st1

E! E st+1

F! F st+1

E! E st+1

RE st+1 Q st K st ;RE st+1 Q st K st :(2) Firms’Problems

(1

Y s

t

=

A exp eA (st ) K (st 1 ) H (st )

F

E )(1

t
p (s ))H F (st ) F(1)

H E (st ) E

(1

)

;
(34)

24

with:t= (1p s

exp eB (sFp st = 1 +Kp s t =Kp (st )Fp (st )

)

t+1

(st )
M C st +(st ) 1

M C st (1exp eB (sK st 1) (1R E st =

Q st
(

= Et

1

I (st ) exp(eI (st ))I (st 1 )exp eB (

st+1

t+1

st 1 ;(st ) p(st+1 )

1

Fp st+1 ;tt+1) C (s ) Y (s )C (st+1 ) Y (st )

H st

(1

F

E )(1

)

H F st2)

H E st

E (1

)

(36)

;

1

1

I (st+1 ) exp(eI (st+1 ))I (st )

2

I (st+1 )I (st ))

1 exp(eI (st+1 )) :(37)

(3) FIs’Problems
Equilibrium conditions for credit contracts are given by (27), (28), and (29) and by
the following equations:
Z log ! (s ) 0:5 F
F

G F ! F st

1
=p
2

)

!

I (st ) exp(eI (st ))I (st 1 )tt+1
) C (s ) Q (s )C (st+1 )F (1Kp st+1 ;(35)

Y (st ) =K (st ) + Q (st+1 ) (1Q (st )

1(st ) p(st+1 )E) ;F

I (st ) exp(eI (st ))I (st 1 )

0:5

p

t
t+1
) C (s ) Y (s )C (st+1 ) Y (st )H st W st = A exp eA st

Q st(st 1 ) p
(st )

+

t

F

1

25

2

exp

vF2
2

dvF ;

(38)

Z log ! (s ) 0:5 E
E

1
=p
2

G E ! E st

p1
2

1

1
! F (st ) F

p1
2

exp

1

:5

exp

E

! F (st ) = p12! F (st ) R 1
p

2

F

R

log ! F (st )+0:5 2
F
F

R

!E
t

log ! E:5

log ! F( ) 0:5
st

2
vF

exp

2
vF
2

exp

F

1

2
E

2

E

(st ) 0:5 2F

!

;

!

;

(40)

(41)

dvF

(42)

dvF ;

2

( ) 0:5 2E

log ! E st

E
= p12
1
! E (st ) R 1+ p2
log ! E (st )+0:5 2 exp
EE

log ! F (st ) 0:5 2F@! E (st )! E (st )

2

(39)

dvE ;

@GE (! E (st ))

F

+

vE2
2

exp

@! F (st )G0E ! E (st )=2E@GF (! F (st ))G0F ! F (st )
=

t

x2
2

exp
2
vE
2

dvE

(43)

dvE ;

E

0F

! F st@ F ! F (st )
1
=p
F
t
F
@! (s )
2 ! (st )
1
+p
2

Z 1

exp
log ! F (st )+0:5 2
F

vF2
2

F

26

exp

:5

F

dvF

p

1
2

log ! F (st )
0

B
B
exp B
@
F

2

0:5 2FF!

log ! F (st )+0:5 2F
F

2
(44)

2

1

C
C
C;
A

0E

! E st@ E ! E (st )
1
=p
exp
E
t
E
@! (s )
2 ! (st ) E
Z 1
1
vE2
dvE
+p
exp
log ! E (st )+0:5 2
2
E
2
E

E

E

! E st+1

0:5 2E

E

1
p
2

exp

:5

2

!

log ! E (st ) + 0:5 2E
E

E

(45)

RE st+1 Q st K st

GE ! E st+1

= RtF st+1

:5

log ! E (st )Q st K st

N E st(46):(4) Laws of Motion of State Variables

K st =

1

I (st ) exp(eI (st ))I (st 1 )0:5

N i st+1 =

i

E

2

!

I st + (1) K st 1 ;V i st + W i st ;

(47)

(48)

with:
V F st1

F! F st+1

V E st1

E! E st+1

W i st(1)

iY! E st+1

RE st+1 Q st K st ;RE st+1 Q st K st ;st ;where i = F or E.

(5) Policies and Shock Process
Policies for the shock process are given by equations (16), (17), (20), (21), (22), (23)and (24).

27

2

!

