Service Expenditure and Intertemporal
Intertempo ral Elasticity of
Substitution in Japan ∗Masafumi Kozuka
Faculty of Policy Studies, University of Marketing and Distribution Sciences
3-1 Gakuen Nishi-machi, Nishi-ku, Kobe city
Hyogo, 6512188, Japan
Research Fellow, Graduate School of Economics, Kobe University
2-1 Rokkodai-cho, Nada-ku, Kobe city
Hyogo, 6578501, Japan

Abstract
In this paper, we employ a cointegration approach to empirically analyze
consumer behavior related to service expenditure in Japan. The model we
employ is a CRRA utility function considering service and non-durable
expenditures. The ratio of service expenditure reached 50% in the 1980s in
Japan, and it has been increasing. It indicates that service expenditure is an
important factor in analyzing consumer behavior. The empirical results showthat the intertemporal elasticity of substitution of service expenditure ispositive, significant and greater than that of non-durable expenditure. These
results are caused by the growing ratio of selective service expenditure.
Keywords: Service e xpenditure,
xpenditure , i ntertemporal e lasticity of s ubstitution,
ubstitution ,c ointegration
JEL Classification Number: C32, E21∗

The author wishes to thank Ryuzo Miyao, Shigeyuki Hamori, Masahiko

Shibamoto and Takao Fujii for their valuable comments. We also thank Shinobu
Nakagawa (Bank of Japan) for valuable suggestions at the 2009 Autumn Annual
Meeting of the Japan Society of Monetary Economics. However, the remained
errors are mine. This work was supported by KAKENHI (19730218), Grant-in-Aid
for Young Scientists (B).

1

1. Introduction
In this paper, we employ a cointegration approach to empirically analyze
consumer behavior related to service expenditure in Japan.
The ratio of service expenditure to total consumption is considered toincrease as economic growth is promoted. For example, the ratio of service
expenditure reached 50% in the 1980s in Japan, and it increased after that, asshown in Fig. 1.
When we analyze consumption behavior with macroeconomics data, weusually focus on the intertemporal elasticity of substitution (hereafter, IES)
because the parameter IES implies a relationship between the interest ratelevel, conventional

instruments

of monetary policy,

andconsumption

expenditure. In particular, durable goods are considered to have positive andhigh IES because of their expensiveness and durability 1 . On the other hand,service expenditure cannot be accumulated and this character is the same asthat of non-durable consumption goods. Therefore, economic conditions are
not considered to influence the purchase of services and the service
expenditure trend is stable. For this reason, utilizing data of service isregarded as inappropriate one in empirical studies focusing on IES 2 .
However, the Bank of Japan (1998) claims that service expenditure is notstable because the ratio of service expenditure to total consumption is highand the consumption trend is not stable. The Bank of Japan (1998) states that“selective service expenditure” is not always necessity, and that expenditure
for selective services fluctuates according to the economic conditions.
Moreover, the trend of selective service expenditure is similar to that ofdurable consumption goods, which fluctuates according to the income trend, inother words, the economic conditions.
The Bank of Japan (1998) presents empirical results showing that service
expenditure can be explained by the income factor and consumer confidence
based on the sample period from 1976:Q2 to 1997:Q1.

For example, see Mankiw (1985) and Ogaki and Reinhart (1998a).
The empirical study by Ogaki and Reinhart (1998a) performs estimation ofEuler equation excluding service expenditure.
122

