Asset Portfolio Choice of Banks and In‡ation
Dynamics
Kosuke Aokiyand Nao Sudoz
March 14, 2012

Abstract
Since the middle of 1990s, the Japanese banks have drastically tilted their asset
portfolio towards the government bonds, reducing their lending to …rms. In thispaper, we investigate the causes and consequences of the changes by introducing
the banks’asset portfolio decision into an otherwise standard New Keynesian dynamic stochastic general equilibrium model. The banks in our model constructtheir portfolio under the so-called value at risk constraint that requires banks repay their debt regardless of the realization of the asset returns. Consequently, thebanks’asset composition is a¤ected by the maximum loss of the asset returns andthe banks’net worth, in addition to the expected asset returns. We …nd that anincrease in down-side risks, deterioration of the banks’net worth, and slow down of
total factor productivity growth induce the banks to hold more government debt,
dampening investment and reducing in‡ation. We estimate the model by Baynesian estimation and …nd that such banks’ portfolio decision plays an importantrole in the accumulation of government bond and de‡ation since the latter 1990s.

Keywords: Value at Risk Constraint; Banks’Asset Allocation; De‡ation; Lost Decade.
The authors would like to thank Takatoshi Ito, Toshiki Jinushi, Munehisa Kasuya, Koichiro Kamada,Takeshi Kimura, Takashi Kozu, Eiji Maeda, Koji Nakamura, Kenji Nishizaki, Masashi Saito, Takatoshi
Sekine, Yosuke Takeda, Tsutomu Watanabe, participants at the fourth University of Tokyo – Bank ofJapan conference in November 2011, and the sta¤ of the Research and Statistics Deparmtent, the Bankof Japan, for their useful comments. The views expressed in this paper are those of the authors and do
not necessarily re‡ect the o¢ cial views of the Bank of Japan.
yAssociate Professor, Department of Economics, University of Tokyo (E-mail: kaoki@e.u-tokyo.ac.jp)
zDeputy Director, Research and Statistics Department, Bank of Japan (E-mail:nao.sudou@boj.or.jp).

11

Introduction

The long-lasting recession in Japanese economy since 1990s is often attributed to changes
in the real side of the economy, such as the slow down of total factor productivity andreduction of mandatory working hour1 . Recent studies such as Hoshi and Kashyap(2004, 2010), Caballero, Hoshi, and Kashyap (2008) and Hirose and Kurozumi (2010),
on the contrary, provide an alternative view, by emphasizing a channel through which
the malfunction of …nancial intermediation adversely a¤ects the economic activity. In
fact, the banking sector has been under constant shifts in economic environment during
the period. From the beginning of 1990s, the full-dress enforcement of Basel Committee
agreement is called for, and the banks face the need to meet the capital requirement. In
1997, the banking crisis triggered by a collapse of Sanyo and Yamaichi Securities hit theeconomy, deteriorating the banks’pro…t structures and balance sheets2 .
In this paper, we explore the qualitative and quantitative role played by the banking
sector during the lost decades. We shed lights on how the banks re-constructed theirasset portfolio under the changing economic environments, and its consequences to themacroeconomy, paying special attention to in‡ation dynamics34 .
To do this, we focus on another peculiar change in the economic environment–secularand accelerating increase in government bond issuance–during the lost decade. Upper
panel of Figure 1 displays the time path of government bonds outstanding relative to
GDP5 . The government bonds have a clear positive trend since the mid 1990s, partlyre‡ecting the government’s …nancial need for the successive implementation of economic
stimulus packages and a growing spending associated with social security6 . This expansion of government debt is, in fact, closely tied to the banks’ …nancial intermediation
activity. Figure 2 displays the banks’ asset allocation as well as the ratio of the government bond outstanding held by the banks over the total government debt. Clearly,
1

Hayashi and Prescott (2002), based on a simple growth model, show that a slow down of growth in
the total factor productivity can account for the economy downduring the 1990s. See also Otsu (2011)
for the role played by a labor wedge.
2
Kaihatsu and Kurozumi (2010) develop a model where frictions associated with the non-…nancialpart of the economy and the …nancial sector are both incorporated and evaluate their relative importances quantitatively.
3
Sugo and Ueda (2008), estimating a dynamic stochastic general equilibrium (DSGE) model a là
Smets and Wouters (2003) based on the Japanese data, report that most of the variations in in‡ation
in long horizon are accounted for by the variations in the target in monetary policy rule.
4
Hayakawa and Maeda (1997) and Sudo (2011) argue that the banking crisis aggravates the …nancial intermediation activity, encourages the households’ precautionary saving, and lowers velocity ofcirculation of money and price level.
5
The government bond includes treasury discount bills, central government securities and FILP
bonds, local government securities, and public corporation securities unless otherwise noted.
6
There is a growing literature about the accumulation of government bond in Japanese economy
from the perspective of government debt sustainability, including Doi et al. (2011) and Imrohologlu andSudo (2011). See Enomoto and Iwamoto (2008) for the welfare implication of …scal policy undertaken
during the lost decade.

2the banks’purchase of the government bonds starts to rise in the mid 1990s, while thebanks’ loan claim declined around the same period. As a consequence, a bulk of thegovernment bond outstanding is held by the banks. This observation suggests that thebanks’asset allocation has shifted from the loan claim to the government bond purchase,particularly since the latter half of 1997.
In order to explore the mechanism behind the banks’asset allocation and its macroeconomic implication, we incorporate an asset portfolio choice of banks into an otherwise
standard New Keynesian DSGE model. The banks collect savings from the households
and invest them into the two assets, the loan claim, which is equivalent to the investmentin the productive capital, and the government bonds. The banks choose their portfolio
so as not to violate the value-at-risk constraint (hereafter VaR constraint). Under the
VaR constraint, the banks are required to repay their debt, regardless of the realizationof the asset returns. While the returns from holding the loan claim and the government
bond are uncertain and can be lower than the deposit rate, the banks construct theirasset portfolio so that they do not go under even if the maximum losses are realized forboth assets. The VaR constraint of this kind is analyzed by Adrian and Shin (2011) asa source of cyclical ‡uctuations of bank leverage. By incorporating two assets into themodel, we depart from Adrian and Shin (2011) in that we investigate the banks’asset
portfolio decision as well as their asset size and that we focus on the linkage between thebanks’asset choice and the macroeconomic activity in a full-‡edged DSGE model.
The central mechanism in our analysis is the banks’ risk taking capacity7 . When
the VaR constraint is absent, the banks’ optimal asset portfolio decision implies thatthe expected returns from the two assets are equalized in equilibrium. When the VaR
constraint is present in the economy, the banks’asset portfolio is depends not only on
the expected returns but also on the maximum loss from holding those assets and thebanks’ net worth. For instance, when the downside risk of holding the loan claim increases, the banks rearrange their asset portfolios so as to avert the bankruptcy in thestate where the worst asset return realizes. The banks maintain their solvency even in
the worst state, by investing more in the asset whose maximum loss is smaller. Changes
in institutional environment, such as reinforcement of banks’capital requirement, maya¤ect the economy in the similar manner to changes in the downside risks8 . Such institutional initiatives encourage the rearrangement of the banks’asset portfolio by directly
controlling the banks’risk taking capacity.
The banks’net worth also plays a signi…cant role in the banks’asset portfolio decision.
7

In the current paper, we focuse on the economy where banks risk taking is limited because of theVaR constraint. Consequently, the amount of capital accumulated in the economy is scarce comparedwith the economy where such constraint is absent. By contrast, recent studies including Korinek (2011)
and Kato and Tsuruga (2011) investigate the economy where the …re-sale externality of assets leads toan ex-ante excessive investment by an individual bank.
8
Gerali et al. (2009) show that the deterioration of the banks’net worth or reinforcement of capitalrequirement may increase the lending rate and dampen the output, based on the model where lending
rate increases with the banks’net worth.

