Global COE Hi-Stat Discussion Paper Series 277

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

External Shocks and Japanese Business Cycles:
Evidence from a Sign-Restricted VAR

Hi-Stat Discussion Paper

Hiroshi Morita

January 2013

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

External Shocks and Japanese Business Cycles :Evidence from a Sign-Restricted VAR∗
Hiroshi Morita †15 January 2013

Abstract
This paper investigates the sources of Japanese business ﬂuctuations since the1990s taking into account both external shocks (e.g., risk premium and foreign
demand shock) and domestic supply and demand shocks. We use the sign-restricted
VAR model based on the theoretical model to identify these. The presented results
show that 20% to 40% of the forecast error variances in output can be explainedby external shocks. Further, we demonstrate that supply shocks are the maininﬂuencing factor in Japanese business ﬂuctuations throughout the sample period
and that risk premium shocks have played an important role in post-2008 Lehman
shock recession.

Keywords: External shock, DSGE model, sign-restricted VAR
JEL codes: F41, E32∗

We would like to thank my supervisor Etsuro Shioji for the helpful comments and encouragement.
We also acknowledge Naohito Abe, Tuan Khai Vu, Jun-Hyung Ko for their valuable comments. Finally,
We would like to express gratitude to Hitotsubashi University’s GCOE Program for the grant that madeit possible to complete this study. Of course, all errors are our own.
†
Graduate School of Economics, Hitotsubashi University, E-mail: hiroshi.morita1013@gmail.com

1

1

Introduction

The Japanese economy is greatly inﬂuenced by external factors, such as the exchange
rate, foreign demand, and oil prices. However, researchers have paid especially close
attention to the external shocks that have inﬂuenced the Japanese economy since theLehman shock in 2008, notably because of the subsequent large reduction in the country’s
output and exports. For example, Kawai and Takagi (2009) and Shioji and Uchino (2011)
examine the eﬀect of the Lehman shock using the vector autoregression (VAR) modeland emphasize the ﬁnding that external shocks play an important role in the Japanese
economy. Similarly, Shioji et al. (2011) indicate the importance of external shocks on
the Japanese economy by estimating the open economy Dynamic Stochastic General
Equilibrium model using the Bayesian MCMC method.
In line with these previous studies, this paper also investigates the role of external
shocks in Japanese business cycles. However, it contributes to the body of knowledge
on this topic by identifying risk premium and foreign demand shock as external shocks
that have aﬀected the Japanese economy since the 1990s in addition to supply and demand shock. Moreover, we employ the sign-restricted VAR model developed by Uhlig(2009) and recently used by Peersman (2005), Mountford and Uhlig (2009), and Pappa(2009) in order to overcome the problems in an identiﬁcation of structural shocks andmisspeciﬁcation of the model that have limited previous studies. A sign-restricted VAR
model identiﬁes shocks by restricting the shape of the impulse response functions (IRFs),
making the consideration of the order of exogeneity among the variables unnecessary. In
addition, this particular type of model clariﬁes what kind of shock is identiﬁed because
the restrictions are based on theoretical models. Given these advantages, the struc2

tural shocks described in this paper are more correctly identiﬁed compared with previous
studies that have adopted the Cholesky decomposition. Although estimating the model
estimation using Bayesian methods allows structural shocks to be explicitly deﬁned in
the theoretical model, thereby simplifying their interpretation, the correct results can failto be estimated if the model is built inaccurately. The sign-restricted VAR can overcome
this problem, however.
In this paper, the sign restrictions imposed on the VAR model are derived from thetheoretical model, namely the Real Business Cycle (RBC) and New Keynesian (NK)models. First, the theoretical IRF for each structural shock is calculated under these twomodels and then the features that are common to both models are adopted as restrictions.
Through this approach, the paper mitigates the possibility of misspeciﬁcation in theestimation model.
Speciﬁcally, this paper examines the degree to which business ﬂuctuations in Japan
can be explained by external shocks and investigates which shocks play an importantrole in each phase of the business cycle. For that purpose, we perform the forecast
error variance decomposition (FEVD) and historical decomposition (HD) as well as IRF
analysis. These methods enable us to evaluate the eﬀect of external shocks not only
qualitatively but also quantitatively. Although a number of previous studies have used
these tools to analyze Japanese business cycles (e.g., Miyao, 2000, 2006), to our knowledge
this paper is the ﬁrst to perform a HD taking external shocks into consideration.
The results of the FEVD indicate that 20% to 40% of the variations in output can be
explained by external shocks. Further, the HD clariﬁes that supply shock mainly explains
the growth in output throughout the sample period. However, the ﬁndings also demon-3strate that external shocks play a major role in the phases of all business ﬂuctuations.
In particular, foreign demand shock has contributed to the economic recovery since 2002,
while risk premium shock explains a large part of the reduction in output and exports
since the Lehman shock. These results conﬁrm the importance of external factors in linewith the ﬁndings of previous studies.
The remainder of this paper is organized as follows. In Section 2, the theoreticalmodel is built in order to ascertain the feasible sign restrictions. The theoretical IRFs
are also drawn under various parameterizations and restrictions are derived from thecommon IRF features. In Section 3, we describe the empirical methods and data used inthis paper. Section 4 presents the estimation results of the IRF, FEVD, and HD analyses.
Section 5 concludes.