;

C

Equilibrium Conditions of Alternative Models

In addition to the benchmark model, we consider two alternative models for comparative
convenience. The …rst is the Non-FA model, in which no …nancial accelerator mechanism
is incorporated. The equilibrium conditions under this model are given by equations (16),(17), (20), (21), (22), (23), (24), (30), (31), (32), (34), (35), (36), (37), and (47), andby the following equations instead of equations (33) and (36), respectively, under thebenchmark model, :Y st = C st + I st + G st exp eG (st ) ;R st = Et

Y (st ) =K (st ) + Q (st+1 ) (1Q (st )

)

:

(49)

(50)

The second model is the BGG model in which only entrepreneurs are credit constrained. The equilibrium conditions in this model are given by equations (7), (16), (17),(20), (21), (22), (23), (24), (30), (31), (32), (34), (35), (36), (37), (39), (41), (43), (45)and (47), and by the following three equations instead of equations (29), (33), and (36),respectively, under the benchmark model:
0=
+

X

st+1

E

1

st+1
0E

! F (st+1 )0E (st+1 )Es! E st+1

t+1

R

E

s

RE st+1
0E

t+1! E (st+1 )0E (st+1 )E

st+1 R(st );(51)

Y st = C st + I st + G st exp eG (st )+E

G E ! E st

R E st Q st 1 K st 1 + C E st ;

(52)

with:
C E stE

1! E st+1= R stE! E st+1

E

GE ! E st+1

RE st+1 Q st K st

Q st K st

N E st28

RE st+1 Q st K st ;

:

(53)

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31

Table1: Parameters(1) Parameters
Parameter

Value
.99
.025
.35
-1
.99
6
3
.3
.2

β
δ
α
R

ε
η
χ
GY

-1

Description
Discount Factor
Depreciation Rate
Capital Share
Risk Free Rate
Degree of Substitutability
Elasticity of Labor
Utility Weight on Leisure
Share of Governement Expenditure at Steady State(2) Calibrated Parameters
Parameter

Value

Description

σE
σF
μE
μF

0.269755
0.091600
0.015812
0.078367

S.E. of Entrepreneurial Idiosyncratic Productivity at Steady State
S.E. of FIs' Idiosyncratic Productivity at Steady State
Bankruptcy Cost Associated with Entrepreneurs
Bankruptcy Cost Associated with FIs

γE
γF

0.983840
0.962437

Survival Rate of Entrepreneurs
Survival Rate of FIs(3) Steady State Conditions
Condition-1

R =.99Z E =Z F +.0186/4
Z F =R +.0032/4
F (ω E )=.03/4
F
F (ω )=.03/4
En =.5
n F =.1

Description
Risk free rate is the inverse of the subjective discount factor.
Premium for entrepreneurial borrowing rate is .0186/4.
Premium for FIs' borrowing rate is .0032/4.
Default probability in the FE contract is .03/4.
Default probability in the IF contract is .03/4.
Entrepreneurial net worth/capital ratio is set to .5.
FIs' net worth/capital ratio is set to .1

Table2: Parameter estimates

Prior distribution

Posterior distribution

ρB
ρI
ρA
ρG
ρR
ρP

Beta
NormalBeta
Beta
Normal
Gamma
Beta
Beta
Beta
Beta
Beta
Beta

0.5
4
0.5
0.75
1.5
0.125
0.5
0.5
0.5
0.5
0.5
0.5

0.15
1.5
1.5
0.1
0.125
0.5
0.2
0.2
0.2
0.2
0.2
0.2

0.60648.67390.07390.84471.48320.02380.91450.37700.87190.80450.05900.680010th
percentiles
0.55366.65390.00800.8193
1.34860.01040.88990.24440.82580.73030.01080.5268

σE
σB
μE
μB
γF
γB

NormalNormalNormalNormal
Beta
Beta

0.27
0.092
0.016
0.078
0.984
0.962

0.01
0.005
0.002
0.01
0.01
0.01

0.26550.07620.0146
0.06200.98430.96210.24930.07000.0116
0.04340.97080.94590.28170.08290.01810.0804
0.99840.9780σ (ε B )σ (ε I )σ (ε G )σ (ε A )σ (ε R )σ (ε NF )σ (ε NE )σ (ε P )Inv. Gamma
Inv. Gamma
Inv. Gamma
Inv. Gamma
Inv. Gamma
Inv. Gamma
Inv. Gamma
Inv. Gamma

0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01

Inf
Inf
Inf
Inf
Inf
Inf
Inf
Inf

0.00190.02560.00800.01110.00150.08140.37360.08960.00150.02110.00720.01000.00130.07020.3351
0.06770.00230.02990.00880.01230.0017
0.09110.41370.1114

Distr.
ξp
κ
γp
θ

φπ
φy

Mean

S.D.