3

When the net worth deteriorates, the banks’repayment capacity in a worst state becomes
smaller than otherwise. In such a case, the banks avert bankruptcy by reducing theleverage as is shown by Adrian and Shin (2011), and by shifting the asset portfolio fromthe asset with a large maximum loss to that with a smaller maximum loss.
We then draw some implications of the bank portfolio decisions under VaR constraint
for the economic activity. Suppose that the uncertainty of capital return increases andhence the maximum loss of loan claim holding increases. The banks facing the VaR
constraint reduce their investment in the loan claims, purchasing more government bondwhose maximum loss is more limited. This implies that loan supply, reducing output(investment in particular) and in‡ation. The initial e¤ect in‡uences the expected asset returns and the banks’retained earnings in the subsequent periods, bringing aboutfurther e¤ects to the economy.
Our model’s implication is consistent with Japan’s experience since 1990. Japan
experienced the slow down in the growth of total factor productivity, the increased
enforcement of banks’capital requirement, the burst of bubbles in the early half of the
1990s, and the banking crisis in the latter half of the 1990s followed by an increase in thebad loans and deterioration of the banks’net worth. In our model, all of these events may
induce the banks’asset portfolio tilted toward the government bond purchase, generating
downward pressure on the in‡ation.
Our analysis is closely related to Braun and Nakajima (2011). They study the impact of accumulated government debt on the price level, focusing on the banks’ asset
allocation. The banks in their model hold the government bond as collateral to …nancetheir asset purchase. So far as the they have optimistic view about the future bondprice, they purchase the government bond by raising the fund from other agents, using
the government bond as collateral. Consequently, pile-up of the government bond andde‡ation coexist in the economy. While our paper also stresses the implication of thebanks’ asset allocation, the economic mechanism behind the banks’ government bondholding di¤ers from the one discussed in Braun and Nakajima (2011). In our paper,
the key determinant of the banks’asset portfolio is the severity of the VaR constraint.
Whenever the constraint is tightened, the banks tilt toward less risky assets from therisky assets.
Another research in line with our work is Brunnermeier and Sanikov (2011). They
construct a model economy where the market imperfection is present in the …nancial
intermediation activity. Whenever the adverse shock hits the economy, the agents tilt
their asset toward the safe asset, yielding de‡ation. This is because safe asset is in
nominal term in their paper, and the higher demand for the safe asset results in thedecrease in the price level. Although the same mechanism can be present in our model,
the channel through which the banks’asset allocation a¤ect the in‡ation is di¤erent. In
our model, ‡ight to safer asset prevents the capital accumulation, dampening the output
and generating the in‡ation.
Regarding the role played by uncertainty, our analysis is also related to the work by
4

Fernandez-Villaderde et al. (2011). They empirically …nd, using the structural vector
autoregression, that a higher volatility in the productivity lowers the price level andthe output, and provide a theoretical framework to analyze the relationship between
uncertainty and the households’asset allocation. In their model based on the inventory
model of money demand, they show that facing a larger uncertainty, the households
prefer safer and more liquid asset, money, to riskier goods.
The rest of the paper is organized as follows. Section 2 presents our model with banks
that endogenously choose the asset portfolio under the VaR constraint. In addition,
we explore the qualitative property of our model using a simpli…ed setting. Section
3 demonstrates our economy’s quantitative implications based on the model estimatedusing the Japanese data from 1980Q1 to 2007Q4. Section 4 concludes the analysis anddiscuss the future extension of our analysis.

2

The Model Economy

This section describes the structure of our model. The economy consists of seven typesof agents: household, banks, intermediate goods producers, wholesale goods producers,…nal goods producers, government and central bank. See Figure 3 for model’s brief
outline.
The representative household supplies labor inputs to the intermediate goods producers, receive wage, make deposit to the banks, and receive repayment for the deposit
in turn. She has no means to access to the …nancial market and cannot own the …nancial
assets but the bank deposit. The banks collect the deposits from the household, andinvest them on the two assets: the loan claim to the capital goods used by the intermediate goods producers, and the government bond. The banks construct their asset
portfolio composition so as not to violate the VaR constraint. The intermediate goods
producers hire the labor supply and capital goods from the household and the banks,
respectively, to produce the …nal goods. The wholesale goods producers produce thedi¤erentiated …nal goods from the intermediate goods. They are monopolistic supplierof the …nal goods, and set their prices so as to maximize their pro…t. The …nal goods
producers convert the di¤erentiated wholesale goods to the …nal goods. The government
collects lump-sam tax from the household and issues the government bond to …nance thegovernment debt and the government expenditure. The central bank controls in‡ation
by adjusting the nominal interest rate according to a Tayor rule.

2.1

Household

The in…nitely-lived representative household makes decision for consumption and deposit
holdings. She is barred from the …nancial market. She thus possess no real capital stock
nor government bond, and hold all of her saving in the form of bank deposit.

5The household has preference over the consumption goods c (st ) ; and work e¤ortl (s ), as described in the expected utility function, (1)
t

E0

1
X
t=0

t

t

t

U (c s ; l s ) = E01Xtlog c st + log 1

l st

;

(1)

t=0

where 2 (0; 1) is the discount factor and is the weighting assigned to leisure.
The budget constraint of the household is given by the equation below:
c st + d st = r d st 1 d st 1 +W (st ) tl s +P (st )

st

st

(2)

where d (st ) is the household’s deposit, rd (st 1 ) is the real deposit rate repaid by thebanks for the deposit made in period t 1, W (h; st ) is the nominal wage rate, P (st ) is
the price index, (st ) is the sum of the real pro…ts of the intermediate goods producers
and the banks that are returned to the household as dividends. (st ) is the lump-sum
real tax collected by the government. We assume that the deposit is risk-free asset, andthe real deposit rate is the real risk-free rate.
The …rst-order conditions associated with the household’s intertemporal decision is
given byUc (c st ; l st ) = rd st Et Uc (c st+1 ; l st+1 );where Uc denotes the marginal utility with respect to the consumption. Because thehousehold’s only …nancial asset is banks’deposit, her consumption growth is dependent
on the risk-free rate.
Since the labor market is competitive, we have
W (st )Ul (c (st ) ; l (st ))=;Uc (c (st ) ; l (st ))P (st )
where Ul denotes the marginal utility with respect to the leisure.

2.2

Banks

The outline of banks’choice
There is a continuum of risk-neutral banks, indexed by i 2 (0; 1) : Each bank i collects
deposit d (i; st ) from the households, and purchases the loan claim, namely capital stock,
B (i;st )k (i; st ) ; and the real government bond b (i; st ); from the …nal goods producers
P (st )and the government, respectively. The expenses are …nanced by the deposit d (i; st )and the bank i’s own real net worth n (i; st ) : The bank i’s balance sheet each period istherefore given by6

k i; st +B (i; st )= n i; st + d i; st :P (st )

(3)

The bank i receives returns from the two assets invested in the previous period, repays
the deposit to the households, and retains the rest of the earnings as the own net worth:Consequently, the bank’s net worth evolves according to the following law of motion:n i; st+1 = rk st+1 k i; st + rb st+1 b i; strd st dt i; st ;(4)

where rk (st+1 ) and rb (st+1 ) are the real return to the loan claim and the government
bond, respectively. Note that the real return to the government bond is given by thepolicy rate RB (st ) set by the central bank, divided by the in‡ation rate (st+1 ) throughthe relationship below.
rb s

t+1

RB (st )=:(st+1 )The bank i keeps the net worth accumulation up to the period when it exits fromthe economy.9 We assume that the bank’s exiting probability each period is exogenously
given by 1(st ) : The continuation value of the bank i is then given by
V n i; st

= Et

t;t+1

st V n i; st+1

+ 1

st

n i; st+1;(5)

where n (i; st ) is the net worth held by the bank i; and t;t+1 denotes the households’
stochastic discount factor from the period t to the period t + 1:
In choosing the asset portfolio composition between the two assets, the bank i considers a VaR constraint similar to the one discussed in Adrian and Shin (2011), together
with the expected average returns of the two assets. Namely, the bank i constructs theasset portfolio in period t so that it is able to repay all of its debt to the household
even if the two assets yield the maximum loss. Denoting the maximum loss from holding
the two assets by rk (st+1 jst ) and rb (st+1 jst ) ; respectively, the value at risk constraint isexpressed by
rk st+1 jst k i; st + rb st+1 jst b i; strd st d i; st

0:

(6)

Here, we assume that the loan claim holding has a larger risk compared with the government bond holding, so that rk (st+1 jst ) < rb (st+1 jst ) 10 : There are two possible interpretation as to the time varying maximus loss. On the one hand, shocks to economic
9

Following Gertler and Karadi (2011), we assume that the bank transfers all of the accumulated net
worth to the household when it exits from the economy.
10
In the current paper, we concentrate our analysis on the equilibrium where the banks hold both of
the two risky assets, and the worst returns of the two risky assets are smaller than the risk-free rate, sothat the two equations below hold.