2

Theoretical modelThis section derives the sign restrictions from the theoretical model. First, we constructa small open economy NK model that is a variant of the one presented by Leeper et al.
(2011). Their model is a medium-scale two-country model that has real and nominal
rigidities and that was built to analyze the eﬀect of ﬁscal policy. Therefore, a NonRicardian, who is faced with liquidity constraints, and debt ﬁnancing are incorporated
into the model. Further, a local currency pricing approach is adopted; in other words,
domestic intermediate goods ﬁrms set their export prices in a foreign currency unit.
The most important feature of their model is that the benchmark NK model nests
the RBC model. By contrast, in previous studies that have adopted the sign-restricted
VAR model (e.g., Braun and Shioji (2007); Pappa (2009)), sign restrictions have been4

based on the common features of the IRFs generated from the RBC and NK models. On
this point, Leeper et al. (2011)’s model has advantageous characteristics for the present
analysis.
However, this paper does not estimate the model using Bayesian methods; it rather
employs a simpler model compared with that of Leeper et al. (2011). Speciﬁcally, severalof the settings used to capture the properties of the actual data (e.g., habit formationand capital utilization rate) are omitted from the model proposed herein. Instead, we
explicitly introduce import goods ﬁrms that set their import goods prices under Calvo(1983)-type price stickiness in order to examine how the degree of pass-through inﬂuencessuch prices.

2.1

Households

The economy consists of two types of households: (i) optimizing or Ricardian households
denoted by R and (ii) rule-of-thumb or Non-Ricardian households denoted by N . While
Ricardians can access capital markets, Non-Ricardians do not own any assets and simply
consume their current disposable incomes in each period. A fraction µ ∈ [0, 1] of the
population is Non-Ricardians and the remaining is Ricardians. Regardless of the typeof household, each household belongs to the type i labor union. Thus, each provides adiﬀerentiated labor input, n(i) and obtains a nominal wage, W (i).
R
Ricardian households choose their real consumption cRt (i) and hours worked nt (i) tomaximize lifetime utility

5

[ R 1−γ
1+λ ]ct (i)− 1 nRt (i)U = E0
−
β
1−γ
1+λ
t=0
∞
∑

t

(1)

subject to the ﬂow budget constraint

R
R
R
R
Pt cR
t (i)+Pt it (i) + Bt (i) + St Ft (i) + Pt τt (i)

(2)

R
k R
∗
R
R
(i) + Wt (i)nR
St Ft−1= Rt−1 Bt−1(i) + Rt−1
t (i) + Pt rt kt−1 (i) + Dt (i)and the capital accumulation equation{RktR (i) = (1 − δ)kt−1
(i) +

( R
)}
it (i)
1−s R
iR
t (i)
it−1 (i)(3)

where β, γ, and λ denote the discount rate, risk aversion, and inverse of the Frisch labor
elasticity, respectively. Capital letters denote nominal variables, and Pt is the price ofa ﬁnal good. Ricardians receive interest payments from domestic and international oneperiod risk-free nominal bonds denoted by Bt and Ft , respectively as well as wage income
Wt nt , rental income from capital rtk kt , and dividends Dt . However, they consume cRt andRinvest iR
t , and they pay a lump-sum tax denoted by τt . The gross nominal interest rate

paid for domestic and international bonds are Rt and Rt∗ . Since the international bondand its interest payment are denominated in foreign currency units, they are converted
into home currency units by multiplying by a nominal exchange rate St . Concerning
capital accumulation, we assume an investment adjustment cost s(·)iR as in Christiano

6

et al. (2005), where s(1) = s′ (1) = 0 and s′′ (1) > 0.1
In return, Non-Ricardians simply consume all their current disposable incomes. By
denoting the consumption of and hours worked by type i Non-Ricardians as cNt (i) andnNt (i), they thus face the following budget constraint in each period:NN
P t cNt (i) = Wt (i)nt (i) − Pt τt (i)(4)

where τtN denotes the lump-sum tax paid by Non-Ricardians.

2.2

Wage setting

As mentioned above, each household provides a diﬀerentiated labor input nt (i) for intermediate goods ﬁrms. A perfectly competitive labor force produces a composite eﬀective
labor nt according to
[∫ 1
nt =

nt (i)εw −1εw] ε εw−1
w
di

(5)

0

where εw denotes the elasticity of substitution across the diﬀerent types of labor inputs.
As a result of the labor bundler’s problem, the demand function for each diﬀerentiatedlabor input is expressed as(
nt (i) =1

Wt (i)
Wt)−εw
nt , for all i,

In this paper, we deﬁne investment adjustment cost as κ ≡ 1/s′′ (1)7(6)

and the aggregate nominal wage is equal to
[∫ 1
1−εw

Wt =

Wt (i)] 1−ε1
w
di
.

(7)

0

Here, we assume that labor demand is uniformly distributed regardless of types of households.
With respect to wage setting, we follow the modeling used in Gali et al. (2007) andColciago (2011), in which each labor union i sets its nominal wage Wt (i) to maximize
the weighted average of the lifetime utility of Ricardians and Non-Ricardians. In eachperiod, a labor union resets the optimal nominal wage Wt∗ (i) with a probability 1 − ρw .
Thus, the problem for a labor union i is written as
∞
∑

[

1−γ
1−γ
cN
− 1 nt+s (i)1+λcR−1t+s (i)t+s (i)
+
µ
−
max
E
ρ
Λ
(1
−
µ)
t
w t,t+sWt∗ (i)
1
−
γ
1
−
γ
1+λ
s=0

]
(8)

R −1
subject to (2), (4), and (6), where Λt,t+s = β s (cRdenotes the stochastic discountt+s /ct )factor. In the symmetric equilibrium, the ﬁrst-order condition can be expressed as

Wt∗ (i) =

∑
1+λ
Et ∞
εw
s=0 ρw Λt,t+s nt+s
],
[
nt+s
nt+s
εw − 1 E ∑∞ ρs Λ
+
µ
(1
−
µ)
t
s=0 w t,t+s
Pt+s cR
Pt+s cN
t+s

(9)

t+s

and combining this with (7), the evolution of the aggregate nominal wage is given by11−εw 1−εw
Wt = [(1 − ρw )Wt∗ 1−εw + ρw Wt−1
]
.

