Discussion Papers In Economics
And Business

Output Composition of Monetary Policy
Transmission Mechanism in Japan
Ippei Fujiwara

Discussion Paper 03-07

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANOutput Composition of Monetary Policy
Transmission Mechanism in Japan
Ippei Fujiwara

Discussion Paper 03-07

April 2003

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANOutput Composition of Monetary Policy
Transmission Mechanism in Japan
Ippei Fujiwara∗†
Research and Statistics Department, Bank of Japan,
and Osaka University
Preliminary Version, March 2003

Abstract
In this paper, I investigate the output composition of monetary policy
transmission mechanism in Japan. It is usually thought that the investment channel, namely the process that a change in interest rate alters thecost of capital and therefore investment, is more predominant in Japan.
Yet, in the United States, it is commonly argued that the consumption
channel through intertemporal substitution is more prevalent than theinvestment channel.
The aim of this paper is twofold; 1) to understand which of the twochannels; the consumption channel and the investment channel, is moresignificantly predominant in the monetary transmission mechanism ofJapan based on the analysis with VAR and DSGE models, and 2) tocontribute the research concerning the ”Output Composition Puzzle” advocated by Angeloni, Kashyap, Mojon and Terlizzese (2002) for the factthat the consumption channel is more prevalent in the United States but inEuro area investment channel is the predominant driver of output changes.
The results obtained from the Japanese models are consistent with ourintuitive conclusion that the investment channel is more important.

JEL Classification: C33; E50.
Key words: VAR; DSGE; Monetary Policy Transmission;
Output Composition Puzzle;∗ Author’s correspondence: ippei.fujiwara@boj.or.jp† The author would like to thank Ed Nelson (Bank of England) for sharing the code for the
DSGE which is used to evaluate the impulse response obtained by VAR. Further I appreciate
the helpful comments from Kosuke Aoki (Universitat Pompeu Fabra), Kanemi Ban (Osaka
University) and seminar participants at Osaka university. Importantly, the view in this paper
should not be taken of the Bank of Japan nor any of its respective monetary policy or otherdecision making bodies. Further, any errors is my responsibilibily alone.

1

1

Introduction

In this paper, I research on the output composition of monetary policy transmission mechanism in Japan. As conventionally known, raising of interest rates
leads to the decrease in the output and eventually price level. However, channel
to this end is not quite obvious, although it may be considered apparent fromintuition based on our experiences. Usually, it is thought that the investment
channel, namely the process that the interest rate change made by the central
bank alters the cost of capital and therefore investment, is more predominant.
Yet, in the United States, it is commonly argued that the consumption channel
through intertemporal substitution is more prevalent than investment channel.
Recently, Angeloni, Kashyap, Mojon and Terlizzese (2002) concludes throughthe analysis from VAR (Vector AutoRegression), DSGE (Dynamic Stochastic
General Equilibrium) and Large Macroeconometric Models employed in central
banks that in the United States the consumption channel is the main transmission channel, but on the other hand, in the Euro area, it is only playing a minor
role in monetary transmission. With plausible parameter calibration, it statesthat the phenomenon in the United States cannot be explained theoretically by
DSGE model and names these facts as the ”Output Composition Puzzle.”
The aim of this paper is twofold; 1) to understand which of the two channels;
the consumption channel and investment channel, is more significantly predominant in the monetary transmission mechanism of Japan based on the analysis
with VAR and DSGE models, and 2) to contribute the research concerningthe ”Output Composition Puzzle.” The results are consistent with our intuitive conclusion that the investment channel is more significant in the monetarytransmission mechanism in Japan.
This paper consists as follows. First, I construct four VAR models withdifferent identification which can account for responses in consumption and investment respectively to nominal interest rate shock. Then, the results obtained
from VAR models are compared with those from DSGE model, the parameterof which is estimated as well as calibrated so that it can explain the macroeconomic dynamics underlying in Japanese macroeconomic data. Finally, findings
here are summarised in conclusion.

2

VAR Models

The research on monetary policy transmission mechanism using VAR is quite
vast. Indeed, the seminal paper on identified VAR of Sims (1980), which iswell-known for the ”Sims critique” on traditional large macromodels for theirimplausible identifications, is also on monetary transmission. Since then, quitea large number of researches with various identification schemes have been published. Among them, it is popular to identify the system for contemporaneous
relationships between macroeconomic variables. For example, some such as
Christiano, Eichenbaum and Evans (1999) use Choleski decomposition, whichis called as the recursive framework for identification, and others such as Leeper,2Sims and Zha (1996) employ non-recursive framework for identifying monetary
policy shocks.
As for the research on Japanese monetary policy, Iwabuchi (1990) is the firstattempt to investigate monetary transmission mechanism in Japan using identified VAR, which employs non-recursive structure for the analysis. Since then,researches which are similar to Iwabuchi (1990) but slightly different in aim havebeen published with various identification. Miyao (2000), Kimura, Kobayashi,
Muranaga and Ugai (2002), and Fujiwara (2003a) examine the stability of monetary transmission mechanism with identified VAR on monetary policy transmission. Kasa and Popper (1997) and Shioji (2000) construct monetary VAR
models with reserve market so that they could embed the actual implementing scheme of monetary policy. Sugihara, Mihira, Takahashi and Takeda (2000)
tries to find out robust conclusions on monetary transmission mechanism by constructing VAR models with various identification scheme such as recursive, nonrecursive and long-run restriction introduced by Blanchard and Quah (1989).
Further it estimates the model with both non-differenced and differenced series.
Overall, Teruyama (2001) surveys the recent developments in VAR on monetarytransmission mechanism in Japan.
However, concerning the output composition of monetary transmission mechanism which is the central aim of investigation in this paper, prior researches
have been paying little attention to the detailed structure of the transmission
channel, that is, to understanding which transmission channel; consumption
channel through intertemporal substitution or investment channel through costof capital, is more predominant driver of output changes after monetary policy
shocks. As prior researches on this field in Japan tend to include only one output variable, usually industrial production,1 we have not yet been well-informed
about whether changes in output level and price level is brought mainly throughconsumption or investment.
Even, considering the researches on the United States and the Euro area,
there have not been many researches with VAR models which can account for the
output composition. One example can be found in Christiano, Eichenbaum andEvans (2001). It estimates VAR with ten variables; consumption, investment,
GDP, GDP deflator, real wage, labour productivity, corporate profit, federal
funds rate, M2 and S&P 500 stock price index, so that it could judge whether
DSGE with time-varying capital utilisation they create can reproduce realistic,in other words, very similar impulse responses to those obtained from VAR
models. However, its main aim lies not on understanding the output compositionof monetary transmission mechanism.
The seminal research which induces attention on the importance of understanding output composition is recent research conducted by Angeloni, Kashyap,
Mojon and Terlizzese (2002). It estimates four VAR models each for the UnitedStates and the Euro area in order that the difference in the monetary transmission mechanism between them could be scrutinised. For the United States,
1 This may be due to the fact that the VAR on monetary policy transmission is normallyestimated on monthly data so that the more information could be extracted.