7

environment, including an increase in downside risk about the asset return and an increase in uncertainty about macroeconomic outlook, lower the maximum loss of theassets. On the other hand, institutional changes, including reinforcement of capital requirement also bring the similar e¤ect. While the size of these maximum losses may beendogenously a¤ected by the economic surroundings, in the current paper, we treat themas given, concentrating our analysis on how these variations of losses a¤ect the economy.
The banks’maximization problem
In Adrian and Shin (2011) where there is only one type of asset, the VaR constraint
in‡uences the size of bank’s leverage. By contrast, in our model where there are two
assets in the economy, the VaR constraint in‡uences the asset portfolio allocation as
well as the size of the leverage. The bank i’s optimization problem is formulated as the
maximization of the value of the net worth at the last period it exists, which is shown by
equation (5) ; subject to the bank i’s balance sheet equation (3) ; the law of motion forthe bank i’s net wort accumulation (5) ; and the VaR constraint (3) : Because the banks
are risk-neutral, we …rst guess that the value function of the bank i is given by
V n i; stst n i; st ;=then the equation (5) is reduced tomax V n i; st= Et

1qk (st+1 ) k (i; st )st+1 @ +qb (st+1 ) b (i; st ) A+rd (st ) n (i; st )

st

t;t+1

st

+ 1

0

qk st+1 k i; st + qb st+1 b i; st + rd st n i; st:

The corresponding …rst order condition gives

Et

"

(

(st+1 ) + 1(st ))q k (st+1 )

t+1)
t;t+1 qk (s

#

= Et

"

(

(st+1 ) + 1(st ))q b (st+1 )

t+1)
t;t+1 qb (s#(7)
Here qk (s )rk (s ) rd (s ) and qb (s )rb (s ) rd (s ) denote the excess
return to the loam claim holding and that to the government bond holding relative
to the deposit, respectively. Similarly, q k (st+1 )rk (st+1 ) rd (st ) and q b (st+1 )
t+1

t+1

t

t+1

rk st+1 jst
t+1

rb s

t

js

t+1

rd st

< 0;

t

< 0:

rd s

8

t

:

rb (st+1 ) rd (st ) denote the excess return to the two risky assets when the worst returnto the assets realize.
The equation (7) provides the bank’s fundamental principle in allocating their assets
into the loan claim and the government bond. When the VaR constraint is e¤ective,
there is no need that expected excess returns of the two assets are not equalized at theequilibrium. Instead, banks’ asset portfolio is constructed so that the expected excess
returns weighted by the maximum loss of each asset are equalized. Under the premisethat the loan claim is riskier than the government bond, so that rk (st+1 ) < rb (st+1 ) ; theexpected excess return of the loan claim needs to exceed that of the government bond,Et rk (st+1 ) > Et rb (st+1 ) ; for compensation:
From equations (6) and (7) ; we obtain the expression for (st ) :st = Et

h

st

t;t+1

st ) rd st

st+1 + (11

qk st+1 =q k st+1

i

:
(8)

Aggregation
The banks exit from the economy with probability 1(st ) each period, and theaggregate banks’net worth evolves according to the following law of motion;n st =st

rk st k st 1 + rb st b st 1rd st 1 d st 1;

where n (st ) is the aggregate banks’ net worth. An increase in the exiting probability
reduces the bank’s net worth. As shown in the equation (6) ; the reduced net worth help
tighten the banks’VaR constraint, a¤ecting the banks’asset portfolio allocation in thesubsequent period
d1112 .

2.3

Intermediate Goods Producers

The intermediate goods producers produce intermediate goods y (st ) ; selling them tothe wholesale goods producers with the price Py (st ) : They hire labor inputs l (st ) fromthe household and borrow the e¤ective capital v (st ) K (st 1 ) from the banks. Both the11

Based on the …nancial accelerator model developed by Bernanke, Gertler, and Gilchrist (1999),
Gilchrist and Leahy (2002) and Nolan and Thoenissen (2009) study the consequence of the exogenous
deterioration of the entrepreneurial net worth to the economy. There the exogenous net worth change
is considered as an irrational innovation in expected return to the entrepreneurial net worth or shock to
the technology associated with the e¢ cacy of the …nancial intermediation.
12
There are alternative ways to incorporate the shocks to the banks’ net worth into the model. In
Gertler and Karadi (2011), the existing capital stock becomes out of date, deteriorating the value ofthe banks’loan claim and net worth. In Aoki and Nikolov (2011) where the banks’investment on the
bubble is analyzed, the collapse of the bubble leads to a deterioration of the banks’net worth.

9input and output market of the intermediate goods producers are competitive. The
maximization problem of the intermediate goods producer is given by
max
t
t 1

y(st );v(s )k(sPy (st ) y (st ));l(st )P (st )

W st l st ;r~ st v st k st 1

subject toy st = v st k st 1

A st Z st l st

1

(9)

;

where v (st ) is the capital utilization rate, k (st 1 ) is the capital stock, r~ (st ) is the real
return to the use of e¤ective capital, A (st ) is the stationary component of technology
level, Z (st ) is the non-stationary component of technology level, and 2 [0; 1] is thecapital share. The …rst order conditions of the intermediate goods producers yield thefollowing equality.
Py (st )1
1
v st k st 1
A st Z st l st;
P (st )
Py (st )W (st )
1=
(1
) v st k st 1
A st Z stl st
P (st )P (st )
r~k st=:

The capital utilization rate is determined by the banks. Assuming that choosing
capital utilization v (st ) ; together with the capital stock k (st 1 ) ; incurs the real cost ofv k (st 1) (v (st ))
+1

+1

1

;

to the banks, then the banks’optimal capital utilization rate is expressed by
r~k st = ( + 1)v vt ;

where v and are parameters that govern capital utilization rate. Consequently, thebanks’net return to the investment on the productive capital rk (st ) is given by
rk st k st = r~k st k st

vk

st 1

v st

+1

) k st ;+ (1where 2 [0; 1] is the depreciation rate of the capital stock. Similarly, the real wage paid
to the household is expressed by
W (st )
= s st (1P (st )

) v st k st 1

10

A st

1

Z st

1

l st

:

2.4

Wholesale and Final Goods Producers

Optimization problem of wholesale and …nal goods producers
The wholesale goods sector contains a continuum of …rms, each producing di¤erentiated products, as indexed by z 2 [0; 1] ; from the intermediate goods by the linear
production technologyx(z; st ) = y(z; st ):Here, x(z; st ) denotes the di¤erentiated wholesale goods made by the wholesale goods
producer z and y(z; st ) is the intermediate goods used as inputs by the producer z.
The …nal goods producer purchases these di¤erentiated goods in a competitive market, producing the …nal goods from wholesale goods by the following CES aggregate
technology"Z

x st =# 1"("s(s)t )
t

1

( )
x(st ; z) "(st ) dz
" st

1

0

;

" st > 1

where " (st ) 2 (1; 1) denotes the time-varying elasticity of substitution between thedi¤erentiated goods. Given this CES technology of the …nal goods, the demand for eachdi¤erentiated goods x (z; st ) is given by a function of the price of its product p(z; st );the aggregate price index P (st ), and the aggregate demand for the …nal goods x (st ) ; as
below"(st )

p(z; st )P (st )tx(z; s ) =x st :

Each wholesale goods producer z maximizes its pro…t by choosing the product priceoptimally. The maximization problem of each di¤erentiated producer is given by

max
Et
t+j

p(z;s

)

1
X
j=0

j

2

6
6
6
j 1;j 66
4p(z;st+j )P (st+j )1 "(st )(st+j )Py
P (st+j )
2

x (s

t+j

p(z;st+j ))"(st )P (st+j )p(z;st+j )p(z;st+j 1 )p(st+jp(st+j

3

1

)

2)

x (st+j )2
p(z;st+j )P (st+j )"(st )x (st+j )

7
7
7
7;
7
5

where the third term denotes an adjustment cost that producer pays in changing its
product price p(z; st ); and is the parameter that governs the size of adjustment cost.
Because all of the di¤erentiated goods prices p(z; st ) set by the wholesale goods
producers are identical at the symmetric equilibrium, we obtain the Phillips curve of theeconomy from the …rst order condition of this …rm’s maximization problem.
11