8

(10)

2.3

Firms

2.3.1

Final goods firms

Final goods ﬁrms are assumed to face perfectly competitive markets. They produce ﬁnal
goods yn,t by combining a bundle of domestic intermediate goods yh,t and a bundle ofimported intermediate goods yf,t according to the following CES production function:
[

1
η

η−1
η

1
η

η−1
η

yn,t = ω yh,t + (1 − ω) yf,t

η
] η−1

(11)

where η is the elasticity of substitution between domestic and imported intermediate
goods, and ω ∈ [0, 1] denotes the degree of home bias in producing ﬁnal goods. Similar to
ﬁnal goods, bundles of domestic and imported intermediate goods are produced according
to the following technology[∫ 1yh,t =

yh,t (j)

θp −1
θp

[∫ 1

p
] θ θ−1p

dj,

and yf,t =0

yf,t (m)

θp −1
θp

p
] θ θ−1
p
dm

(12)

0

where θp is the elasticity of substitution between diﬀerentiated intermediate goods.

2.3.2

Domestic intermediate goods firms

Domestic intermediate goods ﬁrms j ∈ [0, 1] that are faced with a monopolistically competitive market produce diﬀerentiated intermediate goods according to the Cobb–Douglas
production function:

yh,t (j) = At kt−1 (j)α nt (j)1−α .

9

(13)

where At denotes total factor productivity (TFP), which is given exogenously. Intermediate goods are assumed to be not only purchased by ﬁnal goods ﬁrms in the home country,
but also exported abroad.
Although the market for intermediate goods is monopolistically competitive, the factor
market faced by intermediate goods ﬁrms is assumed to be competitive. As a result of
the cost minimization problem for intermediate goods ﬁrms, the real marginal cost mct
is given by()α
wt(1 − α)rtk
mct =.
(1 − α)At
αwt

2.4

Price setting

2.4.1

Domestic intermediate goods firms(14)

As noted above, domestic intermediate goods ﬁrms sell their goods in both home andforeign markets. These prices are charged separately according to the demand in eachmarket. In the home market, demand for ﬁrm j’s output yh,t (j) is given by(

Ph,t (j)yh,t (j) = ωPh,t)−θp (

Ph,t
Pt

)−η
yn,t ,(15)

where Ph,t (j) is the output price in the home market set by ﬁrm j and Ph,t is an aggregate
price index of domestic intermediate goods, which is derived from a proﬁt maximization
problem of ﬁnal goods ﬁrms and intermediate goods bundlers. Similarly, demand for ﬁrm

10

j’s output yx,t (j) in the foreign market is assumed to be(yx,t (j) =

∗
(j)
Px,t
∗
Px,t

)−θx
ytF or(16)∗∗
where Px,t(j) and Px,t
are the export price charged by ﬁrm j and an aggregate exported

goods price index, respectively, which are denominated in the foreign currency unit, whileytF or is aggregate foreign demand, which is given exogenously.
According to the demand functions (15) and (16), intermediate goods ﬁrms set theirdomestic and export prices under a Calvo (1983) mechanism. Therefore, the problem ofdomestic intermediate goods ﬁrms j setting Ph,t (j) is written as

max EtPh,t (j)∞∑[]ρsh Λt,t+s Ph,t (j)yh,t+s (j) − Pt+s yh,t+s (j)mct+s

(17)

s=0

subject to (15), where ρh denotes the probability that they cannot reoptimize their do∗
mestic prices. Likewise, the problem of setting export prices Px,t(j) ismax
Et∗

Px,t (j)

∞
∑

[ ∗
]
ρsx Λt,t+s Px,t(j)St+s yx,t+s (j) − Pt+s yx,t+s (j)mct+s

(18)

s=0

subject to (16), where ρx also denotes the probability that they can not reoptimize theirexport prices.
Solving these problems, a log-linearized NK Phillips curve (NKPC) is obtained asfollows:π̂h,t = βEt π̂h,t+1 +(1 − ρp )(1 − βρp )[m̂ct − P̂h,t + P̂t ]
ρp

11

(19)

∗
∗
π̂x,t
= βEt π̂x,t+1+(1 − ρx )(1 − βρx )∗[m̂ct − Ŝt − P̂x,t+ P̂t ]
ρx(20)

where a hat denotes the log deviation from the steady state.

2.4.2

Imported goods firms∗
Imported goods ﬁrms m ∈ [0, 1] import diﬀerentiated foreign goods yf,t (m) at prices Pf,tdenominated in the foreign currency unit and sell them to ﬁnal goods ﬁrms at prices
Pf,t (m) denominated in the home currency unit. It is assumed that imported goods
ﬁrms are also faced with a monopolistically competitive market and thus set their prices
Pf,t (m) under Calvo (1983)-type price stickiness. Thus, in each period they reset theirprices with a probability 1 − ρf in order to maximize the discounted sum of proﬁt ﬂows

max EtPf,t (m)

∞
∑

[
]
∗
ρsf Λt,t+s Pf,t (m)yf,t+s (m) − Pt+s yf,t+s (m)St+s Pf,t+s

(21)

s=0

subject to demand for imported goods yf,t (m)(Pf,t (m)yf,t (m) = (1 − ω)Pf,t)−θp (

Pf,t
Pt

)−η
yn,t

(22)

where Pf,t is the aggregate import price index. As for the problem of domestic intermediate goods ﬁrms, the NKPC is given byπ̂f,t = βEt π̂f,t+1 +(1 − ρf )(1 − βρf ) ∗[P̂f,t + Ŝt − P̂f,t + P̂t ].
ρf

12

(23)

2.5

Fiscal policy and monetary policy

The government budget constraint is

Bt + Pt τt = Pt gt + Rt−1 Bt−1

(24)where gt denotes real government spending and is regarded as an exogenous variable. As
shown in Gali et al. (2007) and Leeper et al. (2011), tax is assumed to respond to thedebt-to-GDP ratio. Hence, a ﬁscal rule is written byτ̂t = ϕb b̂t−1 + ϕg ĝt(25)

where τ̂t ≡ (τt − τ )/y, b̂t ≡ (Bt /Pt − B/P )/y, and ĝt ≡ (gt − g)/y.
In return, the monetary authority sets the nominal interest rate rt following the Taylor
ruler̂t = ϕπ πt + ϕs Ŝt(26)

where r̂t denotes the log deviation of the net nominal interest rate from the steady-statevalue. Further, the nominal interest rate is also assumed to respond to the log deviationof an exchange rate Ŝt by following Lubik and Schorfheide (2005) and Adolfson et al.
(2007).