3they construct VAR models based on Christiano, Eichenbaum and Evans (1999),
Gorden and Leeper (1994), those with the extension made to include GDP components, further Christiano, Eichenbaum and Evans (2001) and Erceg and Levin(2002). Concerning the Euro area, the VAR models of Peersman and Smets(2003) with M3 and without M3, Gali (1992) with extension to include GDP
components, and Christiano, Eichenbaum and Evans (2001) modified for theEuro data are examined. As has been mentioned, it concludes that the consumption channel is more prevalent in the United States but in the Euro area
investment channel is the predominant driver of output changes and names thisfact as the ”Output Composition Puzzle.”
As VAR model on monetary transmission mechanism with output decomposition is hardly found in researches on Japan,2 I construct four VAR models
based on (1) Gorden and Leeper (1994), (2) Christiano, Eichenbaum and Evans(2001), (3) Erceg and Levin (2002) and (4) Leeper, Sims and Zha (1996).3
While the recursive structure of contemporaneous relation is assumed in thefirst three, the non-recursive structure, whose methodology is established by
Bernanke (1996), Blanchard and Watson (1986) and Sims (1986), is applied to
the last case. After brief explanation on VAR models examined here,4 outlinesof these models are described. Finally, we investigate output composition ofmonetary transmission in Japan from results obtained by the VAR models.

2.1

VAR Primer

VAR models here are estimated and identified as follows.
2.1.1

Estimation

The basic building block consists of a vector time series Zt . The vector Zt
evolves over time according to:Zt = B0 + B1 Zt−1 + B2 Zt−2 + ... + Bq Zt−q + ut
where Eut u0t = V. The vector ut is assumed to be uncorrelated with past valuesof Zt .
2 The only research I could find is Morsink and Bayoumi (2000), but it estimates the VAR
separaterly for each GDP component.
3 Detailed information on data employed in these VAR models are as follows; investment,
consumption and rest of GDP components: seasonally adjusted series at 1995 price from SNA(Cabinet Office), CPI: seasonally adjusted Consumer Price Index at 2000 price (Ministry of
Public Management, Home Affairs, Posts and Telecomunications) , commodity price: Nikkei
Shohin Sisuu (Nikkei Shinbun), call rate: with collateral bases before 1995 and without collateral bases after 1995 (Bank of Japan), money supply: seasonally adjusted M2+CD, however
disconnection due to the different difinition is solved by using quartely growth rate (Bankof Japan), stock price: TOPIX (Tokyo Stock Exchange), bond yield: newly issued 10 years
government bonds (The Japan Bond Trading Co.), profit to revenue ratio: computed from
”Financial Statements Statistics of Corporations by Industry, Quarterly” (Ministry of Finance), and labour productivity: computed from SNA and ”Labour Force Survey” (Ministryof Public Management, Home Affairs, Posts and Telecommunications)
4 I here refer to Vigfusson (2002).

4

q

Estimation of the VAR’s coefficients {Bj }j=0 can be done equation by equaPtion by OLS. The matrix V can be estimated from the sample residuals (1/T ) ût û0t .
In this paper, VAR models are estimated for two periods. As concluded byMiyao (2000) and Fujiwara (2003a), the structural break has occurred around1995 with quite high possibility. So, two estimated period from 1980/Q1 to
2002/Q3 and 1980/Q1 to 1996/Q1 are chosen to obtain the robust result on
output composition of monetary transmission mechanism.
As for the lag length, the number of lags, q, is set at the optimal lag length
suggested by two information criteria, Akaike Information Criteria (AIC) and
Schwarz Bayesian Information Criteria (SBIC). It is always one according to
SBIC while AIC suggests two at the most. Therefore, results from both one andtwo lags cases are shown. However, impulse responses of the longest lag length
recommended either by SBIC or AIC are only demonstrated here because there
are no major changes in impulse responses within the reasonable lag length.
2.1.2

Fundamental Shocks and The Structural VAR

The next step is to calculate the structural matrix A0 . The values of ut are
not the standard structural shocks as they are usually auto-correlated. Instead,
we assume that the relationship between the VAR disturbances ut and thefundamental economic shocks εt is given by
A0 ut = εt ,A0 Zt = A0 B1 Zt−1 + A0 B2 Zt−2 + A0 ut= A0 B1 Zt−1 + A0 B2 Zt−2 + εt .
We need to know the value of A0 in order to calculate impulse responses. To
find a unique A0 however requires further assumptions. Many matrices mightsolve the equation0
A−1
0 (A0 )

−1= V.