" st

Py (st )P (st )

1

0:5

st

1

2

st

+1
st+1

+

1

st
st+1

1

x (st+1 )= 0: (10)x (st )The market clearing condition
The market clearing condition of the intermediate goods and the wholesale goods are
given byZ 1

x st ; z dz = y st ;
0
Z 1
t
x s
x st ; z dz=
0

The …nal goods serves as the household’s consumption, investment to productivity
capital, and the government expenditure. The market clearing condition of the …nal
goods is given byc st +k st

2.5

(1

) k st 1 +G st = x st

2

st

1

2

x st

vk

st 1 v st+1

Government and Central Bank

The government collects a lump-sum tax P (st ) (st ) from the household and issues agovernment bond B (st ) to …nance the repayment RB (st 1 ) B (st 1 ) to the banks andgovernment expenditure P (st ) G (st ) : We assume that a balanced budget is maintainedin each period t as follows:
RB st 1 B st 1 + P st G st = P st

st + B st :(11)

The government tax policy is an increasing function of the outstanding government bondthat is speci…ed by the following equation:st = T b st 1b (st 1 )x (st );

(12)

where 2 (1; 1] is an elasticity of lump-sum tax with respect to the government debt
status, indicating that an increase in bond leads to an increase in tax, and T is a constantparameter.
12

The central bank sets the nominal interest rate according to a simple Taylor rule
given byln RB st = (1M ) ln R +M ln RB

st 1 + (1M)

st + r st ;

ln

(13)

where R is constant, M 2 [0; 1] is the autoregresive coe¢ cient of the polity rate, and> 1 is the policy weight attached to the in‡ation rate and r (st ) is an i.i.d. shock to
the monetary policy rule13 .

2.6

Shock Process

The exogenous shocks in our economy, the shock to the markup-related elasticity " (st ) ;the bank’s net worth (st ) ; the maximum loss of the two assets rk (st ) and rb (st ) ; thestationary component of technology A (st ) ; the non-stationary component of technology
Z (st ) ; and government expenditure G (st ), evolve according to the equation below:
ln " stln st= ln " + " st ;= (1) ln +

ln rk st= (1ln rb sttln A sln Z stu Z stln G st= (1rk ) ln r k +rb ) ln r b +

ln

s

t 1

+

(14)
(15)

t

s ;

rk ln r k

st 1 + r k st ;(16)

rb ln r b

t 1

(17)

s

t 1

t

+ rb s ;t= (1+ A s ;A ) ln A + A ln A st 1t= ln Z s+ uZ s ;t 1= Z uZ s+ Z st ;t 1= (1+ G st ;G ) ln G + G ln G s

(18)
(19)
(20)
(21)

where " ; ; rk ; rb ; A ; Z ; and G 2 (0; 1) are the autoregressive root of the corresponding shocks, and " (st ) ; (st ) ; rk (st ) ; rb (st ) ; A (st ) ; Z (st ) and G (st ) are theexogenous i.i.d. shocks that are normally distributed with mean zero.

2.7

Equilibrium Condition

An equilibrium consists of a set of prices, fW (st ) ; P (st ) ; Py (st ) ; rk (st ) ; r~k (st ) ; rd (st ) ;tttrb (st ) ; RB (st )g1(st ) ; k (st ) ; v (st ) ; x (st ) ;t=0 , and the allocations fc (s ) ; l (s ) ; d (s ) ;ty (st )gg1
(st )g1
t=0 ; for a given government policy fG (s ) ;t=0 , realization of exogenous
13

Our parameterization of the policy parameters and are both greater than unity implies that
our economy is in the Ricardian regime for both …scal and monetary policy. Relatedly, in the current
paper, we do not consider the case of the government’s default. In Non-Ricardian regime with government defaults, in‡ation rate is only uniquely pinned down when the central bank responds to in‡ation
aggressively. See, for example, Kocherlakota (2012).

13

variables f " (st ) ; (st ) ; rk (st ) ; rk (st ) ; A (st ) ; Z (st ) ; G (st ) ; r (st )g1
t=0 ; the ex;andinitialconditions
fB
g;fd
pected worst returns frk (st ) ; rb (st )g1
1
1 g; fk 1 g
t=0such that for all t; i; and z :(i) the household maximizes her utility given the prices;(ii) the bank i maximizes its pro…ts given the prices and the expected worst returns;(iii) the intermediate goods producer maximizes its pro…ts given the prices;(iv) the wholesale goods producer z maximizes its pro…ts given the prices;(v) the …nal goods producer maximizes its pro…ts given the prices;(vi) the government budget constraint holds;(vii) the central bank sets a policy rate following the Taylor rule; and(viii) markets clear.

2.8

Steady State Analysis

Before investigating the model’s dynamics, we explore the model’s mechanism at thesteady state to show the determinants of the banks’portfolio composition. In particular,
we focus on how the returns from holding the two risky assets rb and rk are a¤ected by
the banks’ VaR constraint, and how the banks’ decision as to the portfolio allocation
between the government bond b and the loan claim k is made14 . For illustrative purpose,
we made two simplifying assumptions in this subsection: (1) the households supply labor
inelastically, l = 1; and (2) the banks’capital utilization cost is zero, = 015 :Evaluating the portfolio choice equation, the VaR constraint equation, and the lawof motion of the bank’s net worth at the steady state values, we have,
rk
rd
(rk

rd ) k + (rb

rb rd
rd
=
;
rk
rd r brd ) b =
rd n;
n =

1

rd

(22)
(23)
[(rk

rd ) k + (rbrd ) b] :(24)

Notice that the household’s Euler equation at the steady state implies that
rd =
14

1

:

The de…nition of the steady state in our economy needs to be carefully stated. Suppose that wede…ne the steady state as the economy where all of the exogenous shocks are absent and every endogenous
variables grow at the constant rate. The banks’ asset allocation then becomes indeterminate because
the their portfolio choice is dependent on the riskiness of the assets. In the current paper, we de…ne thesteady state following the Devereux and Sutherland (2010, 2011) where the banks take the possibility
that worst scenario of the asset return realize into the consideration. Consequently, the risks of holding
the assets a¤ect the banks’portfolio at the steady state.
15This assumption implies that the capacity utilization is unity.

14

The three equations above yield the excess return from holding the two risky assets, andthe spread of the two risky assets;

rb

rd =

rk

rd =

rk

rb =

1

rd

(rd

rb ) ;(25)(rdrk ) :(26)(rbrk ) :

(27)

rd
1

rd
rd

1

rd
rd

According to the equation (25) and (26), the excess return from holding the two risky
assets and the spread between the two assets are expressed by the expected worst returns
from holding the two risky assets rb and rk , together with the bank’s survival probability:
When the risk of holding the loan claim rk increases, for instance, the bank’s VaR
constraint becomes tightened unless the bank reduces the loan claim. Consequently,
the bank requires a higher spread in holding the loan claim than otherwise. The thegovernment bond yield is una¤ected by the change in rk : The similar mechanism works
if the risk of holding the government bond rb increases:
By contrast, a reduction in the survival probability lead to a rise in the two excess
returns. As indicated by the equation (24) ; the smaller probability prevents the banksfrom accumulating the net worth. Because the scarcity of the net worth tightens the
VaR constraint by deteriorating the bank’s balance sheet, it results in the reduction of
the bank’s purchase of both of the two risky assets. The excess returns for the two assets
therefore increase to clear the demand.
Next, we discuss how the banks allocate their asset between the loan claim k andthe government bond b. Because the return from holding the loan claim rk equals to thereturn to the capital stock in the economy, we have1

rk = AZk+ (1):

Since the loan claim is equivalent to the capital stock in the equilibrium, we have
k=

rk

(1
AZ

)

1
1

:

(28)

Taking that
1 < 0 into the consideration; a higher return for the loan claim implies
a smaller size of a loan claim and thus a smaller investment in the economy. Based on
the discussions above, an increase in the risk of holding the loan claim or a decline in
the banks’surviving probability reduce the loan claim through a rise in the return rk :15

The bank’s decision as to the holding of the government bond is a¤ected by thegovernment policy regarding taxing and budget balance. From the equations (11) and(12) ; we haverb b = T b + b;
b =

rb

1
T

1

x=

rb

1

1

AZk :