13

2.6

Rest of the model

2.6.1

Risk premium and foreign assets

As described in Shioji et al. (2011), the interest rate of a foreign bond denominated in
the foreign currency unit rt∗ is linked to a constant world interest rate rw through theuncovered interest rate parity condition with a risk premium term that depends on the
net foreign asset position (St Ft /Pt Yt ){rt∗ = rw + ψ()}
St F texp −− 1 + urisk
t
Pt Yt

(27)

where urisk
denotes the risk premium following an exogenous process. In this speciﬁcation,t
if the home country is a net borrower (i.e., Ft < 0), it has to pay an interest payment
higher than the world interest rate to the foreign country.
In addition, the dynamics of the net foreign asset are written by∗∗
St Ft = Rt−1
St Ft−1 + St Px,tyx,t − Pf,t yf,t .

(28)

This implies that the trade balance equals the capital account balance in each period.

14

2.6.2Market clearing condition and resource constraint

Aggregate consumption, lump-sum taxes, capital, investment, domestic and internationalbonds, and dividends are given byRRN
ct = (1 − µ)cRt + µct ; kt = (1 − µ)kt ; Bt = (1 − µ)Bt ;R
τt = (1 − µ)τtR + µτtN ; it = (1 − µ)iRt ; Ft = (1 − µ)Ft ;Dt = (1 − µ)DtR .

The clearing conditions in the factor and goods markets are expressed as
∫ 1
nt =

∫ 1
nt (j)dj; kt =0

kt (j)dj;
0yn,t = ct + it + gt

and the resource constraint is

yt = yh,t + yx,t .

15

2.6.3

Exogenous variables

With respect to the evolution of exogenous variables urisk, ytf or , At , gt , we assume thetfollowing AR(1) processrisk= ρrisk ûriskûriskt−1 + et
t

(29)

f or
ŷtf or = ρf or ŷt−1+ eft or(30)Ât = ρa Ât−1 + eat(31)ĝt = ρg ĝt−1 + egt(32)

where erisk, eft or , eat , egt represent risk premium, foreign demand, supply, and demandt(government spending) shocks, respectively.

2.7

Calibration

The model period is assumed to be one month in order to match the frequency of thedata used in the empirical analysis. The calibration parameters are set based on theﬁndings of previous studies. Some parameters that characterize the degree of rigidity
and stance of monetary policy take two kinds of values. Speciﬁcally, we choose the shareof Non-Ricardians, an investment adjustment cost, Calvo parameters on prices and wage,
and the monetary policy response of the exchange rate as our parameters. By doing
so, the IRF that corresponds to various economic situations can be computed using a
combination of these parameter values. Finally, only robust signs are adopted as the
restrictions imposed on the empirical model.
In previous analyses using macro data, the share of Non-Ricardians in Japan has

16been estimated to be approximately 30% (Hatano, 2004; Iwata, 2008). Conversely, inthe study by Kohara and Horioka (2006) that uses micro data, the same value has been
estimated to be between 8% and 15%. In this paper, we set the share of Non-Ricardians
as [0.001, 0.5] in order to include the values estimated by previous studies.
The baseline value of the investment adjustment cost, which grows as the value oflowers, is set as 0.15 based on the ﬁndings of Sugo and Ueda (2008), while the lower
bound is set as 5, at which point investment can be carried out at a lower cost comparedwith that in the baseline case.
For the upper values of prices and wage rigidities, we choose 0.8, which is somewhat
larger than the average values estimated by Iiboshi et al. (2008), Sugo and Ueda (2008),
and Iwata (2008). Likewise, the lower values of these parameters are set as 0.2 for two
main reasons. First, an extremely small value (e.g., 0.001) is unrealistic, as it makes it
diﬃcult to ascertain the common features of IRFs. Second, since Pappa (2009) adopts
0.25 for the degree of price stickiness in the RBC case, this paper adopts a smaller value.
The feedback parameter for the exchange rate under the Taylor rule is most controversial. First, it is uncertain whether the central bank determines the interest rate in
response to the exchange rate. Moreover, the interest rate in Japan since the second halfof the 1990s has fallen into a static state because of the country’s zero interest rate policy.
However, some studies have found that the interest rate reacts to the exchange rate.
For example, Nakazawa et al. (2002) estimates a VAR model and reports that the call rate
negatively responds to depreciation shock in the exchange rate. Nakazawa (2002) also
conﬁrms that monetary policy reacts to a variation in the exchange rate by estimating
the Taylor rule directly. However, the values of the feedback parameter for the exchange

17

rate estimated by Nakazawa (2002) are small or not signiﬁcant in the sample period used(1987M7–2001M3). Therefore, this paper adopts 0.001 as the lower bound of at which
point the interest rate hardly reacts to the exchange rate, and 0.1 as the upper bound,which is twice the value used by Nakazawa et al. (2002).
All other parameters are summarized in Table 1. In the next subsection, we draw
theoretical IRFs under these parameterizations and ascertain the sign restrictions imposedon the VAR model from their common features.