In general, one can choose between two different approaches. The simpler
and more common is the recursiveness assumption. One implements this asto be the lower Choleski decomposition
sumption by defining the matrix A−1
0of V.
The other approach is to not to assume recursiveness but rather assume
that enough entries are zero or otherwise constrained that only a unique A0
solves the above equation and satisfies these further assumptions. Following themethodology established by Bernanke (1986), Blanchard and Watson (1986) andSims (1986), the matrix A0 is found as the matrix that maximize the likelihood
function as below.5
5 However, the uniqueness of this A

0 can be difficult to establish.

5

L (A0 , V ) = −
2.1.3

T
T
T
2
log (2π) + log |A0 | − trace(A0 V A0o )22
2

Impulse Responses

Having found the A0 matrix, the next step is to calculate the impulse responses
to a fundamental shock. The basic idea is the following. Suppose that the VAR
has the following form.
Zt = B1 Zt−1 + B2 Zt−2 + A−1
0 εt
We suppose that the j − th fundamental errors take on the value one while
the other fundamental errors are set equal to zero. The impulse response is how
the variables in the VAR respond to this shock. The impulse response in thefirst period isΓj (1) = A−1
0 ej
where the j-th element of ej is equal to one and all other elements are zero. The
vector Γj (1) has length being equal to the endogenous variables with the sameordering as Zt . The second period impulse response isΓj (2) = B1 A−1
0 ej .
The third is−1
Γj (3) = B1 B1 A−1
0 ej + B2 A0 ej .

Note that if the matrix A0 were the identity matrix, then the impulse response functions for all shocks would be the moving average representation of
the VAR.
2.1.4

Constructing Confidence Intervals for Impulse Responses

The procedures use simulation to calculate the confidence intervals around theimpulse response functions. These confidence intervals are pointwise confidence
intervals.
The confidence interval is constructed with the following steps. The first stepis to generate the artificial data under the null hypothesis that the estimatedmodel correctly represents the data. The artificial data is created by using
the estimated coefficients along with error terms. These error terms are here
generated by Bootstrapping method, where the error terms are generated bysampling randomly with replacement from the residuals of the original vector
autoregression.
Having generated the artificial data, the next step is to estimate a VAR on
this data. Using the estimated variance covariance matrix, a new A0 matrix isestimated. The impulse response is calculated using these new estimates.
The above steps are repeated 100 times to generate a large sample of impulse
responses. The procedure then calculates the confidence intervals with 5 and 95
percentile values of the sample for the lower and upper bounds.
62.2

VAR Based on Gordon and Leeper (1994)

The model consists of eight variables; consumption c, investment i, the rest of
GDP components y, CPI p, commodity price com, bond yield rl, call rate r andM2+CD m. All variables except for interest rate are log of actual value.6 Although original Gorden and Leeper (1994) restricts the information set available
to central bank when setting the short-term interest rate by excluding contemporaneous data of output and its components as they should not be accessible,
they can affect the decision of interest rate changing by central bank in themodel examined here. Further, commodity price is added to avoid the pricepuzzle.7
When deriving the impulse responses, the order of the variables is set as
above and simple recursive framework is employed for identification. The change
in call rate can only have the contemporaneous effect on money supply and it
is assumed that the central bank exploits all the information except for current
money supply when determining call rate.
2.2.1

Impulse Responses to Nominal Interest Rate Shock

Chart 1 shows the impulse responses to nominal interest rate shock for estimatedperiod from 1980/Q1 to 2002/Q3 and Chart 2 presents those for 1980/Q1 to
1996/Q1. 8
Almost the same impulse responses are obtained in both cases. Raising thenominal interest rate by the central bank lowers the level of money supply andthese altogether reduce consumption, investment and the rest of GDP components. Price level and commodity price also decrease eventually reflecting thesedevelopments although with temporally increase in price level initially. This
is indeed the price puzzle. Notably, this price puzzle almost disappears in thecase when the estimated period is 1980/Q1 to 1996/Q1. 9 As a result, long-termbond yield also become lower.
Concerning output composition, which will be analysed later, investment
channel seems to be more predominant. As for the significance of the responsesof each component, confidence intervals propose that the responses of consumption and investment are almost significantly negative in the case when estimationis conducted until 1996/Q1.
6 VAR models are estimted with level in this paper. Sims, Stock and Watson (1992) claims
that even if variables are non-stationary, the VAR should be estimated with levels as differencing throws away important information.
7 Price puzzle is the symptom that the price level tends to rise after the positive interest
rate shock. As for the discussion of price puzzle, see Hanson (2000).
8 AIC suggest that the optimal lag length for the estimated period 1980/Q1 to 2002/Q3 istwo. Therefore, in this case, impulse responses when number of lags is two are demonstrated.
9 Fujiwara (2003a) implies that one of the causes of price puzzle may be the coexistence ofequilibrium dynamics and dis-equilibrium dynamics in economic time series.