Mean

90th
percentiles
0.658810.54240.13860.8706
1.6277
0.03640.93710.50390.92100.87440.10570.8257

Table3: Correlation with alternative indicators

E

Z (+4)-R(+4)
E

Z (+3)-R(+3)
E
Z (+2)-R(+2)
Z E (+1)-R(+1)
E
Z (0)-R(0)E
Z (-1)-R(-1)
Z E (-2)-R(-2)
Z E (-3)-R(-3)
Z E (-4)-R(-4)

Spread of interest
Spread of interest
rate on contracted
rate on new shortshort-term loan rate
term loan rate
0.463
0.244

0.422

DI forlending attitudeof FIs
0.587

DI forfinancial position

0.502
0.532
0.544
0.559
0.571
0.579
0.576

0.230
0.209
0.163
0.091
0.039
0.022
-0.012

0.469
0.523
0.575
0.626
0.673
0.715
0.724

0.604
0.636
0.667
0.689
0.697
0.693
0.667

0.568

-0.042

0.689

0.609

Table4: Variance decompositions
Table4a: The Full Sample PeriodA

Investment
OutputInflation

ε
0.049
0.230
0.261

B

ε
0.034
0.148
0.358

G

ε
0.001
0.299
0.017

I

NF

ε

NE

R

ε
0.644
0.226
0.057

ε

0.046
0.010
0.030

0.222
0.036
0.066

ε
0.004
0.051
0.144

εI
0.654
0.287
0.079

ε NF
0.062
0.023
0.071

ε NE
0.211
0.041
0.082

εR
0.006
0.041
0.211

εI
0.615
0.202
0.042

ε NF
0.135
0.040
0.143

ε NE
0.181
0.012
0.042

εR
0.004
0.033
0.211

Table4b: During 1990-1999
Investment
OutputInflation

εA
0.016
0.174
0.194

εB
0.050
0.150
0.267

εG
0.001
0.285
0.014

Table4c: During 1995-1999
Investment
OutputInflation

εA
0.034
0.209
0.274

εB
0.030
0.107
0.200

εG
0.001
0.397
0.018

Notes: The variance decompositions are given by the variance of macroeconomic variables accounted for by each of the listed shocks divided by
the variance of corresponding macroeconomic variables accounted for by all of the shocks, based on the full sample period(the upper table), andlost decades(the middle and low table).

Table5: Variance decompositions under the alternative model

Table5a: Variance decompositions of investment under the alternative model
εA
0.049
0.030
0.036

Chained BGG
BGG
noBGG

εB
0.034
0.036
0.027

εG
0.001
0.000
0.000

εI
0.644
0.736
0.936

ε NF
0.046
n.a.
n.a.

ε NE
0.222
0.188
n.a.

εR
0.004
0.009
0.000

Notes: The variance decompositions are given by the variance of investment accounted for by each of the listed shocks divided by the variance ofinvestment accounted for by all of the shocks, based on the full sample period.

Table5b: Variance decompositions of spreads under the alternative model(1) Entrepreneurial Borrowing Spread (Z E -R )εChained BGG
BGG

A

ε

B

ε

G

ε

I

ε

NF

ε

NE

ε

R

0.004
0.001

0.005
0.017

0.000
0.001

0.022
0.008

0.253
n.a.

0.697
0.955

0.012
0.018

εA
0.303
n.a.

εB
0.267
n.a.

εG
0.025
n.a.

εI
0.083
n.a.

ε NF
0.020
n.a.

ε NE
0.012
n.a.

εR
0.191
n.a.

F

(2) FIs' Borrowing Spread (Z -R )Chained BGG
BGG

Notes: The variance decompositions are given by the variance of spreads accounted for by each of the listed shocks divided by the variance of
spreads accounted for by all of the shocks, based on the full sample period.