2.8

Sign restrictions

Figure 1 shows the theoretical impulse response of the real exchange rate, real exports,
output, and price to risk premium, foreign demand, supply, and demand shock.
The ﬁrst row in Figure 1 depicts the responses to risk premium shock. Risk premium
shock raises the real exchange rate (i.e., depreciation) and increases export quantities
through a fall in the export price. When price rigidity is high, export quantities growby a low degree in order for export price to remain relatively steady. The response of
the ﬁnal goods price takes various signs according to the values of the parameters in the
short run. Similarly, the responses of output also diﬀer for each parameter value, and thespeciﬁc quantitative feature cannot be ascertained.
The responses to foreign demand shock are shown in the second row. Export quantities
naturally increase and output also rises in response to foreign demand shock. However, as
price rigidity lowers, the export price reacts more positively to a rise in foreign demand
and the persistency of responses in exports and output is thus small. In response toforeign demand shock, the real exchange rate appreciates as expected. With respect to18

aggregate price, a particular sign cannot be determined since its response varies according
to the degree of stickiness in the import price.
The third row indicates the responses to supply shock. As seen in traditional theoretical analysis, supply shock reduces aggregate price and increases output because any
technological improvement lowers marginal cost. Moreover, a decrease in marginal costlowers the export price. Hence, export quantities positively respond to supply shock.
Further, the real exchange rate depreciates because of a falling domestic price.
Finally, the last row in Figure 1 shows the responses to demand shock. Similar to
supply shock, positive responses to price and output are obtained in line with traditional
theory. Although the real exchange rate does not indicate a signiﬁcant sign at the moment of the shock, it shows a positive response from the second period to the seventh
period. Further, reﬂecting the growth in the real exchange rate, the sign of exports isindeterminant in the ﬁrst period, but positive thereafter.
Based on these results, we create sign restrictions, which are summarized in Table
2. These sign restrictions are generally imposed for the ﬁrst three months, which are
divided into two periods; the ﬁrst period (i.e., the moment of the shock) and the periods
thereafter. For example, the theoretical responses of the exchange rate and exports
to demand shock do not show signiﬁcant signs in the ﬁrst period. In such a case, sign
restrictions are only imposed from the second to the third periods. By contrast, a positive
restriction is imposed on the response of output to foreign demand shock in the ﬁrst period
in order to be consistent with the result of the theoretical model. For the response of theexchange rate, no restrictions are imposed in the ﬁrst period by taking the J-curve eﬀect

19

into consideration, although the theoretical result indicates a positive sign.2
The short-run restrictions imposed on the ﬁrst three periods can distinguish foreign
demand shock from other shocks and supply and demand shock. More precisely, foreign demand shock is the only shock that causes an appreciation in the exchange rate.
Moreover, supply and demand shocks are identiﬁed by a price response. However, risk
premium shock is not discriminable from supply and demand shock by using such shortrun restrictions.
Thus, this paper additionally adopts the following conditions based on the calibration
results. First, it is assumed that the response of output to demand shock in the ﬁrst
period is larger than that of risk premium shock in order to disentangle risk premiumand demand shock. Further, risk premium and supply shock are discriminated by thecondition that output responds to supply shock more greatly from the 10th period to the12th period compared with risk premium shock. In other words, supply shock is assumed
to have a long-run eﬀect on output compared with risk premium shock. These conditions
are represented by one asterisk (∗) and two asterisks (∗∗) in Table 2. The four structural
shocks can be identiﬁed by all these restrictions.

2

The J-curve eﬀect implies that the response of trade balance to a variation in the exchange rate
shows the opposite sign to that expected in the short run. Gupta-Kapoor and Ramakrishnan (1999) andHsing (2005) indicate the existence of the J-curve eﬀect in Japan.

20

3

Estimation Model and Data

3.1

Sign-restricted VAR model

The sign-restricted VAR model is estimated by the following process. First, we estimate
the reduced form VAR model:

Yt = B0 + B1 Yt−1 +B2 Yt−2 + · · · + Bp Yt−p + ut

(33)

ut =A0 εt(34)

ut ∼ N (0, Σ), εt ∼ N (0, I)(35)

where Yt is a vector of endogenous variables, B = [B0 , B1 , · · · , Bp ] is a vector of constants
and matrices with coeﬃcients, and ut is a vector of reduced form residuals with thevariance-covariance matrix, Σ. A0 is a lower triangular matrix given by the Cholesky
decomposition of Σ and εt is a vector of structural shocks that are mutually independentand normalized to be of variance 1.
Second, we draw random samples of B and Σ from their posterior distributions.
Using the non-informative Normal-Wishart family as the prior distribution, the posterior distributions of vec(B) and Σ−1 respectively become N (vec(B̂), Σ̂ ⊗ (X ′ X)−1 ) andW (Σ̂−1 /T, T ), where B̂ and Σ̂ are OLS estimators, X is the matrix of the explanatory
variables, and T is the sample size. Third, the structural shocks and matrix of contemporaneous relations among the endogenous variables are calculated from each draw. In
this step, we randomly generate the orthogonal matrix Q, namely Q′ Q = I. Using this21

matrix, eq. (34) can be rewritten as

ut = A0 Q′ Qεt= Aε̃t .

(36)

Then,

E [Aε̃t ε̃′t A′ ] = E [A0 Q′ Qεt ε′t Q′ QA′0 ]= A′0 A0 = Σ(37)Therefore, we construct a new set of structural shocks, ε̃t and contemporaneous relations,A, with the variance-covariance structure maintained. Some numbers of IRFs can becalculated from a set of (B, Σ) by generating a Q matrix randomly. As explained by Fry
and Pegan (2007), the present paper generates a Q matrix as the following procedure. Ina four-variable VAR model, we use a 4 × 4 Givens matrix Q12 , Q13 , Q14 , Q23 , Q24 , andQ34 , where Qij (θ) is a matrix with cos(θ) in the (i, i) and the (j, j) elements, − sin(θ) inthe (j, i) element, and sin(θ) in the (i, j) element. The diagonal element of this matrix isone, while the oﬀ-diagonal elements are equal to zero. Then, the Q matrix is deﬁned as

Q = Q12 (θ1 )Q13 (θ2 )Q14 (θ3 )Q23 (θ4 )Q24 (θ5 )Q34 (θ6 )where θk , k = 1, · · · , 6 are drawn randomly from a uniform distribution U (0, π).
Finally, the IRFs are calculated based on each draw (B, Σ, A). If they satisfy the sign
restriction in Table 2, they are candidates as valid IRFs and are reserved; otherwise, they22are discarded. We repeat this process until we have 300 valid IRFs as our ﬁnal samples.