7

2.3

VAR Based on Christiano, Eichenbaum and Evans(2001)The model consists of ten variables; consumption c, investment i, the rest of
GDP components y, CPI p, real wage w, labour productivity q, call rate r,
profit to revenue ratio π, M2+CD m and TOPIX s. All the variables except forr and π are log of actual value. The original Christiano, Eichenbaum and Evans(2001) employs the aggregate real corporate profit, however the profit ratio is
employed in this model. This is due to the fact that the aggregate profit datais almost disconnected in Japan because of bankruptcy of large companies etc.
in 1990s.
The order of the variables when deriving impulse responses is set as above
and simple recursive framework is employed for identification. The change incall rate can only have effects on corporate profit, money supply and stock pricecontemporaneously and it is assumed that central bank knows all the current
information on non-financial variables when determining call rate.
2.3.1

Impulse Responses to the Nominal Interest Rate Shock

Chart 3 shows the impulse responses to nominal interest rate shock for estimatedperiod from 1980/Q1 to 2002/Q3 and Chart 4 presents those for 1980/Q1 to
1996/Q1. 10
Both charts show that the impulse responses are almost the same. A positive
shock on call rate reduces corporate profit and money supply, and therefore,
stock price falls. These developments in financial variables bring lower level ofconsumption, investment and rest of GDP components. Price level and real
wage initially increase but decrease soon after.11 These developments result in
lower labour productivity.
Again, concerning output composition, investment channel seems to be more
important and confidence intervals imply that the responses of consumption
and investment are almost significantly negative in cases where estimation isconducted until 1996/Q1.

2.4

VAR Based on Erceg and Levin (2002)

The model consists of six variables; consumption c, investment i, the rest of
GDP components y, CPI p, commodity price com, and call rate r. All thevariables except for r are log of actual value.
The order of the variables when deriving impulse responses is set as above
and simple recursive framework is employed for identification. The change in callrate has no contemporaneous effect on other variables but current information of
all the macroeconomic variables are used by the central bank to set the interest
rate.
10 In both cases, lag length is one.

11 Degree of this price puzzle is less significant in the case when estimated period is 1980/Q1
to 1996/Q1

8

2.4.1

Impulse Responses to the Nominal Interest Rate Shock

Chart 5 shows the impulse responses to nominal interest rate shock for estimatedperiod from 1980/Q1 to 2002/Q3 and Chart 6 presents those for 1980/Q1 to
1996/Q1. 12
Here again, impulse responses obtained in both cases are nearly the same. A
positive shock on call rate decreases consumption, investment and rest of GDP
components and therefore, commodity price becomes lower. Although initially
increasing, price level eventually decrease reflecting these developments.13
As for output composition, investment is likely to be more predominant
driver in GDP changes. Their responses are almost significantly negative whenestimation is conducted from 1980/Q1 until 1996/Q1.

2.5

VAR Based on Leeper, Sims and Zha (1996)

Leeper, Sims and Zha (1996)14 claims that it is unrealistic to include the contemporaneous information about demand and price level into the information
set which the central bank possesses at the time when changing nominal interest rate. Instead, they think it appropriate to restrict this information set toinclude only leading indicator of price level, commodity price in this case, andmoney supply. Further, consistent with the definition of leading indicator, it isassumed that all variables have contemporaneous effect on commodity price.
Based on this identification scheme, the model for Japanese data is constructed as follows. The model consists of seven variables; CPI p, consumptionc, investment i, the rest of GDP components y, commodity price com, call rater and M2+CD m. All the variables except for r are log of actual value.
Then, the structural matrix A0 is constructed as follows.


a1
 a5

 a7

A0 = 
 a9
 a13

 0
a23

a2
a6
o
a10
a14
0
a24

a3
0
a8
a11
a15
0
a25

a4
0
0
a12
a16
0
a26

0
0
0
0
a17
a20
0

0
0
0
0
a18
a21
a27


up
0
0 
 uc
0 
 ui
0 
 uy
a19 
 ucoma22  ura28
um

The matrix above is obtained by non-recursive identification. As for theparameters, no restriction has been made on the sign of components of thestructural matrix.
12 AIC suggest that the optimal lag length for both estimated periods is two.

Therefore,
impulse responses when number of lags is two are demonstrated.
13 Price puzzle is more significant in the case when the estimated period is from 1980/Q1 to
2002/Q3.
14 Largest model introduced in Leeper, Sims and Zha (1996) consists of thirteen variables.
It includes consumption but not investment.

9

The concept behind this matrix is as follows. Top row shows that pricelevel receives contemporaneous effects from GDP components. The second row
to the fourth row show that while consumption and investment are affected
only by current price level, the other GDP components have some effect fromconsumption and investment as well as price level. This is because other GDP
components include imports and exports which should be highly correlated contemporaneously with consumption and investment. Fifth and sixth rows are as
explained above. The last row is about money demand function. it shows thatmoney demand function should have contemporaneous effects from price level,
GDP and call rate.
The change in call rate can only have simultaneous effects on money supply
and commodity price.
2.5.1

Impulse Responses to the Nominal Interest Rate Shock

Chart 7 shows the impulse responses to nominal interest rate shock for estimatedperiod from 1980/Q1 to 2002/Q3 and Chart 8 presents those for 1980/Q1 to
1996/Q1. 15 Almost the same impulse responses are obtained in both charts.
A positive shock on call rate decreases consumption, investment, and money
supply. Initial increase in rest of GDP components, price level and commodity price is somewhat puzzling, but they are eventually decreasing due to therestraining effect of tightening monetary policy.
Similar to the above three models, the investment channel looks to be playing
a more important role in monetary transmission.