T

(29)

Here we assume that in‡ation rate is unity as the steady state. These governmental
equations suggest, for a value > 1; that the banks tilt toward holding of the government
bond as the corresponding return increases. Under the current tax policy, an increase in
the government’s interest rate payment is met by the comparable increase in government
bond issuance, leading to a higher government bond holding by banks. Similarly to theworking mechanism that determinants the loan claim k, the increasing risk of holding
the government bond, given by a decline in rb ; or the disruption of the bank’s net worth,given by a decline in ; leads to an increase in the bank’s government bond holding,through a rise in the government bond yield.
Lastly, we discuss how the bank allocates its asset between the government bond holding and the loan claim to the …rms. From the equations (28) and (29) ; the government
bond holding relative to the loan claim is given by
rb 1
b
=
k
T

1

rk

(1

)

:

According to the above equation, any changes in the economic environments that boost
the return to the two risky assets rb and rk ; including the increasing risk of lending to the…rms, that of holding the government bond, or the disruption of the bank’s net worth,cause the bank to purchase more of the government bond compared with the loan claim
to the …rms.
To summarize, the key determinants behind the banks’tilting toward the government
bond are the relative increase in the risk of holding the real asset and the shortage ofthe banks’net worth. In the next subsection, we depart from the steady state analysis,
and explore the implication of the bank’s asset allocation to the in‡ation dynamics, by
log-linearizing our model around the steady state.

2.9

VaR Constraint and In‡ation Dynamics

By log-linearizing equations (7) and (13) around the steady state; we have

16

Et

=

rk
rk

rd

r^k st+1

rd
rk

+ Et

rd
rd

rb

rd

+

rk
rd

rk

r^k st+1

rd
rd

rd
rk

rd

rb

Et

rb
rb

rd

r^b st+1

Et

rb
rd

r^b; st+1

rb(30)

r^d st :^ b st = ^ st :R

(31)

Here ^ (st ) denotes the log deviation of a variable
Taking the following relationship(st ) from its steady state value.

^ b;tr^b st+1 = R^ st+1

into our consideration, we have^ st =

1

Et ^ st+1 + a1 r^k st+1 + a2 r^k st+1

a3 r^b st+1 + a4 r^d st

:

(32)

Here, a1 ; a2 ; a3 ; and a4 are all positive values that are denoted by
rb rd rk
rb rd r k
rb rd r b
; a2 =; a3 =rd rk rd
rb rd r krd rd r b
rd
rd
rd
rb rd
rd
+
a4 =
:
rb
r b r d rk rd
r d r b rd r k

a1 =The equation (32) indicates the qualitative link between the banks’asset allocationand in‡ation rate in the economy. Other things, including the in‡ation expectation
Et [^ (st+1 )] ; being equal, in‡ation is determined by the four variables, r^k (st+1 ) ; r^k (st+1 ) ;r^b (st+1 ) ; and r^d (st ) : Suppose the return from holding the loan claim is high, an ample
capital is accumulated, yielding a strength to the economy and generating in‡ation. The
decrease in the risk of holding the loan claim r^k (st+1 ) or the increase in the risk of holding
the government bond r^b (st+1 ) causes the in‡ation through the similar mechanism. The
rise in the deposit rate r^d (st ) generates in‡ationary pressures to the economy. While ahigher deposit rate prevents the net worth accumulation of the banks, it encourages thebanks’purchase of the loan claim relative to the government bond, increasing the capital
goods in the economy. The mechanism behind is that under the premise thatr k < r b < rd < rb < rk ;the excess return to the government bond is sensitive to a change in the deposit ratecompared with that to the loan claim. Consequently, the banks’ asset allocation tilt
towards the real capital, leading to in‡ation in the economy.
17

3

Quantitative Analysis

In this section, we investigate the quantitative implication of our model, including the role
played by the banks’VaR constraint. Based on the Japanese data, we …rst estimate themodel’s parameters and extract the eight structural shocks, the markup shock " (st ) ; thebank’s net worth shock (st ) ; the shock to the maximum loss of loan claim rk (st ) ; theshock to the maximum loss of government bond rk (st ) ; the temporary technology shocktt
A (s ) ; the permanent technology shock Z (s ) ; and the government expenditure shocktr (s ) ; using the Bayesian technique. We then explore the model’s equilibrium responseto these exogenous shocks. In particular, we discuss how the VaR constraint a¤ects
the model’s dynamics after the shocks. Next, we explore the quantitative contributionof each shocks in explaining the variations of macroeconomic variables, including thebanks’asset allocation, in‡ation, and GDP.

3.1

Data

Our benchmark dataset includes eight time series of the Japanese economy from 1980Q1
to 2007Q4: (1)the labor input16 , corresponding to l (st ) in the model, (2)the real private
investment, based on National Accounts of Japan, corresponding to k (st ) (1) k (st 1 )in the model, (3)the sum of treasury discount bills, central government securities and
FILP bonds, local government securities, and public corporation securities held by thedomestically licensed banks, de‡ated by the GDP de‡ator, constructed from Flow ofFunds, corresponding to b (st ) in the model, (4)stock price index of banks de‡ated by
the GDP de‡ator, based on the data of Tokyo Stock Exchange, corresponding to n (st ) in
the model; (5)the capacity utilization of manufacturing industry based on the indices ofindustrial production, corresponding to v (st ) in the model; (6)the GDP de‡ator, basedon National Accounts, corresponding to P (st ) in the model, (7)the call rate set by the
Bank of Japan, corresponding to RB (st ) in the model, and (8)the real GDP based on
National Accounts of Japan, corresponding to x (st ) in the model. All of the series, otherthan the series (5) and (7) ; are …rst di¤erenced. The series (5) and (7) are used in level.

3.2

Prior and Posterior Distribution of the Parameters

The parameter values used for our quantitative analysis are reported in Table 1. The
parameter values are quarterly unless otherwise noted. Since our model is a standard
New Keynesian model except that our model incorporates the banks’ asset portfolio
choice, we set some of the parameters to the conventional values. These parameters arereported in Table 1(2).
16

To construct the labor input series, we follow the methodology adopted in Hayashi and Prescott(2002).

18

Other parameters are estimated by the Bayesian technique, because they are speci…cin the current model. The third to the …fth columns of Table 1(1) report the priordistribution of the estimated parameters. The last three columns in Table 1(1) display
the posterior mean and the con…dence intervals of the model parameters.

3.3

Impulse Responses

In this subsection, we investigate the economy’s dynamic response to structural shocks.
Figure 4 to 11 display the economy’s impulse response function to a negative shockto the technology growth rate Z (st ) ; a negative shock to the stationary component oftechnology A (st ), a negative shock to the banks’surviving probability (the deteriorationof the banks’ net worth) (st ), a negative shock to the maximum loss of loan claimttrk (s ), a negative shock to the maximum loss of government bond purchase rb (s ), atpositive shock to the monetary policy rule r (s ), a positive shock to the markup " (st ),and a negative shock to the government expenditure G (st ), respectively. All of theequilibrium paths are approximated by the log-linearization around the steady state.
In order to underscore the role played by the VaR constraint in the economic variations, we plot the equilibrium response to a comparable shock under the alternative
economy in which the VaR constraint is absent (labeled as “no VaR” and denoted by
the line with black circles), together with the equilibrium response under the economy
with the VaR constraint (labeled as “benchmark” and denoted by the line with whitecircles). The economy of “no VaR,”is equivalent to our benchmark economy, except thatthe constraint equation (6) is not e¤ective. Because the banks no longer take the assets’maximum loss or the net worth into consideration, the their investments are independent
from these factors, and the expected return are equalized in the equilibrium.
As shown in Figure 4, the permanent downward shift in the technology permanently
dampens economic activity, investment, and banks’ net worth, yielding the downward
pressure to the in‡ation. Although this shock also generates the in‡ationary pressure bydirectly lowering the productivity of the wholesale goods production, this e¤ect is o¤set
by the weakened household’s demand caused by the output decline. Compared with thecase where the VaR is absent, the shock under the benchmark economy generates quantitatively larger macroeconomic e¤ects. This is because of the endogenous developmentof the banks’net worth after the adverse shock. Since the technology shock reduces thebanks’net worth, the banks under the VaR constraint shrink their leverage and avert thedefaults. Consequently, less capital is accumulated in the economy, leading to a further
decline in output. Figure 5 shows the economic response when the negative temporaryshock strikes the economy. In this case, the response of in‡ation becomes positive, as
the marginal cost increase of the wholesale goods producer, stemming from the lowered
productivity, becomes dominant mechanism. The output falls only temporarily, but themagnitude of the fall is greater under the VaR model than the no VaR model.
Figure 6 displays the macroeconomic consequence of the banks’net worth disruption.
19