3.2

Data and specification

The endogenous variables in our VAR model are the log of the real eﬀective exchange
rate (REER), real exports, consumer price index (CPI), and indices of all industry activity (IIA), which is regarded as a proxy of GDP.3 The data are all monthly and thesample period is 1990M1–2011M10 (see Figure 2). Except for the REER, the series areseasonally adjusted.4 In the actual estimation, because an increase in the REER implies
depreciation, we multiply it by -1 to make it consistent with the speciﬁcation presented
in the theoretical model. Hereafter, the term “output” indicates the IIA.
The estimated system contains a constant term and a consumption tax dummy(1997M4). In addition, it is estimated in levels because taking a diﬀerence may lose
important information contained in the original series, as pointed out by Sims et al.
(1990). The number of lags is chosen to be six as suggested by the Akaike information
criterion. In this framework, based on the sign restrictions derived from the theoreticalmodel, we identify four types of structural shock, risk premium (exchange rate), foreign
demand, aggregate supply, and aggregate demand, respectively: ε′t = [εrisk
εft εst εdt ].
t

3

Data for the REER and real exports are downloaded from the Bank of Japan website. Data on the
CPI and IIA are from the Ministry of Internal Aﬀairs and Communication and the Ministry of Economy,
Trade, and Industry, respectively. These data are taken from the Nikkei NEEDS-Financial QUEST
database.
4
With respect to real exports and the IIA, seasonally adjusted series can be obtained from the data
source. By contrast, because the series of the CPI, especially before 2000, is not seasonally adjusted inthis data source, we perform a seasonal adjustment using X-12-ARIMA.

23

4

Empirical results

4.1

IRF analysis

Figure 3 depicts the estimated IRFs. The solid lines and shaded areas indicate the medianof sampled IRFs and one standard error bands, respectively. This ﬁgure conﬁrms that
the IRFs follow the sign restrictions. However, it is worthwhile exploring the responses
for which no sign restrictions are imposed. First, output responds to risk premium shock
negatively, while price responds positively, in line with the ﬁndings of Shioji et al. (2011).
Second, the price response to foreign demand shock shows a negative sign in the shortrun. In addition, it is conﬁrmed that both supply and demand shock have a long-run
eﬀect on output, meaning that the IRFs are diﬀerent from zero at a signiﬁcant level.

4.2

FEVD

The results of the FEVD are presented in Figure 4. The estimated time horizon is 15
months as in the IRF analysis. This ﬁgure shows the relative importance of each shockin terms of the variations in each variable. The primary ﬁnding is that external shocks(i.e., risk premium and foreign demand shock) explain approximately 20% to 40% of theforecast error variances in output, as shown in the bottom right-hand ﬁgure. This result
is somewhat larger than the values reported by Shioji et al. (2011) because the eﬀects
of shocks that are identiﬁed only in their paper (e.g., monetary policy and foreign priceshock) might be included in external shocks in our analysis.
Additionally, a large part of the variation in real exports can be explained by foreign
demand shock in the ﬁrst period. From the second period onwards, foreign demand shock24

continues to play a major role in the variation in real exports. In addition, the bottom
right-hand ﬁgure shows that price is mainly explained by domestic shock, (i.e., supply
and demand shock). These results concur with the ﬁndings of Shioji et al. (2011). With
regard to the real exchange rate, we ﬁnd that foreign demand shock (supply shock) is
the main inﬂuencing factor on its ﬂuctuation in the short (long) run. The results of the
FEVD conﬁrm that some of the ﬂuctuations in output are caused by external shocks.
Hence, it can be concluded that the Japanese economy is subject to external factors.

4.3

HD

The result of the HD of output is shown in Figure 5. The solid line denotes the estimatedseries of output and the dotted line denotes the decomposed series of each shock. Further,
the shaded areas show the recessions dated by the Cabinet Oﬃce, the Government ofJapan. First, we ﬁnd that the supply shock series roughly traces the movement of output
throughout the sample period. This ﬁnding implies that supply shock (i.e., variation
in TFP) plays an important role in Japanese business cycles, as previously pointed by
Hayashi and Prescott (2002) and Miyao (2006). In the next step, we investigate thesources of these business ﬂuctuations by dividing the whole sample period into three subperiods: the depression of the 1990s following the collapse of the bubble economy, therecovery since 2002, and the recession after the Lehman shock.
First, two factors are mainly recognized as having caused the depression in the 1990s(i) a shortage of aggregate demand and (ii) a downturn in productivity (i.e., TFP). This
paper supports both these hypotheses.
In the two charts on the right-hand side of Figure 5, the contributions of demand and25foreign demand shock show a downward trend at the beginning of the 1990s and explain
the majority of the movement in output. However, the contribution of demand shockchanges to an upward trend after November 1992, while the negative trend in supply
shock is observed from the mid-1990s. This negative supply shock is considered to havecaused the low growth in output after moving out of recession at the beginning of the
1990s. Further, foreign demand shock denotes a negative contribution from 1997, whichmight reﬂect the fall in exports because of the onset of the Asian currency crisis.
Additionally, the inﬂuence of ﬁscal policy is conﬁrmed in our results. The contributionof demand shock changes at several time points in the bottom chart on the right-hand side(e.g., 92M11, 95M04, 95M10). These points roughly correspond to the announcements
or implementation of ﬁscal stimulus packages by the government,5 which is evidence thatﬁscal policy positively aﬀected the economy in the 1990s. In summary, the long depression
in the 1990s was caused by negative (but not simultaneous) shocks in demand and supply.
A shortage in demand was ﬁrst caused by overinvestment in the bubble period, which led
to low productivity growth throughout the decade.
Second, the export-led recovery from 2002 stemmed from a boom in the US and economic growth in emerging countries. In this paper, the positive contribution of foreign
demand shock is observed in this period, supporting such a view. Moreover, as shown inthe bottom chart on the left-hand side in Figure 5, supply shock also plays an importantrole in economic recovery. This implies that not only depression but also economic recovery can be explained by the variation in TFP.6 By contrast, the contribution of demand
shock is small albeit with an upward trend. In other words, consumption and investment
5
6

Fukuda and Yamada (2011) detail when ﬁscal packages were announced.
Inaba (2007) also points out the importance of supply shock in the recovery period after 2002.