Figure 1: The time paths of macroeconomic variables used for estimating the model.
(1) Output(2) Investment

0.04

0.10
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
-0.08
-0.10

0.02
0.00
-0.02
-0.04
-0.06
1980

1985

1990

1995

2000

2005

1980

2010

1985

(3) Consumption(4) Interest Rate

0.04

0.04

0.02

0.03

0.00

0.02

-0.02

0.01

-0.04

1990

1995

2000

2005

2010

1990

1995

2000

2005

2010

1995

2000

2005

2010

0.00
1980

1985

1990

1995

2000

2005

2010

1980

1985

(5) Inflation(6) Net Worth of FIs

0.02

0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5

0.01

0.00

-0.01

-0.02
1980

1985

1990

1995

2000

2005

2010

2000

2005

2010

(7) Net Worth of Entrepreneurs
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
1980

1985

1990

1995

Notes: Shaded area are period of the recession.

1980

1985

1990

Figure 2: Identified shocks to entrepreneurial net worth and FIs' net worth.
Figure2a: Time Paths of the identified shocks to entrepreneurial net worth and FIs' net worth.
(1) Shocks to Entrepreneurial Net Worth
0.6(2) Shocks to FIs' Net Worth
0.08

0.4

0.04

0.2
0.00
0.0
-0.04
-0.2
-0.08

-0.4

-0.12

-0.6

81 83 85 87 89 91 93 95 97 99 01 03 05 07 09 11 13

81 83 85 87 89 91 93 95 97 99 01 03 05 07 09 11 13

Notes: 1.Shaded area are period of the recession.
Notes: 2.The identified shocks series to the entrepreneurial net worth and the FIs' net worth are smoothed by taking four-quartercentered moving average.

Figure2b: Comparision of the identified shocks between Japanese economy and U.S. economy(1) Shocks to Entrepreneurial Net Worth(2) Shocks to FIs' Net Worth

0.6

0.08

0.4

0.04

0.2
0.00
0.0
-0.04
-0.2
-0.08

-0.4
-0.6

Japan

U.S.

81 83 85 87 89 91 93 95 97 99 01 03 05 07 09 11 13

-0.12

Japan

U.S.

81 83 85 87 89 91 93 95 97 99 01 03 05 07 09 11 13

Notes: The identified shocks series to the entrepreneurial net worth and the FIs' net worth are smoothed by taking four-quartercentered moving average.

Figure 3: Impluse responses of the macroeconomic variables to the unexpected impairment of FIs'
networth and entrepreneurial net worth, the unexpected increase in investment adjustment cost, andthe unexpected decline of technology level.
(1) Investment
2(2) Output

10-3

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8
0
2
4
6
8
Quarter
FI's Net Worth Shock

10

12

14

16

18

20

0
2
Quarter

Entrepreneurial Net Worth Shock(3) Tobin's Q
10

10-3

4

6

8

10

12

14

Investment Adjustment Cost Shock

16

18

20

TFP shock(4) Inflation

10-3

4

10-3

3

5

2
0
1
-5

0

-10

-1
-2

-15
0
2
4
6
8
Quarter
FI's Net Worth Shock

10

12

14

16

18

Entrepreneurial Net Worth Shock(5) Net Worth of FIs
40

0
2
4
6
8
10
12
Quarter
Investment Adjustment Cost Shock

20

16

18

20

TFP shock(6) Net Worth of Entrepreneurs

10-3

50

20

0

0

-50

-20

-100

-40

-150

-60

-200

-80

-250

10-3

-300

-100
0
2
Quarter

4

6

8

10

12

FI's Net Worth Shock

14

16

18

0
2
Quarter

20

Entrepreneurial Net Worth Shock(7) Nominal Interest Rate
2

14

4

6

8

10

12

14

Investment Adjustment Cost Shock

16

18

20

TFP shock(8) Entrepreneurial Borrowing Rate

10-3

4

1

2

0

0

10-3

-2

-1
0
2
Quarter

4

6

8

FI's Net Worth Shock

10

12

14

16

18

20

Entrepreneurial Net Worth Shock02
Quarter

4

6

8

10

12

Investment Adjustment Cost Shock

14

16

18

TFP shock20

Figure 4: Historial contribution of each structural shocks in investment variations, output variations,and inflation variations.
(1) Investment
0.3

0.2

0.1

0.0

-0.1

-0.2
Monetrary Policy
TFP

OthersEntrepreneurial Net WorthInvestment Adjustment Cost
FI's Net Worth-0.3
82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13(2) Output
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
Monetrary Policy
Investment Adjustment Cost
Entrepreneurial Net Worth
total

-0.08
-0.10

Others
TFP
FI's Net Worth-0.12
82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13(3) Inflation
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06

Investment Adjustment Cost
Monetrary Policy
Entrepreneurial Net Worth
total

TFP
Others
FI's Net Worth-0.08
82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13