Note that in the economy where the VaR constraint is absent, the banks’ net worth
cannot be a source of the economic ‡uctuations. The deterioration brings about de‡ation
and recession to the economy. There are two channels in which the net worth shockin‡uences the banks’ investment decisions. First, as pointed out by Adrian and Shin(2011), the banks shrinks their balance sheet, reducing the purchase of both the loan
claim and government bond. When their net worth is scarce, the banks …nd it di¢ cultto repay their debt in the case that the maximum loss realize. Second, the banks reduce
the purchase of the loan claim disproportionately compared with the government bond.
Since the maximum loss of the loan claim is large, the banks tilt their assets toward
relatively safer asset, as the VaR constraint is tightened. The both channels lead toa reduction in the aggregate investment on the real capital, dampen the output andsuppress the in‡ation.
Figure 7 displays the equilibrium response to the increase in the maximum loss inholding the loan claim. As indicated by the equation (7) ; since the loan claim becomes
relatively riskier than otherwise, the banks tilt the asset portfolio toward the government
bond whose expected return weighted by the maximum loss is now higher. The reduced
loan claim implies a decline in the productive capital, leading to a depressionary pressure
to the economy.
Figure 8 displays the equilibrium response to the increase in the maximum loss inholding the government bond. In this case, since the government bond holding becomes
relatively risky, the banks shift the asset portfolio towards loan claim. They reduce
the government bond, increasing the capital goods purchase, following the equation (7) ;resulting in the output expansion and in‡ation17 .
The responses of our model economy to the positive markup shock, contractionary
monetary policy and government expenditure shock, are, in general, not qualitativelydi¤erent from those under the standard New Keynesian model, as shown in Figure 9, 10,
and 11, respectively. The rise in markup dampens output and raises in‡ation, and thecontractionary policy shocks lower both output and in‡ation. Similarly to the outcomeof the shocks discussed above, because of the endogenous evolvement of the banks’net
worth, the markup shocks and government expenditure shocks yield larger quantitative
response of the economy under the benchmark model than the no VaR model. Afterthe monetary policy shock, the rise in the policy rate increases the government debt
repayment to the banks, help accumulate the banks’net worth. Consequently, adversee¤ect of the shock is o¤set.
17

The mechanism behind the expansionary e¤ect of the shocks to the maximum loss of the government
bond depends on our setting that the economy is closed economy. Suppose that there is a room forthe domestic banks to invest overseas, the capital ‡ow may go overseas, reducing domestic capital
accumulation.

20

3.4

The Role of VaR Constraint

To summarize the e¤ect of incorporating the VaR constraint into the model, we report
the steady state values and the theoretical moments of the macroeconomic variables
around the steady state, under the benchmark model and the no VaR model, in Table 2.
The values of shared parameters in the two models are set to equal values. Because threeof the structural shocks, shocks to the banks’net worth " (st ) ; shocks to the maximum
loss of the loan claim "rk (st ), and shocks to the maximum loss of the government bond"rb (st ), are absent in the no VaR model, we report the standard deviations for the twosettings, a case where all of the eight shocks are present and a case where …ve out of theeight shocks are present in the economy, for comparison.
According to Table 2(1), the output and capital accumulation are smaller, and government bond accumulation is larger at the steady state under the VaR. Because the VaR
constraint suppresses the banks’risk taking capacity, the banks tilt toward government
bond holding compared with the economy where such constraint is absent. Consequently,
capital and output are reduced.
Table 2(2) reports the standard deviation of the growth rate of macroeconomic variables. It is seen that the VaR ampli…es the macroeconomic e¤ect of exogenous shocks
hitting the economy. Under the VaR model, in addition to the direct e¤ect of shocks,
the endogenous development of the banks’net worth leads to a further variations in thebanks’leverage and the asset portfolio allocation, giving a higher volatility to the growth
rates.

3.5

Contribution of Structural Shocks during Lost Decades

Using the estimated model parameters and extracted shocks, we investigate the role ofeach structural shock in explaining macroeconomic variations during the lost decades.
Table 3 displays the decomposition of the variations in GDP, in‡ation, and government
bond purchase into the eight shocks for the two sub-sample periods: period before thebubble burst (from 1981Q1 to 1990Q4), which we call period I, and the period during
and after the banking crisis (from 1997Q1 to 2007Q4), which we call period II.
In explaining GDP variations, temporal shocks to the technology play the key role.
During the period II where the average output growth rate is signi…cantly slower thanthat during the period I, the technology shock remains as the key source of the GDP‡uctuations. The contribution of other shocks are quantitatively limited, and most ofthem contribute negatively to the GDP growth.
In explaining in‡ation variations, the quantitative role played by the permanent technology shock rather than the temporal technology shock is signi…cant. One reason behind
this observation stems from that the in‡ation rate is forward-looking variable that is lessa¤ected by the temporal change in the technology. Comparing the two sub-sample periods, it is seen that the monetary policy shock ranks the second important shock during
the period I and the banks’net worth shocks contributes the most in the period II. Both21

the permanent technology shock and the bank’s net worth shock contribute the reduction in in‡ation from period I to period II. As the impulse response exercise suggests,a slow down of the technology growth, a deterioration of the banks’net worth, and anincrease in the maximum loss of the government bond reduce the supply of capital tothe economy, by shrinking the banks’leverage and changing the banks’asset portfolio
allocation toward government bond, leading to lowered output and in‡ation.
While the growth rate of government bond purchase increases from period I to period
II, the bulk of the variations is accounted for by the shocks to the permanent technology
shock. Comparison between period I and period II suggests that a slow down of thetechnology growth in period II is responsible for the accumulation of the government
bond and reduction of the capital. Contribution of the monetary policy shock is large
during period I while it is negligible during period II. During period I, the policy rate
is well above zero, leaving a room for the government bond purchase to response to amonetary policy shock. During period II, the variation of the policy rate is limited andthe government bond variation is a¤ected less by the shock. During period II, the shocks
to the banks’ net worth and the maximum loss of the loan claim play the importantrole. The deterioration of the banks’ net worth lowers government bond growth by
reducing the banks’leverage. The shocks to the maximum loss contribute negatively to
the government bond growth by shifting the banks’asset portfolio from the loan claim.
Contribution of the shocks to the maximum loss of the government is negligible. Possible
interpretation behind this result is that the default risk of the Japanese government is not
actualized, and the government bond is regarded as safe asset even after the enforcementof capital requirement.
Our analysis above suggest that shocks to the banks’net worth and the maximum
loss of the assets are not the dominant shocks in explaining the output and in‡ation.
This results, however, does not indicate that VaR is not important in explaining the
economic ‡uctuations As discussed in subsection above, the VaR plays the importantrole in amplifying the macroeconomic e¤ect of exogenous shocks through the endogenousdevelopment of the banks’net worth.

4

Conclusion

During the lost decades, the Japanese economy has experienced the long-lasting de‡ationand the unprecedented government debt. Focusing on that the banks’asset allocation
increasingly shift to the government bond holding from the lending to the …rms during
the period, we propose a theoretical explanation that stresses the implication of thebanks’asset allocation to the macroeconomy.
To this end, we introduce the banks’ portfolio allocation between the government
bond holding and the loan claim to the …rm into an otherwise standard New Keynesianmodel. The banks in the model choose their asset allocations so that the value atrisk constraint is not violated. Our model implies that a slow down of the total factor
22

productivity growth rate, the disruption of the banks’net worth after the bubble burst,
and an introducing of the capital requirement, encourage the banks to accumulate thegovernment bond holding, reducing the loan claim to the …rms. As the real capital
investment is reduced, the output growth slows down, leading to de‡ation.
Our results have policy implications when the economic recession is associated withthe reduction of banks’ risk taking behaviors. In the economy where the uncertainty
about capital investment plays as the key obstacle, the policy aiming to reduce theminimum loss of investment may be e¤ective.