26

seldom increased despite it being perceived as a genuine period of economic recovery.
On the ﬁnal point, the results presented in this paper indicate that negative risk
premium shock and demand shock mainly explain the fall in output following the Lehman
shock in September 2008, while the negative contribution of supply shock is also conﬁrmed
throughout this recessionary period.
Surprisingly, the contribution of foreign demand shock to output is small. The top
right-hand chart in Figure 6 helps explain that a fall in real exports following the Lehman
shock can be explained by risk premium shock. This result suggests that a fall in realexports is not caused by a decrease in foreign demand, but rather by an endogenous
response to an appreciation in the exchange rate. In this period, the data indicate thatthe exchange rate appreciates before of the reduction in exports. Since the fall in realexports is an endogenous response, the movement of output can also be explained by risk
premium shock as opposed to foreign demand shock. Indeed, Figure 7 conﬁrms the low
degree of inﬂuence of foreign demand shock on output.
In summary, we can conclude that the rapid fall in output after the Lehman shock was
mainly caused by negative risk premium shock, i.e., an appreciation of the real exchange
rate. The negative contribution of supply shock also played a major role throughout therecessionary period from August 2008. These results indicate that business ﬂuctuations
were caused by diﬀerent shocks for each period and that the role of external shocks hasgrown in recent years.

27

5Conclusion

This paper investigated the sources of Japanese business ﬂuctuations by taking accountof external shocks, such as risk premium and foreign demand shock. For this purpose, an
NK open macroeconomics model was ﬁrst constructed in order to ascertain the featuresof each structural shock. Then, we estimated the sign-restricted VAR model based ontheoretical IRFs and conducted the FEVD and HD as well as IRF analysis. From theseanalyses, the eﬀects of external shocks were evaluated qualitatively and quantitatively.
The results of the FEVD clarify that 20% to 40% of the forecast error variances in
output can be explained by external shocks, supporting the well-recognized notion that
the Japanese economy is greatly inﬂuenced by external factors. This ﬁnding conﬁrms theimportance of taking account of external shocks when examining the Japanese economy.
In addition, the results of the HD allow us to draw four main conclusions. First, in thewhole study period, supply shock explains the variation in output more than any othershock. Second, the long depression in the 1990s was caused by a combination of negative
supply and demand shock; however, these negative shocks did not happen simultaneously.
While negative demand shock explained the fall in output at the beginning of the 1990s,
negative supply shock played a major role in the second half of the 1990s. Third, theeconomic recovery since 2002 has stemmed from an increase in foreign demand and an
improvement in productivity. Finally, the main factor behind the rapid fall in output andexports since the Lehman shock has been negative risk premium shock. In other words,
the rapid appreciation of the real exchange rate has reduced real exports endogenously,
leading to a considerable decline in output.
The ﬁrst three ﬁndings are consistent with the results presented by previous studies.
28

By contrast, the latter result is a novel ﬁnding by this paper. Further, the ﬁnding that anappreciation of the exchange rate is a main factor in the reduction in output is diﬀerent
from that presented by Shioji and Uchino (2011).
We also show that the role of external shocks is larger in recent business ﬂuctuations,
namely from the economic recovery from 2002 to the recession since the Lehman shock.
This ﬁnding implies that the Japanese economy has been increasingly aﬀected by opening
its borders to global trade partners. Therefore, future analyses based on an open economy
framework in Japan are crucial when the eﬀects of a policy can be predicted or veriﬁed.

29

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33

Appendix A

Table and Figure
Table 1: Calibration Parameters

Parameter
β
δ
α
γ
λ
ω
µ
κ
ρp , ρx
ρf
ρw
θp
εw
θx
η
ψ
sg
ϕg
ϕb
ϕπ
ϕS
ρi

Value
0.9975
0.01
0.3
1.5
2
0.88
[0.001, 0.5]
[0.15, 5][0.2, 0.8]
[0.2, 0.8]
[0.2, 0.8]
6
6
1
1
0.01
0.2
0.03
0.12
1.5
[0.001, 0.1]
0.95

Description
Subjective discount rate
Depreciation rate
Share of capital
Risk aversion
Inverse labor supply elasticity
Degree of home bias
Share of Non-Ricardians
Investment adjustment cost
Calvo parameters on domestic and exported prices
Calvo parameters on imported prices
Calvo parameters on wages
Elasticity of substitution in production
Elasticity of substitution in labor input
Price elasticity of exported goods
Elasticity of substitution bet. domestic and imported goods
Parameter on the risk premium
Steady-state share of government spending
Elasticity of tax to government spending
Elasticity of tax to debt
Monetary policy response of an inﬂation rate
Monetary policy response of an exchange rate
persistency of exogenous shocks

Notes: The values of parameters are basically set up according to the previous studies. With respect tothe value of ω, it is set on the basis of the import inducement coeﬃcient in the Input-Output Table asin Shioji et al. (2011).

34

Table 2: Sign restrictions
Risk premium shock
Foreign demand shock
Supply shock
Demand shock

exchange rate
1 2-3 10-12
+
+
−
−
+
+
+

1
+
+

exports
2-3 10-12
+
+
+
+

1
∗
+
+
+

output2-3 10-12
∗∗

1

price
2-3 10-12

+
+

−
+

−
+

Note: Sign restrictions are set to be consistent with the theoretical impulse response functions. Blank
spaces mean that no sign restrictions are imposed. In this table, one asterisk (∗) represents that the
response of output to demand shock in the ﬁrst period is larger than that of risk premium shock, while
two asterisk (∗∗) denotes that supply shock has a long-run eﬀect on output compared with risk premium
shock. In addition, no sign restriction are imposed in the response of exports to risk premium shockat the ﬁrst period by taking into the J-curve eﬀect into consideration, although the theoretical result
indicates a positive sign.