2.6

Output Composition in Monetary Transmission

In this subsection, results which have been just obtained above are first summarised in ”contribution ratio” so that we could measure the output compositionof monetary transmission mechanism in Japan. Contribution ratio is a measureadvocated by Angeloni, Kashyap, Mojon and Terlizzese (2002), ”the ratio ofchanges in the components of GDP to the overall movements in GDP.” Since
VAR models are estimated in logs for GDP components, this ratio is computed
as the ratio of cumulative responses16 of the components to GDP response, eachrelative to baseline, and then weigh the component movements by their shares
in GDP. According to the historical average since 1980/Q1, each GDP components weight is set as follows; consumption: 0.55, investment: 0.15, rest of GDP
components: 0.3.
Contribution ratios for consumption and investment in both lag one and lag
two cases are demonstrated below.
15 AIC suggest that the optimal lag length for the estimated period 1980/Q1 to 2002/Q3 istwo. Therefore, in this case, impulse responses when number of lags is two are demonstrated.
16 Cumulative responses are used so as to eliminate the distortion from temporal noise.

10Consumption• lag 1

4q
8q
12q

GL
0.14
0.20
0.24

1980:2-2002:3
CEE EL0.43 0.15
0.40 0.20
0.36 0.24

LSZ
0.50
0.47
0.47

GL
0.10
0.25
0.28

1980:2-1996:1
CEE EL
0.50
0.27
0.43
0.29
0.39
0.30

LSZ
0.57
0.47
0.43

GL
0.20
0.21
0.21

1980:2-2002:3
CEE EL
LSZ
0.40 0.06 -0.01
0.41 0.17 0.68
0.36 0.22 0.44

GL
-0.16
0.13
0.17

1980:2-1996:1
CEE EL
0.46
0.24
0.46
0.30
0.42
0.31

LSZ
0.18
0.23
0.21

GL
0.53
0.69
0.70

1980:2-2002:3
CEE EL0.18 0.67
0.54 0.72
0.67 0.71

LSZ
0.62
0.57
0.54

GL
0.58
0.64
0.65

1980:2-1996:1
CEE EL-0.11 0.56
0.35
0.61
0.51
0.64

LSZ
0.49
0.49
0.53

GL
0.39
0.74
0.88

1980:2-2002:3
CEE EL0.08 0.57
0.48 0.95
0.61 0.94

LSZ
0.42
0.53
0.58

GL
0.40
0.65
0.76

1980:2-1996:1
CEE EL-0.12 0.35
0.24
0.54
0.38
0.60

LSZ
0.29
0.56
0.70

• lag 24q
8q
12q

Investment• lag 14q
8q
12q
• lag 24q
8q
12q

Overall, as expected in the impulse response analysis, contribution ratio ofinvestment is larger than that of consumption. The average of contribution
ratio of consumption from 16 VAR models is 0.25 at the end of first year after
the shock, 0.33 at the end of second year after and 0.32 at the end of thirdyear after. On the other hand, those of investment are 0.37, 0.58 and 0.65.
This is consistent with our intuition on the monetary transmission mechanism
in Japan.

11

3

DSGE Model

Inspired by real business cycle (RBC) model such as Kydland and Prescott(1982) and King, Plosser and Rebello (1988), analysing macroeconomic phenomenon with small general equilibrium model has become very popular in thefield of monetary economics. Usually, sticky prices as in Calvo (1982) and Taylor (1993) type policy rule are added to the standard RBC models as above sothat we could investigate the role of monetary policy. This framework of analysis17 is often called dynamic stochastic general equilibrium model (DSGE).18 It
would not be any exaggeration to say that DSGE is now the central analytical
tool in modern macroeconomics. 19
However, application of DSGE to Japan is not as popular as that of VAR.
Only a small number of researches can be found on Japanese economy, suchas Orphanides and Wieland (2000), Kimura and Kurozumi (2002), Fukunaga(2002), Hayashi and Prescott (2002), and Jung, Teranishi and Watanabe (2002).
Furthermore, most of these models have paid no consideration to stock variables
and therefore do not endogenise investment.20 Hence, as they are not usuallysuitable to the analysis on output composition of monetary transmission, I here
construct a DSGE model on Japanese economy by only slightly modifying andre-calibrating Nelson (2002). As the aim of constructing DSGE here is to judge
whether the impulse responses obtained above VAR models can be considered
realistic from theoretical model, it should be based on standard macroeconomic
theory.21 Nelson (2002) takes very standard approach to modelling. It incorporates equations derived from the utility maximisation of consumers and profit
maximisation of firms with habit formation, capital adjustment cost, estimatedpolicy rule as in Rotemberg and Woodford (1997) and New Keynesian Phillips
curve as in Calvo (1983) and Fuhrer and Moore (1995).

3.1

The Model

The DSGE model examined in this paper consists of thirteen equations below.
All equations are expressed as the log deviation from the steady state.22
17 Goodfriedn and King (1997) names this analytical framework as ”New Neo-Classical Synthesis”.
18 Several solution methods are now available such as Uhlig (1999) and Klein (2002). All
are based on the seminal research by Blanchard and Kahn (1981).
19 Taylor (1999) collects the research with this technique in its early stage.
20 Fukunaga (2002) includes investment in the system. However, the focus in Fukunaga(2002) is rather on the effect of imcomplete financial market than to obtain just impulse
responses per se of Japanese economy.
21 It may not be appropriate to use the word standard in economics. The word standard heremeans the robust theory which is employed in many researches. For example, such researches
as the financial accelerator model of Bernanke, Gertler and Gilchrist (1999), the credit cycleof Kiyotaki and Moore (1997), the limited participation model of Christiano and Eichenbaum(1995), and search and matching in labour market as Mortensen and Pissarides (1994) areexcluded from candidates as they are more specific in topic.
22 As for the detailed explanation for the derivation of equations here by solving agents’optimising problem and their log-linearisation are demonstrated in Fujiwara (2003b). This
will be distributed upon request.