23

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25

(Figure1)
Accumulation of Government Debt and Deflation(1)Government bond outstanding over GDP(times)

1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
80

FY

85

90

95

00

05

10

95

00

05

10

(2)Inflation dynamics(annual growth rate)

4
3
2
1
0
-1
-2
-3
-4
80

CY

85

90

(note) Statistics Released from the Ministry of Finance and Cabinet Office.

(Figure2)

Banks' Asset Allocation(1) Portion of government bond holding over the total asset : domestically licensed banks
20

（％）

18
16
14
12
10
8
6
80

FY

85

90

95

00

05

10

(2) Portion of loan claim over the total asset : domestically licensed banks
75

（％）

70
65
60
55
50
80

FY

85

90

95

00

05

10

(3) Portion of government bond outstanding held by domestically licensed banks
46

（％）

42
38
34
30
26
22
18
80

FY

85

90

95

00

05

10

(note1) Statistics Released from the Ministry of Finance and the Bank of Japan.
(note2) Dotted line in (3) displays the portion of government bond held by the banks including postal savings.

(Figure3)

Capital

Goods Producers○Produce goods from laborand capitalInterest Rate
Banks
Wage
○Invest on loan claim to firms
andgovernment

Deposit Rate

○Make a deposit to banks

own net worth

assetHouseholds

bondpurchase, using deposit and○ConstructLabor

portfolio,

considering the Value at Risk

Depositconstraint.
Taxation

Bond Purchase

Government○Tax households to financerepayment and expenditure○Central Bank adjusts Policy

Repayment

1Rate, following Taylor Rule.

(Figure4)

Economic Response to Permanent Technology Shock(1)Output(2)Inflation
0

0
-0.01

Benchmark

-0.02

-0.01

no VaR

-0.02

-0.03

-0.03

-0.04
-0.05

Benchmark-0.04

no VaR

-0.06
-0.05

-0.07
-0.08

-0.06
0

4

8

0

12 16 20 24 28 32 36 40(3)Loan Claim plus Bond Purchase48

12 16 20 24 28 32 36 40(4)Capital Return Spread

0.02
0.002
0
1E-17
-0.02

-0.002-0.04-0.004
Benchmark-0.06-0.006

Benchmarkno VaR-0.08-0.008

-0.1

-0.01
0

4

8

12

16

20

24

28

32

36

40

(5)Bond Purchase over Loan Claim

0

4

8

12

16

20

24

28

32

36

40

32

36

40

(6)Banks' net worth
0.03

0.01
Benchmark0.005

no VaR

0.02
0.01

Benchmark

0
-0.01

0

-0.02
-0.03
-0.04

-0.005

-0.05
-0.06

-0.01

-0.07

0

4

8

12 16 20 24 28 32 36 40

0

4

8

12

16

20

24

28

(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

(Figure5)

Economic Response to Temporal Technology Shock(1)Output(2)Inflation
0.015

0
-0.01
-0.02
-0.03

0.01

-0.04

Benchmark-0.05

Benchmarkno VaR

-0.06
-0.07

no VaR

0.005

-0.08
-0.09
-0.1
0

-0.11
0

4

8

12

16

20

24

28

32

36

40

(3)Loan Claim plus Bond Purchase

0

4

8

12

16

20

24

28

32

36

40

(4)Capital Return Spread

0

0.001
0.0005

-0.01

0
-0.02

-0.0005

BenchmarkBenchmark-0.001

no VaR-0.03-0.0015-0.002

-0.04
0

4

8

12

16

20

24

28

32

36

0

40

(5)Bond Purchase over Loan Claim

48

12 16 20 24 28 32 36 40(6)Banks' net worth

0.01

0-0.005

0.005

-0.01
-0.0150-0.02-0.025
Benchmark-0.005

Benchmark-0.03
no VaR-0.035

-0.01

-0.04
0

4

8

12

16

20

24

28

32

36

40

0

4

8

12

16

20

24

28

32

36

(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

40

(Figure6)

Economic Response to Shock to Banks' Net Worth(1)Output(2)Inflation

-0.02

0.01
0
-0.01

-0.04
Benchmark-0.02
Benchmark
-0.03

-0.06

-0.04
-0.05

-0.08
0

4

8

12

16

20

24

28

32

36

0

40

(3)Loan Claim plus Bond Purchase48

12 16 20 24 28 32 36 40(4)Capital Return Spread

0

0.12
0.1

-0.05

0.08

Benchmark

0.06
-0.1
0.04

Benchmark

0.02

-0.15

0
-0.2

-0.02
0

4

8

12

16

20

24

28

32

36

40

(5)Bond Purchase over Loan Claim

0

0

0.03

-0.05

0.02

-0.1
Benchmark

0

8

12

16

20

24

28

32

36

40

(6)Banks' net worth

0.04

0.01

4

Benchmark

-0.15

-0.2
0

4

8

12 16 20 24 28 32 36 40

0

4

8

12 16 20 24 28 32 36 40(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

(Figure7)

Economic Response to Shock to Maximum Loss of Loan Claim(1)Output(2)Inflation
0.1

0.04

0.08

0.02

0.06

0

0.04

-0.02

0.02

Benchmark

0
-0.04

-0.02

Benchmark

-0.04

-0.06

-0.06

-0.08

-0.08

-0.1

-0.1
0

4

8

0

12 16 20 24 28 32 36 40(3)Loan Claim plus Bond Purchase48

12 16 20 24 28 32 36 40(4)Capital Return Spread

0.02

0.12
0.1

0.01

0.08
0

0.06

-0.01

0.04

BenchmarkBenchmark

0.02
-0.02
0
-0.03

-0.02
0

4

8

12

16

20

24

28

32

36

40

0

4

8

12 16 20 24 28 32 36 40(5)Bond Purchase over Loan Claim(6)Banks' net worth

0.02

0.25

0.2

Benchmark0.01

Benchmark

0.15
0
0.1
-0.01
0.05
-0.02

0
0

4

8

12

16

20

24

28

32

36

40

0

4

8

12

16

20

24

28

32

36

40

(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

(Figure8)

Economic Response to Shock to Maximum Loss of Bond Purchase(1)Output(2)Inflation
0.002

0.00060.0004

BenchmarkBenchmark0.001

0.000200-0.0002-0.0010

4

8

12 16 20 24 28 32 36 40(3)Loan Claim plus Bond Purchase

0

4

8

12

16

20

24

28

32

36

40

(4)Capital Return Spread

0.00050.002

Benchmark0.001
0Benchmark0-0.0005-0.001
0

4

8

12

16

20

24

28

32

36

40

0

4

8

12 16 20 24 28 32 36 40(5)Bond Purchase over Loan Claim(6)Banks' net worth

0.0001

0.003

0

0.002

-0.0001

0.001
Benchmark-0.0002-0.0003

Benchmark0-0.0010

4

8

12 16 20 24 28 32 36 40

0

4

8

12 16 20 24 28 32 36 40(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

(Figure9)

Economic Response to Markup Shock(1)Output(2)Inflation
0.02

0Benchmark

-0.05
0.01
-0.1

no VaR

Benchmarkno VaR

-0.15

0

-0.01

-0.2
0

4

8

0

12 16 20 24 28 32 36 40(3)Loan Claim plus Bond Purchase48

12 16 20 24 28 32 36 40(4)Capital Return Spread
0.004

0
-0.01

0.003

-0.02
Benchmark-0.03

no VaR
-0.04
-0.05

0.002
Benchmark
0.001

0

0

4

8

12 16 20 24 28 32 36 40(5)Bond Purchase over Loan Claim
0.005

0

4

8

12

16

20

24

28

32

36

40

32

36

40

(6)Banks' net worth
0
-0.01
-0.02

0

-0.03
-0.04

-0.005

Benchmarkno VaR

-0.01

-0.05
-0.06

Benchmark

-0.07
-0.08
-0.09

-0.015

-0.1
0

4

8

12 16 20 24 28 32 36 40

0

4

8

12

16

20

24

28

(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

(Figure10)