Figure 2 shows plots the expenditure for durable consumption goods andselective services in the 1990s and 2000s 3 . This figure shows that thefluctuation of expenditure for selective services is the same as that for durable
consumption goods and that their growth slowed in the 1990s when theJapanese economy was in a recession. This feature implies that theexpenditure for selective services is also adjusted according to the economic
conditions, as is the case with durable goods.
Figure 3 shows the ratio of expenditure for selective services to that for
total services 4 . This figure indicates that the percentage of selective service
expenditure was about 60% in the 1980s and it reached about 75% in the
2000s.
Figure 2 and 3 reveal that the service expenditure situation continued
after the 1990s as stated by the Bank of Japan (1998); the service expenditure
has been adjusted by business trends and might have a positive andsignificant IES.
In this paper, we perform empirical analysis focusing on the IES of service
expenditure with quarterly consumption data (Statistical National Account)from 1980:Q1 to 2006:Q4. Hansen and Singleton (1982), Hamori (1992) andOgaki and Reinhart (1998a,b), utilize Generalized Methods of Moment (GMM)
in order to estimate the Euler equation of consumption. But the ordinal Euler
equation of consumption consists of stationary variables: the real rate ofinterest and the ratio of consumption at the present and the next term. And
consumer behavior is assumed to be explained by stationary nuisance factors:
preference shocks, liquidity constraint and others. Then, the point estimatorobtained from a misspecified model without these factors might containdistortion. However, estimation of the model considering nuisance factors istroublesome.
Ogaki (1992) and Ogaki and Park (1998) developed a cointegration
approach for estimating the Euler equation. In this approach, they employ anadditive separable CRRA utility function, and solve the utility maximization
3
4

The definition of selective services is shown in the note of Fig. 2.
The details of the data are shown in a note of Fig. 3.
3

problem. Then, they derive the marginal rate of substitution (MRS) between
two types of consumption goods and obtain a linear equation for estimating
the intertemporal elasticity of substitution of these expenditures. We
employed this cointegration approach in order to avoid the influence of thestationary nuisance factor. To the best of our knowledge, this paper is the firstattempt to estimate the IES of service expenditure with a Euler equation.
In this paper, Section 2 shows how the model was derived. Section 3
presents the empirical analysis, and Section 4 discusses the results andpresents the conclusion.

2. ModelFirstly, we set the additive separable CRRA utility function u t as
follows:
1− 1

ut = aσ 1 ε1t

C1t

e

1− 1

σ1

1− 1

C σ 2 eε 2t+ 2t
LL (1) .
1− 1σ2Here, C it is expenditure for consumption good i (i = 1,2 ) at period t, a is
the weight andσ i implies the intertemporal elasticity of substitution of

consumption goods i . And

ε it is the stationary preference shock of each C it .

Then, the intertemporal budget constraint is written as(1 + rt +1 )(Yt − Pt1C1t − Pt 2C2t ) = Pt1+1C1t +1 + Pt +21C 2t +1 L ( 2) .
Here, Ptis the deflator of consumption good i (i = 1,2 ) at period t and rt isi

the real interest rate.
Employing (1) and (2), we can obtain the following equation:
1

−

1

σ1

Pt
aC
= 1t1 eε1t −ε 2 t L (3) .
2−Pt
C2tσ 2
And taking a logarithm of (3), it can be rewritten as follows: Pt1 11ln 2  = const. − ln C1t +ln(C 2t )+ (ε 1t − ε 2t )L(4) .
σ1
σ2
 Pt 

( )4

Equation (4) is the linear Euler equation. Here, const. includes weightaand ε 1t − ε 2 t is the error term. In this study, we utilize Equ. (4) as the modelfor estimation. And hereafter, we set Goods 1 as services and Goods 2 as
non-durable goods.

3. Empirical Analysis
In this section, we show the data description firstly. Then, we perform theempirical analysis with time series data: unit root test, cointegration test andestimation of cointegrating vector with DOLS (Dynamic OLS: Stock andWatson 1993).

3.1 Data
We utilize data of expenditure for consumption (service and non- durable
consumption goods) and their deflators taken from the Statistics National
Account (SNA). Here, we utilize 93SNA published in 2008 by the Cabinet
Office of the Japanese government. Per capita consumption is used in manystudies and we also employ monthly population estimation (Ministry ofInternal Affairs and Communication) following previous studies. We obtained
an original data series, and performed seasonal adjustment by X-12ARIMA.