12

3.1.1

Structural Equations From Optimising Behaviour

Consumption
βh2 σ − βh2 + σβh − 1
h (σ − 1)
1 − βhρλβh (σ − 1)Et ct+1 =ct −ct−1 −ψt +λt
σ (1 − βh)σ (1 − βh)σ (1 − βh)1 − βhvariables; c: consumption, ψ: Lagrange multiplier on consumer budget constraint, λ: demand shock23
parameters; β: subjective discount rate, h: parameter for habit formation, σ:intertemporal elasticity of substitution for consumption, ρλ : AR(1) parameteron demand shock
Labour Market Equilibrium
0 = (1 − χ) yt − (1 − χ) nt − µt + ψ tvariables; y: GDP, n: labour, µ: gross markup
parameters; χ: Elasticity of substitution between labour and capital stock
Money Demand11Rt
0 = − ψ t − rmt −εεRSSvariables; rm: real money balance, R: net nominal interest rate24
parameter; ε: reciprocal of intertemporal elasticity of substitution for realmoney balance
Euler Equation
Et ψ t+1 = ψ t − rtvariable; r: net real interest rate
Fisher Equation
Rt = rt + Et π t+1
variable; π: inflation rate
Quasi-InvestmentSSβ (1 − δ) Et xt+1 + β= xt +Yρ (1 − α) K
SS(η − 1) βφη (X1(η − 1) φη (X SS )Et
SS η−1)(1 − χ) yt+1 − (1 − χ) kt+1 − µt+1

η−1 rt23 To be exact, this is a shock to conumer preference.

24 Capital letters with superscript SS denotes the steady state level of the variables.

13

variables: x: quasi investment,25 k: capital stockparameters: δ: depreciation rate, α: labour share, ρ: reciprocal of steadystate markup, φ, η: parameters for capital adjustment cost26
Law of Motion for Capital
kt+1 = δxt + (1 − δ) kt
Resource Constraint
X SS + ηφ X SS
C SS
yt = SS ct +
Y
Y SS

η
xt

Production Function SS SS χχ
ASS N SS
A N
at + αntyt = αY SS
Y SS
 SS χK+ (1 − α)kt
Y SSvariable; a: technology shock
3.1.2

AR Shocks

Aside from the structural equation above, AR(1) process is assumed to the
disturbances mentioned above
Demand Shockλt = ρλ λt−1 + eλt
innovation; eλ : white noise innovation for demand shock
Technology Shockat = ρa at−1 + eat
innovation; ea : white noise innovation for technology shock
3.1.3

Policy Rule

Although several formulas are available such as Taylor rule, here the estimation
method introduced in Rotemberg and Woodford (1997)27 is applied to estimate
the Bank of Japan’s empirical policy rule.
25 Quasi investment is the investment excluding capital adjustment cost.
26 In this paper, capital adjustment cost is defined as φX η .
t
27 Rotemberg and Woodford (1997) first estimates the VAR with R , πt
t+1 and yt+1 andderives monetary policy reaction function by assuming that the monetary policy shock has nocontemporaneous effect on other variables.

14

Rt = 1.2926 ∗ Rt−1 − 0.4728 ∗ Rt−2 + 0.0296 ∗ Rt−3
+ 0.0624 ∗ π t + 0.0179 ∗ π t−1 + 0.1205 ∗ π t−2+ 0.3227/4 ∗ yt − 0.2132/4 ∗ yt−1 − 0.0986/4 ∗ yt−2
+ eRt
innovation: eR : white noise innovation for policy shock
3.1.4

Phillips Curve

Two pricing equations based on optimising behaviour is available in this paper.
Their results will be shown later. The first one is the very popular in monetary
economics, the New Keynesian Phillips curve in the terminology of Roberts(1995) based on staggered price setting advocated by Calvo (1983) where only alimited number of firms can have a chance to change the price. The other one,Hybrid New Keynesian Phillips curve, is based on Fuhrer and Moore (1995)
which is similar setting to Calvo (1983) but past information of inflation is
utilised additionally when setting the new price.
Calvo (1983) αµ is the parameter determined by how frequently firms canchange the price.
βEt π t+1 = π t − αµ µt
Fuhrer and Moore (1995) The weight on the lead (namely lags) are set
according to the estimation results on Japanese data by Kimura and Kurozumi(2002).28
0.65 ∗ Et π t+1 = π t − 0.35 ∗ π t−1 + αµ µt

3.2

Setting Deep Parameters

The table below shows the model calibration.
Table: Model Calibration
28 Note that the sum of the parameters for lead and lags is one. Therefore, implicitly it isassumed that the subjective discount rate is approximately one, which may contradict theassumption of the model explained so far. However, the effect from this approximation isminuscule.

15

Parameters
α
β
σ
h
δ
1/σ
φ
η
1/ρ, µ
ρλ
ρa
αµ
N SS
Z SS
π SS

Description
labour sharesubjective discount factor
intertemporal elasticity of substitution for consumption
habit formation parameter
rate of depreciation
steady state consumption elasticity of money demand
capital adjustment cost parameter 1
capital adjustment cost parameter 2
steady state markup
AR(1) parameter for demand shock
AR(1) parameter for technology shock
price stickinesssteady state fraction of time in employment
steady state level of technology
steady state inflation rate

Quarterly Value
0.650
0.990
0.660
0.800
0.021
1.000
0.750
2.000
1.250
0.220
0.870
0.087
0.330
1.000
0.025