Economic Response to Monetary Policy Shock(1)Output(2)Inflation

0

0.01
0
Benchmark-0.01-0.005
no VaR-0.02

Benchmark

-0.03

-0.01

no VaR

-0.04
-0.05

-0.015
0

4

8

12

16

20

24

28

32

36

40

(3)Loan Claim plus Bond Purchase

0

4

8

12 16 20 24 28 32 36 40(4)Capital Return Spread
0.002

0.005
0.004

0

0.003
Benchmark0.002

no VaR0.001
0-0.002-0.004-0.006

Benchmark-0.001-0.008-0.002-0.003

-0.01

0

4

8

12 16 20 24 28 32 36 40(5)Bond Purchase over Loan Claim
0.007

0

4

8

12 16 20 24 28 32 36 40(6)Banks' net worth
0.02

Benchmark0.015

no VaR

Benchmark
0.01

0.002

0.005
0
-0.005-0.0030

4

8

12 16 20 24 28 32 36 40

04

8 12 16 20 24 28 32 36 40(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

(Figure11)

Economic Response to Fiscal Expenditure Shock(1)Output(2)Inflation-0.0150-0.002-0.004-0.02

Benchmark-0.006

no VaR

Benchmark-0.008

no VaR-0.01-0.025
0

4

8

12

16

20

24

28

32

36

0

40

(3)Loan Claim plus Bond Purchase48

12 16 20 24 28 32 36 40(4)Capital Return Spread
0.001

0Benchmark

-0.01

0

no VaR-0.02-0.001
Benchmark-0.03-0.002-0.04-0.0030

4

8

12 16 20 24 28 32 36 40(5)Bond Purchase over Loan Claim

0

4

8

12

16

20

24

28

32

36

40

(6)Banks' net worth

0

0.005
Benchmark-0.0050no VaR-0.01-0.005-0.015

-0.01

-0.02

-0.015-0.025

-0.02

-0.03

-0.025
0

4

8

12

16

20

24

28

32

36

40

Benchmark0

4

8

12 16 20 24 28 32 36 40(note) Vertical axis denotes the deviation from the steady state and horizontal axis denotes the number of quarter after the shock.

（Table1）
Parameter of Model(1) Estimated Parameters
ParameterκpφAdjustment Cost of PriceMonetary Policy Rule (coefficient for inflation)

ρA

Monetary Policy Rule ARγ

Survival Probability of Banksrk

Maximum Loss of Loan Claimrb

Maximum Loss of Bond Purchase
Fiscal Policy Rule
Fiscal Policy Rule (coefficient for debt)
Government Expenditure Share
Preference about Goods Variety
Permanent Technology Shock AR
Temporal Technology Shock AR
Banks' Net Worth Shock AR
Shock to Maximum Loss of Loan Claim AR
Shock to Maximum Loss of Bond Purchase AR
Government Expenditure Shock AR
Monetary Policy Shock SD
Permanent Technology Shock SD
Temporary Technology Shock SD
Price Markup Shock SD
Banks' Net Worth Shock SD
Shock to Maximum Loss of Loan Claim SD
Shock to Maximum Loss of Bond Purchase SD
Government Expenditure Shock SD

T

ψ
G/ X

ε

ρZ
ρA
ργ
ρr
ρr
ρG

k

b

σr

σZ
σA
σε
σγ
σr
σr
σG
σ θ

k

b

,l

Prior
Dist.
norm
norm
norm
norm
norm
norm
norm
norm
norm
norm
beta
beta
beta
beta
beta
beta
invg
invg
invg
invg
invg
invg
invg
invg

Prior
Mean
4
1.5
0.75
0.9
0.7
0.95
0.01
2
0.17
7
0.75
0.129
0.75
0.75
0.129
0.129
0.009
0.035
0.009
0.009
0.035
0.009
0.035
0.035

(2)Calibrated Parameter

α
β

η
δ

Capital Share in Final Goods Production
Households' Discount Factor
Households' Preference over Leisure
Depreciation Rate

0.35
0.99
0.5
0.025

Prior Std.
1.5
0.125
0.125
0.01
0.01
0.01
0.01
0.125
0.1
0.125
0.22
0.22
0.22
0.22
0.22
0.22
Inf
Inf
Inf
Inf
Inf
Inf
Inf
Inf

mean
6.09
1.19
0.93
0.90
0.70
0.95
0.003
1.97
0.17
6.97
0.98
0.64
0.98
0.83
0.74
0.99
0.005
0.005
0.083
2.646
0.039
0.154
0.005
0.280

Posterior
5%
6.08
1.19
0.93
0.90
0.70
0.95
0.002
1.96
0.16
6.97
0.98
0.63
0.98
0.83
0.74
0.99
0.002
0.005
0.079
2.612
0.034
0.134
0.002
0.260

95%
6.11
1.19
0.93
0.90
0.70
0.95
0.004
1.97
0.17
7.00
0.98
0.64
0.98
0.83
0.75
0.99
0.009
0.005
0.086
2.617
0.042
0.174
0.009
0.320

(Table2）
Effect of VaR constraint on the economy(1) Comparison of the steady state value of macroeconomic variablesyoutput at steady statekbcapital at steady state

σ θ

,

l

b/k

Economy with VaR

Economy without VaR

1.5
6.6
1.5
0.2

2.3
19.3
0.9
0.1

Economy with VaR

Economy without VaRgovernment bond at steady state
relative size of government bond w.r.t. capital(2) Variation of macroeconomic variables around the steady statestd (∆y )std (∆k )std (∆b)
std (∆(b + k ))σ θ

std (π ),lstandard deviation of output growthstandard deviation of capital growthstandard deviation of growth of government bondstandard deviation of leverage
standard deviation of inflation rate

0.30
0.07
0.15
0.07
0.15

[0.26][0.04][0.12][0.05][0.08]

0.20
0.02
0.11
0.03
0.07

(note) [ ] denotes standard deviation of the variable when shocks to the banks' net worth and maximum loss of assets are absent from the econom

(Table3)

Contribution of Structural Shocks in Macroeconomic Variations(1) Output Growth (Quarterly)(a) before 1990 (b) after banking crisis (b)-(a)（1981Q1-1990Q4） （1997Q4-2007Q4）
average growth rate（％）
Permanent Technology ShockTemporary Technology ShockBanks' Net Worth Shock
Shock to Maximum Loss of Capital
Shock to Maximum Loss of Bond
Other ShockMonetary Policy ShockGovernment Expenditure Shock

0.4
5.6
68.8
3.8
2.7
0.0
14.8
1.3
3.1

0.1
2.1
82.0
3.8
2.5
0.0
6.7
0.0
2.9

(▼)
(▼)
(▼)
(▼)
(▼)
(▼)
(▼)
(△)

full sample（1981Q1-2007Q4）

6.7
72.0
4.3
2.7
0.0
10.5
0.8
3.0

(2) Inflation (Quarterly)(a) before 1990 (b)after banking crisis（1981Q1-1990Q4） （1997Q4-2007Q4）
average growth rate（％）
Permanent Technology ShockTemporary Technology ShockBanks' Net Worth Shock
Shock to Maximum Loss of Capital
Shock to Maximum Loss of Bond
Other ShockMonetary Policy ShockGovernment Expenditure Shock

0.3
49.7
5.0
2.3
4.1
0.0
11.4
26.6
0.9

-0.3
30.0
3.2
42.1
14.3
0.0
5.8
3.6
1.0

(b)-(a)full sample（1981Q1-2007Q4）

(▼)

41.9
6.2
13.0
6.0
0.0
9.3
22.8
0.9

(△)
(▼)
(△)
(▼)
(▼)
(△)
(△)

(3) Bond Purchase Growth (Quarterly)(a) before 1990 (b)after banking crisis（1981Q1-1990Q4） （1997Q4-2007Q4）
average growth rate（％）
Permanent Technology ShockTemporary Technology ShockBanks' Net Worth Shock
Shock to Maximum Loss of Capital
Shock to Maximum Loss of Bond
Other ShockMonetary Policy ShockGovernment Expenditure Shock

-0.2
23.1
9.7
3.4
5.7
0.0
17.2
31.6
9.2

0.4
32.5
16.8
20.4
19.9
0.0
4.2
1.9
4.2

(b)-(a)full sample（1981Q1-2007Q4）

(△)

35.0
13.2
5.9
5.8
0.0
9.5
23.0
7.5

(▼)
(▼)
(△)
(▼)
(▼)
(▼)
(△)

(note1) △（▼）indicates that the corresponding shock contributes positively (negatively) during period (b) relative to perio(note2) Other Shock includes contribution of initial values as well as contribution of markup shocks.
The contribution of the former component is, however, negligible compared with the latter component.