3.2 Unit root Test
Then, we performed the unit root test for the variables included in Equ.
1(4): ln( Pt

Pt 2 ) , ln C1 and ln C 2 . And the procedure of the unit root test isPhillips= Perron test (Phillips and Perron 1988) considering the constantterm.
The results of the test for the level of variables indicate that the null
hypothesis of the unit root is accepted with a 5% significance level. And theresults of the test for 1 st difference show rejection of the null. Therefore, it isconsidered that these variables in Equ. (4) obey I(1) process. The results areshown in detail in Table 1. Considering constant and linear trends, onlyln( Pt1 Pt 2 ) and ln C 2 are I(1) variables.
53.3 Cointegration Test
In the previous subsection, we show that all variables in Equ. (4) are I(1)variables. Then, we perform the cointegration analysis in Equ. (4) and it ismore desirable. In this subsection, we perform three types of cointegration
test: the residual-based cointegration test (Engle=Granger test) developed byEngle and Granger (1987), maximum eigenvalue test based on the Vector
Error Correction Model (VECM) by Johansen (1988) and Johansen andJuselius (1990) and residual-based test considering a possible structural
break in the cointegration vector (Gregory and Hansen 1996) 5 .
For the Gregory=Hansen test, we consider only the structural shift in theconstant term.
And as the specification of the model, we utilize Equ. (4) including a1linear trend because ln( Pt

Pt 2 ) and ln C 2 (relative price and non-durable

consumption expenditure) are I(1) variables with a linear trend.
The empirical results of the Engle-Granger test show the rejection of thenull of no cointegration in Equ. (4). The details are shown in Table 2. The test
statistics are -4.908 with an augmented term with degree 0 detected by SBIC.
Next, we show the empirical results of the maximum eigenvalue test.
Following this test, we obtain the results of acceptance of the null in which
the cointegrating rank is 0 at most with 5% significance level. This result
implies there is no cointegration vector among all or some of three variables.
The details are shown in Table 3.
The empirical results with the cointegration test developed by Gregoryand Hansen (1996) indicate the rejection of the null hypothesis of no
cointegration with a possible break in the constant term with 5% significancelevel. The test statistics are provided by the -5.600(C-T model in Gregory andHansen 1996) with no augmented term detected by SBIC.

The cointegration test developed by Gregory and Hansen(1996) is the procedure
considering a possible break point in cointegrating vector. And thus, rejection of the nullof no cointegration does not always imply the existence of a break in the cointegration
vector.

5

6

3.4 Estimation of the Cointegration Vector
In the previous subsection, we show the existence of one cointegration
vector in the linear Euler equation with non-durable and service expenditurein Japan by the residual-based cointegration test. Now, we verify the point
estimator of the cointegration vector in this Euler equation.
Usually, when a regression consisting of I(1) variables has a cointegration
vector, point estimators are super-consistent with T-convergence. However, wehave to estimate them adjusting the correlation between the error term andindependent variables: the existence of endogeneity. Moreover, serial
correlation and heteroskedastisity have certain effects on the t -values of point
estimators via their standard errors.
Therefore, we have to consider these problems when we verify the
cointegration vector so we employ the Dynamics OLD (DOLS) developed by
Stock and Watson (1993), in order to avoid the problem of endogeneity. And we
utilize Newey and West (1987)’s variance-covariance matrix in order to modify
the standard error influenced by serial correlation and/or heteroskedastisity.
In order to perform the DOLS, we add leads and lags of augmented terms,
which consist of 1st difference of independent variables. Then, if thecorrelation between augmented terms and error term is the main cause ofendogeneity; adding these leads and lags can be a solution to this problem.
The model for estimation is as follows: P1 
11ln t2  = const. − ln aC1t +ln (C 2t )σ1
σ2 Pt 

()+ ∑i = − p γ 1i ∆ ln C1,t −i + ∑i = − p γ 2i ∆ ln C 2,t −i + (ε 1t − ε 2t ) L (5).
ppHere, γ 1i and γ 2i are coefficients of leads and lags. And i implies thelength of leads and lags and we set i = 1 because of the short sample periods.
When we consider dummy variable, Dτ , which explains the shift of theconstant term, the model is as follows:7 P1 11ln t2  = const . + γ D Dτ −ln aC1t +ln (C 2t )σ1
σ2 Pt 

()+ ∑i = − p γ 1i ∆ ln C1,t −i + ∑i = − p γ 2i ∆ ln C 2,t −i + (ε 1t − ε 2t ) L (6).
pp

The estimation results of DOLS show that the (reciprocal of) IESs are
positive and significant considering the shift in the constant term. In thisestimation, we modify the standard error with Newey and West (1987)’s
variance-covariance matrix. And they also show that the IES of expenditure
for service is larger than that of expenditure for non-durable consumption
goods 6 . On the other hand, without considering the shift of the constant, theestimated IES of service expenditure is not significant. The details are shownin Table 5.