The grounds for setting the calibrated parameters are as follows.
Labour Share Labour share is set according to Fukunaga (2002) which computes the historical average of nominal labour income against nominal GDP.
Discount Factor Subjective discount factor is the reciprocal of the grossequilibrium real interest rate29 and equilibrium real interest rate is set at 1 %per year.
Intertemporal Elasticity of Substitution for Consumption Estimating
the intertemporal elasticity of substitution σ is an intensively researched area,
as seen in Hayashi and Sims (1983), Hall (1988), Patterson and Pesaran (1992),
Atkeson and Ogaki (1996), and Ogaki and Reinhart (1998). However, eventhough sophisticated econometric techniques are used, the results are not necessarily sensible and stable. Here, I simply estimate it with GMM for the IS
curve as shown in McCallum and Nelson (1999), derived from the same representative consumer’s optimising problem as the model above.
C SS
C SS
(R
−
E
∆p
)
+
νt
t
t
t+1
Y SS
Y SS
This equation is estimated for the period from 1980/Q1 to 1996/Q1. 30 Instrumental variables are time trend, constant, one and two lags of governmentyt = b0 + Et yt+1 − σ

29 Note that since this model is not employing the overlapping generations model as in
Yaari (1965), Blanchard (1985), Buiter (1988) and Weil (1989), which are well summarised
in Frenkel and Razin (1992), steady state exists when the subjective discount factor equals
to the reciprocal of the real steady state gross interest rate. Futher, when this is satisfied,
any level of consumption can be the candidate of the steady state value as consumption Euler
equation is alyways met.
30 Fujiwara (2003a) hints that since the introduction of de-facto zero nominal interest rate
in 1996 the Japanese economy may possibly be in a state that is difficult to explain using

16

expenditure. Estimated results are as follows; where the steady state ratio ofconsumption against GDP is just set at 0.55 which is the historical average since
1980.
Estimated Value(Standard Error)

b0-0.360648(0.260995)

σ0.655399(0.484557)

The result above shows that the estimated value of intertenporal elasticity
of substitution is about 0.66.
Habit Formation Parameter As it is difficult to find any preceding researchwhich shows the degree of the habit formation in Japan, the parameter is initially
set at the value obtained in Fuhrer (2000).31 As this value does not have to
be valid in the case of Japanese economy, results with quite different settings,
namely very high habit formation case (h=0.99) and very low habit formationcase (h=0.4) are also shown to guarantee the robustness of results.
Depreciation Rate Capital depreciation rate is set according to the preceding researches on Japan, i.e. Hayashi and Prescott (2002), and Fukunaga(2002).
Steady State Consumption Elasticity of Money Demand The unitaryelasticity of substitution between consumption and real balance is assumed.
Capital Adjustment Cost Parameters φ and η are set based on Cassarasand McCallum (2000). Like the habit formation parameter, the parameter value
for this particular capital adjustment cost function cannot be found for the caseon Japanese economy and is very hard to be estimated. Therefore, results fromquite different settings, namely very high adjustment cost case (φ=1.5) andvery low adjustment cost case (η=0.25) are also shown so that the robustnessof results are guaranteed.
Steady State Markup Steady state markup is set at around the historical
average of markups computed from corporate profit in SNA statistics.
AR(1) Parameter for Demand Shock This is estimated from errors in IS
curve estimation for obtaining intertemporal elasticity of substitution as above.
AR(1) Parameter for Technology Shockin Fukunaga (2002).

This is set at the value employedstandard macroeconomic theory. Hence, the estimation is conducted for the period before
1996.
31 It would be possible to obtain the parameter for habit formation by employing the estimation method advocated by Fuhrer (2000).

17

Price Stickiness Price stickiness is set at the estimated result by Fuchi and
Watanabe (2001), which is also used in Fukunaga (2002).
Steady state fraction of time in employment
works for eight hours per day on average.

This is set so that each

Steady State Level of Technology This determines the consumption/GDP
ratio in steady state. Therefore, it is fixed at the value which makes this ratio
almost equal to the historical average.
Steady State Inflation Rate One percent inflation annually is assumed
reflecting the recent price developments in Japan.32

3.3

Impulse Responses to Nominal Interest Rate Shock

Chart 9 shows the impulse responses to nominal interest rate shock when New
Keynesian Phillips is employed and chart 10 presents those when the model is
set with Hybrid New Keynesian Phillips Curve.
Although there exist minor differences caused by differences in specification,
the monetary policy transmission mechanisms are all alike. A positive shock
to call rate lowers investment33 through a rise in cost of capital, consumption
through intertemporal substitution and therefore aggregate GDP. In responseto these developments in demand side, inflation rate becomes lower.

3.4

Output composition in Monetary Transmission

Contribution ratio defined above are also used here to measure the output composition of monetary transmission in Japan depicted as a DSGE model.
Consumption
Calvo
Low AC
0.07
0.13
0.18

4q
8q
12q

BASE
0.25
0.29
0.32

High AC
0.32
0.36
0.38

High H
0.07
0.14
0.18

Low H
0.28
0.30
0.33

4q
8q
12q

BASE
0.14
0.20
0.24

Fuhrer-Moore
High AC Low AC High H
0.20
0.07
0.04
0.25
0.14
0.09
0.28
0.20
0.14

Low H
0.17
0.22
0.25

32 This setting has only marginal effects on results, just alters the steady state nominalinterest rate.
33 Note that investment here is quasi-investment. Contribution ratio is also calculated forquasi-investment.