35

risk

0

0

0.5

1

8 10 128 10 128 10 12

0

0.5

1

2

2

2

4

4

4

6

6

6

8 10 128 10 128 10 12

1

1.5

-0.2

0

0.2

0.4

-0.5

6

-0.2
2

4

6

8 10 12

0
2

4

4

4

4

6

6

6

6

8 10 128 10 128 10 128 10 12

0

1

2

-2

-1

0

0

0.5

1

-0.2

0

0.2

0.4

Figure 1: Impulse Response Function (Theoretical model)

8 10 12

0.5

1

2

2

2

Output

2

2

2

2

4

4

4

4

6

6

6

6

8 10 128 10 128 10 128 10 12

Price

Note: The impulse response functions are drawn under the each parameter value in Table 1.

4

0

0.2

0.4

0

0.5

1

0

0.5

1

2

0

6

6

6

0

0.5

0

4

4

4

0

0.5

1

Exports

0.5

2

2

2

Exchange rate

0.5

1

1.5

-1

-0.5

et

t

s

d

ef

et

et

36

Consumer Price Index

Indices of All Industry Activity
4.7
4.65
4.65

4.6
4.6
4.55
4.55

4.5

4.45
Jan90

Jan95

Jan00

Jan05

Jan10

Jan90

Jan95

Jan00

Jan05

Jan10

Real Effective Exchange Rate

Real Export

5
4.8
4.6
4.8
4.4
4.6
4.2
4
4.4
3.8
Jan90

Jan95

Jan00

Jan05

Jan10

Jan90

Jan95

Jan00

Jan05

Jan10

Figure 2: Data
Note: All data has taken logarithm, and seasonally adjusted except for the real eﬀective exchange rate.
The real exports and the real eﬀective exchange rate are downloaded from Bank of Japan’s web page.
The series of Indices of All industry Activity (IIA) and CPI are obtained from Ministry of Economy,
Trade and Industry and, Ministry of Internal Aﬀairs and Communication, respectively.

37

t

t

εrisk

10 15

5

5

5

5

10 15

10 15

10 15

10 15

0

0.005

0.01

0

5

0

5

-10

-5

0

-3

5

5

x 10

5

x 10

5

10 15

10 15

-3

10 15

-3

10 15

x Output
10

0

0.5

1

1.5

-2

-1

0

1

-10

-5

0

5

-1

0

1

2

-3

5

x 10

5

x 10

5

x 10

5

10 15

-3

10 15

-3

10 15

-4

10 15

Price
x 10

Note: This ﬁgure shows the impulse response functions to one standard deviation innovation in each shock. A blue solid lines is a median of the sampled
impulse response functions. A shaded area denotes a 68% credible interval.

Figure 3: Impulse Response Function (Empirical model)

0

-0.01
10 15

0.01

0
5

0.02

0

0

0.01

0.01

0.01
10 15

0.02

0.02

5

0

-0.04
10 15

0.01

-0.02
5

0.02

0

-0.02
5

-0.01

0.02

Real exports

0

0.01

Exchange rate

0

t

εf

εs

εd
t

38

Exchange rate

Real exports

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1

2

3

4

5

6

7

Output

8

9

10

11

12

13

14

15

Price

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

εt

εt

risk

0

εt

f

εt

s

d

0
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Figure 4: Forecast error variance decomposition
Note: This ﬁgure shows the results of the forecast error variance decomposition. In this ﬁgure, colored
regions indicate the ratio explained by a risk premium, a foreign demand, a supply and a demand shockin an order from bottom.

39

Risk Premium ShockForeign Demand Shock

0.1

0.1

0.05

0.05

0

0

-0.05

-0.05

-0.1

-0.1
Jan95

Jan00

Jan05

Jan10

Jan95

Supply Shock

Jan00

Jan05

Jan10

Jan05

Jan10

Demand Shock

0.1

0.1

0.05

0.05

0

0

-0.05

-0.05

-0.1

-0.1
Jan95

Jan00

Jan05

Jan10

Jan95

Jan00

Figure 5: Historical decomposition in output
Note: This ﬁgure shows the result of the historical decomposition in output. A solid line and a dottedline denote the estimated series of output and the portion explained by each structural shock. Further,
the shaded areas show the recessions dated by Cabinet Oﬃce, Government of Japan.

40

Risk Premium ShockForeign Demand Shock

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

-0.1

-0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
Jan95

Jan00

Jan05

Jan10

Jan95

Supply Shock

Jan00

Jan05

Jan10

Jan05

Jan10

Demand Shock

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

-0.1

-0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4
Jan95

Jan00

Jan05

Jan10

Jan95

Jan00

Figure 6: Historical decomposition in real exports
Note: This ﬁgure shows the result of the historical decomposition in real exports. A solid line and adotted line denote the estimated series of real exports and the portion explained by each structural shock.
Further, the shaded areas show the recessions dated by Cabinet Oﬃce, Government of Japan.

41

Risk Premium ShockForeign Demand Shock

0.04

0.04

0.02

0.02

0

0

-0.02

-0.02

-0.04

-0.04

-0.06

-0.06

-0.08

-0.08

-0.1
Jan08

-0.1
Jan08

Jan09

Supply Shock

Demand Shock

0.04

0.04

0.02

0.02

0

0

-0.02

-0.02

-0.04

-0.04

-0.06

-0.06

-0.08

-0.08

-0.1
Jan08

Jan09

-0.1
Jan08

Jan09

Jan09

Figure 7: Historical decomposition in output conditioning on the data before 2008
Note: This ﬁgure shows the result of the historical decomposition in output conditioning on the data
before January 2008. A solid line and a dotted line denote the estimated series of output and the portion
explained by each structural shock.

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