4. Conclusion
In the previous section, we estimate the linear Euler equation considering
expenditure on services and non-durable goods in Japan from 1990:Q1 to
2006:Q4. These empirical results show that a cointegration relation exists inthe Euler equation following Gregory and Hansen (1996)’s procedure, and that
IES of consumption is both positive and significant with a shift of constantterm. Moreover, the IES of service expenditure is higher than that ofnon-durable consumption.
These results indicate that service expenditure was influenced by the
economic conditions and the interest rate level after the 1990s in Japan. Thisphenomenon may be due to the higher weight of selective service expenditure,
which tends to react to the economic conditions, as shown in Figs. 2 and 3.
The sample period we employ is 1990-2006, and the Bank of Japan adopted
a zero interest rate policy from 1999-2000 and 2001-2006. But the realinterest rate, which is considered in the model, still fluctuated under the zerointerest rate policy. And thus, these empirical results on IES to the realinterest rate seem to make a certain contribution.
These empirical results support the hypothesis that the IES of service
6

We have to notice that the results of point estimates are reciprocal of IESs.

8expenditure in Japan is positive and significant; we can apply the Euler
equation for service expenditure in the 1990s and 2000s in Japan. Theintertemporal elasticity of substitution is a parameter that implies the degreeof the response of consumption to the interest rate, a conventional instrumentof monetary policy. Our empirical results suggest that we should consider
service expenditure, which accounts for more than 50% of consumption in
Japan, when analyzing consumers’ behavior and the effects of monetary policy
on consumption.
Our

empirical

results

show

that

the

intertemporalelasticity

ofsubstitution of service expenditure is both positive and significant; however,these results are caused by the existence of selective service expenditure. As
selective service expenditure includes luxury services, the significance andsign of IES will alter depending on the income level and the countries of thesample. We will compare IESs at different income levels and in different
countries as future works.

9References
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Monthly Research Report, June 1998, Research and Statistics
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correction:

Representation,

estimation,andtesting."

Econometrica

Vol.55 No.2, pp.251-276


Fuller, Wayne, A. (1976) "Introduction to Statistical Time Series." New
York: Wiley

Gregory, Allan W. and Hansen, Bruce E.(1996) "Residual-based test for
cointegration in models with regime shift." Journal of Econometrics Vol.70,
pp.99-126



Hamori, Shigeyuki (1992)"Test of C-CAPM for Japan: 1980-1988."

Economics Letters Vol.38, pp.67-72
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L.

Peter

and

KennethJ.

Singleton(1982)"Generalized

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Johansen, Soren(1988) "Statistical analysis of cointegration vectors."

Journal of Economic Dynamics and Control , Vol.12 pp.231-254
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estimation and inference on cointegration-with applications to thedemand for money." Oxford Bulletin on Economics and Statistics , Vol.52
No.2, pp.169-209

MacKinnon, J.G., A. A. Haug, and L. Michelis (1999) “Numerical
distribution function of likelihood ratio tests for cointegration.” Journal ofApplied Econometrics , Vol.14, No.5, 563-77.
Mankiw, N. Gregory (1985) "Consumer Durables and the Real Interest
Rate," Review of Economics and Statistics , Vol. 67, No. 3, August 1985, pp.
353-362.



Newey, Whitney K. and Kenneth D. West (1987) “A Simple, Semi-Definite,
Hetero-skedasticity and Autocorrelation Consistent Covariance Matrix.”

Econometrica ,Vol.55 pp.703-708
10Ogaki, Masao (1992) "Engel’s Law and cointegration."

Journal of

Political Economy 100, pp.1027-1046.