18

Investment
Calvo
Low AC
0.67
0.61
0.54

4q
8q
12q

BASE
0.39
0.35
0.33

High AC
0.27
0.25
0.24

High H
0.53
0.48
0.44

Low H
0.36
0.34
0.32

4q
8q
12q

BASE
0.55
0.49
0.45

Fuhrer-Moore
High AC Low AC High H
0.46
0.67
0.65
0.41
0.59
0.59
0.38
0.53
0.55

Low H
0.52
0.47
0.44

AC
H

0.75
0.80

1.5
0.80

0.75
0.40

0.25
0.80

0.75
0.99

Results suggest that the investment channel is more predominant driver of
GDP changes. The average of contribution ratio of consumption from 10 DSGE
models is 0.18 at the end of first year after the shock, 0.22 at the end of second
year after and 0.23 at the end of third year after. On the other hand, those ofinvestment are 0.45, 0.42 and 0.41.
Angeloni, Kashyap, Mojon and Terlizzese (2002) concludes that the highresponse of consumption to nominal interest rate shock in the United Statescannot be explained by theoretical model with reasonable calibration. Contrary
to this result, without major caveats, the output composition obtained from
VAR models with various identification can be considered as being within therange of explanation by the theoretical DSGE model albeit somewhat smaller
responses of investment in DSGE.34

4

Conclusion

Up to this point, I have shown empirically from VAR models that investment
channel is more important in monetary transmission mechanism. Then, we haveviewed that the same results are also obtained from theoretical DSGE modelof Japanese economy. Therefore, it would be appropriate to conclude that theoutput composition against the shock to nominal interest rate in Japan is not
puzzling yet reasonable since the VAR result on output composition is almost
consistent with that of DSGE model.
So, what makes the output composition between Japan and the UnitedStates so different? Angeloni, Kashyap, Mojon and Terlizzese (2002) points
out three possible explanations for the consumption reaction difference between
34 This may be due to the fact that investment is here quasi-investment which excludes
adjustment cost. Furtheremore, It is not very easy to obtain such a hump-shaped response ofinvestment as in VAR impulse responses from DSGE model because capital adjustment costis only valid for capital stock not for investment.

19the Euro area and the US: 1) lower adjustment cost in Euro area due to higher
labour adjustment cost, 2) More sensitive response of US consumers againstinterest rate changes due to the difference in financial asset composition, and3) government insurance mechanisms which cushions income against interest
rate shock. These explanations are naturally valid for explaining the difference
between Japan and the US. However, two other explanations would be possible; high relative risk aversion35 and saving behaviour of Japanese consumers.
As for the former, this directly means low intertemporal elasticity of substitution. Concerning the latter, the amount outstanding of financial assets owned byhouseholds are much larger in Japan than in the US. This implies that the downward pressure caused by substitution effect from interest rate rise is lessened by
upward pressure from income effect to some extent, although substitution effectsurpasses overall.
Probably, these five points altogether make the consumption response tonominal interest rate shock in Japan less critical. However, the grounds for someof these points may become less certain in the prospecting future. Prolonged
recession since the beginning of 1990s has been changing the labour market
in Japan. The conventional life-time employment cannot be fully guaranteed
any longer and this may result in lower labour adjustment cost. Government
debt has been increasing significantly and therefore future cuts in government
spending is expected. Noteworthy ageing occurring in Japan will see the riseof the propensity to consume and this would result in the decrease of financial
assets. Therefore, it might be possible that the output composition in Japan isgetting closer to that of the US in the near future.
Thus, checking the output composition against the nominal interest rate
shock is useful not only to understand the transmission mechanism so we could
find out what kind of policy mix is effective to stimulate the economy, but also
to be always aware of the possibility of structural breaks. Although the formal
test to possibly explain the difference in output composition between in Japanand in the US is left for future research,36 it is always of importance for thecentral bank to understand the detailed monetary transmission mechanism.
Last but not least, consistent with the results in Miyao (2000), Kimura,
Kobayashi, Muranaga and Ugai (2002) and Fujiwara (2003a), results from VAR
models seem to imply that monetary policy has become less effective since theintroduction of de-facto zero nominal interest rate in 1996. For the VAR estimated from 1980/Q1 to 2002/Q3 which includes the periods for de-facto zeronominal interest rate, upper bounds of confidence intervals for investment andconsumption tend to be above zero. This is suggesting that the effects of monetary policy is weakening recently.
35 Estimated value of intertemporal elasticity of substitution is not siginificantly lower compared to the conventional value of that in the U.S. However, as far as we concentrate on the
difference of the impulse responses, it could be deduced that the intertemporal elasticity of
substitution might be higher in the U.S. than in Japan.
36 In this paper, I show the results from the quite different settings of capital adjustment
cost and habit formation in order to keep the robustness of the result. However to obtainthe convincing values for these parameters would also enhance the credibility of the outcomesfrom the DSGE model.

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26

Chart 1

Chart 2

Chart 3

Chart 4

Chart 5

Chart 6

Chart 7

Chart 8

Chart 9Investment

Consumption
0

0
-0.2
-2

BASE

-0.4

HAC

-4

LAC

-6

HH

-8

LH

-0.6
-0.8

-10

-1
0

5

10

15

0

20

GDP

5

10

15

20

5

10

15

20

Call Rate
0.2

0
-0.5

0.15

-1
0.1

-1.5
0.05

-2

0

-2.5
0

5

10

15

20

5

10

15

20

Inflation
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0

0

Chart 10
Investment

Consumption

6

0.4

4
2

0.2
0

0
-2

-0.2

BASE
HAC
LAC
HH
LH

-4
-6
-8
-10

-0.4
-0.6
-0.8

-12

-1

0

5

10

15

20

GDP

0

5

10

15

20

5

10

15

20

Call Rate
0.2

2
1

0.1

0
-1
0

-2
-0.1

-3
0

5

10

15

20

10

15

20

Inflation
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0

5

0