Ogaki, Masao and Joon Y. Park(1998) "A cointegration approach toestimating preference parameters."

Journal of Econometrics Vol.82-1,

pp.107-134.
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Vol.106-5, pp.1078-1098.

Ogaki, Masao and Carmen M. Reinhart(1998b) "Intertemporal
substitution and durable goods: long-run data." Economics Letters,
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Phillips, P.C.B and S. Ouliaris (1990) “Asymptotic properties of residual
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Phillips, P.C.B. and P. Perron (1988) “Testing for a unit root in time series
regression.” Biometrika , 75, pp.335-346

11Figure 1

Ratio of Each Consumption Expenditure
Expenditur e to Domestic Consumption

Source: Statistical of National Account 2008, “Classification by ‘type of Households
Consumption Expenditure’ ”Annual, Real (Chained) Consumption

12

Figure 2: Selective Service Expenditure and Durable Consumption Goods
Expenditure(Note) We obtained data of durable goods expenditure and household final consumption
expenditures from SNA (published in 2008 by Cabinet Office, annual, chained). The
selective service expenditure consists of eating out, construction and other services,
housework

service,transportationandtelecommunication,

clothing

servicesandcultural-amusement services taken from the household survey conducted by the Ministryof Internal Affairs and Communications. They are deflated by CPI.

13

Fig.3: The Ratio of Selective Services
Servic es in Total
Tota l Service Expenditure(Note) We obtain data of service expenditure from household final consumption
expenditures by category in SNA (published in 2008, annual, chained). The source of theselective service expenditure is the same as that in Fig.3. We exclude insurance premium,medical expense and imputed rent because they are handled differently in the SNA andhousehold survey.

14

Table １

Unit Root Test（
est （ PhillipsPhillips - Perron test）
test ）

With const.

lnP（
lnP （ Price）
Price ）ND（
ND （ NonNon - Durable）
Durable ）SEV ( Service)
Service )X-1.790(4)-2.501(2)-0.009(11)∆X-8.731(4)***-12.911(1)***-15.757(9)***(Note)*** denotes rejection at a significance level of 1%(Critical Value= -3.510), and **donotes 5%(C.V.=-2.890)（ C.V. are shown in Fuller (1976）and they are the case of T=100）

Table 2

Cointegration Test

（ EngleEngle - Granger test）
test ）
Test Statstics-4.908(0)***(Note) *** denotes rejection at a significance level of 1%, and ** donotes 5%. C.V.
are 4.650(1%) and -4.160(5%)（ Phillips and Ouliaris 1990） . The linear trend is includedin the cointegration vector. The numbers in the parentheses are the lag length

following SBIC.

Table 3

Cointegration Test (Maximum E igenvalue Test)
Null

Test stat.

(rank=number of cointegrating rank）

CriticalP -value

value(5％ )rank=023.86925.8530.089

rank ≤ 1

15.17819.387

0.184

rank ≤ 2

7.310

12.5180.313(Note) C.V. are shown in MacKinnon(1999). The linear trend is included in the
cointegration vector. The number of the lag length is 1 following SBIC.

15

Table 4

Cointegration Test

（ GregoryGregory - Hansen Test）
est ）CT-modelTest stat.

Break－ 5.600 (0)**1996:Q2(注 )C.V. are -5.80 (1%) and -5.29 (5%)（ Gregory and Hansen(1996), Table 1, m=2）
The linear trend is included in the cointegration vector（ CT-model） .

** denotes rejection at a significance level of 5%. The numbers in the parentheses
are the lag lengths following SBIC.

Table 5

Point E stimator of C ointegration Ve ctor by DOLS

1 σ D

1 σ SERV

1.174(15.291)***0.124(0.644)

1.035(11.822)***0.443(2.082)**＜ with trend＞
Estimated values（ Modified t -value）＜ with trend, shift in constant＞
Estimated values（ Modified t -value）(Note) Here, t -values are modified with Newey and West(1987)’s variance-covariancematrix. The length of leads and lags is 1.

*** denotes rejection at a significance level of 1%, and ** denotes 5%.

16