Discussion Paper No. 77
Intra-temporal Substitution between Tradable andNontradable Goods: Evidence from the Japanese
Cross-sectional Survey Data
Jun Nagayasu

March , 2018

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku
Sendai 980-8576, JAPANIntra-temporal Substitution between Tradable andNontradable Goods: Evidence from the Japanese
Cross-sectional Survey Data
Jun Nagayasu†

Abstract

Using survey-based Japanese household data, this study estimates the elasticity of
intra-temporal substitution (EIS) between tradable and nontradable goods. Thus,
this research is related to the Backus-Smith puzzle (1993), which states the nontradable sector and low substitution between these goods are the reasons for nonconformance to the purchasing power parity theory. Among other conclusions, we
confirm that consumption behavior differs among households with different social
backgrounds. Furthermore, we find that the EIS is overestimated when household
characteristics and time dimensions are not taken into account in the consumption function. Indeed, the EIS is low and close to zero when properly estimated,
thereby confirming a cause of the Backus-Smith puzzle. Based on these findings,
we conclude that prices are less decisive factors in determining the consumption
composition than what the standard economic theories predict. In contrast, social
factors such as age, cohort, and family size are more directly associated with consumers’ allocation of goods and services.
Keywords: Intra-temporal elasticity of substitution, tradable and nontradable
goods, economic goods and services, survey-based household data, JapanJEL classification: D1†

Tohoku University, Graduate School of Economics and Management, Address: 27-1 Kawauchi, Aobaku, Sendai, Miyagi 980-8576 JAPAN, Email: jun.nagayasu.d8@tohoku.ac.jp, Tel: +81 22 795 6265,
Fax: +81 22 795 6270 The previous version was presented at the Household Finance Conference, theMacroeconomics Workshop at Kyoto/Osaka Universities, and the biannual meetings of the Japan Societyof Monetary Economics and the Japanese Economic Association. I would like to thank Yuji C. Horioka,
Hiroshi Fujiki, Hirokazu Ishise, Yukinobu Kitamura, Shin-ichi Nishiyama, Arito Ono, Masakatsu Okubo,
Takayuki Tsuruga, and Takashi Unayama for constructive comments. I also thank Gabriel Cordoba
for research assistance. All remaining errors are mine. This research was supported by grants-in-aid
for Scientific Research from the Japan Society for the Promotion of Science (Kakenhi Kiban (C) No.
17K03796).

1Introduction

Consumers often make economic and financial decisions subject to budget constraints,
and such decisions are related to the selection of goods and services to maximize theirutility. Moreover, conventional economic theory suggests that, while making consumption
decisions, prices are often assumed to play a key role. The relationship between prices
and the selection of goods and services is summarized in the elasticity of substitution.
Academic research considers two types of substitution. The substitution among economic goods at a particular point in time is called the intra-temporal substitution. On
the other hand, inter -temporal substitution refers to how consumption should be allocated over time and is the major focus of previous studies using time series data. This
trend in the previous literature appears to reflect in part the data availability and the
difficulties in the estimation of inter-temporal substitution using standard statistical methods. That is, while estimates of intra-temporal elasticity are robust, the magnitude ofinter-temporal substitution is reportedly biased unless the intra-temporal substitution isconsidered (Ogaki and Reinhart 1998).
In the past, such substitution has often been between the two types of economic goods
and services: (1) durables versus non-durables (e.g., Ogaki and Reinhart 1998, Pakos
2011), (2) goods purchased by governments versus goods purchased by private consumers(e.g., Bailey 1971, Ho 2001, Okubo 2003, Auteri and Costantini 2010), (3) domestic versus
imported goods (Amano and Wirjanoto 1996), and (4) tradable versus nontradable goods(Cashin and McDermott 2003). These studies are often based on a theoretical derivationthat maximizes the utility of a representative agent (Ogaki and Reinhart 1998, Ogaki
and Park 1992), and such a theoretical framework is shown to be consistent with the timeseries properties of consumption data. Therefore, statistical methods such as cointegration(Engle and Granger 1987) have been popular analytical tools in the past.
Against this background, we shall analyze the elasticity of intra-temporal substitution(EIS) in Japan, particularly between tradable and nontradable goods, using survey-basedhousehold data. Microdata analysis is known to be more reliable than the study of aggregate data. Results from analysis of macroeconomic data suffer from aggregation bias andsuggest a lower value for the elasticity of inter-temporal substitution than microdata analysis even when demographic factors are considered (Attanasio and Weber 1993). Blundell2

et al. (1994) show that excess sensitivity of consumption to income growth, often observed in aggregate data, can be eliminated when household characteristics are included
in microdata analysis. Thus, this paper departs from previous studies in the following
aspects. First, to the best of our knowledge, this study is one of the first to use household
consumption data to estimate the elasticity of substitution in Japan. Microdata allow
us to consider household characteristics, which have been ignored in previous studies, inthe elasticity estimation. This is expected to be important as differences in consumption
patterns across different life stages have been reported by researchers (Modigliani 1966,
Skinner 1988), and dramatic demographic changes have been taken place in Japan. The
Cashin and Unayama (2016) study is one exception that analyzed substitution elasticity
using survey data. They analyzed the impact of the consumption tax increase in April
1997 on consumption behavior, and concluded that the elasticity of inter -temporal substitution was nil in Japan. It suggests that despite perceived increases in prices, consumers
did not rush out to purchase goods prior to the implementation of the tax rate hike.1
Second, as can be seen from the aforementioned literature, this is one of the very firststudies to analyze the degree of substitution between tradable and nontradable goods.
This distinction is important in economic analysis because it modifies the theoretical predictions in many fields of economics. For example, nontradable goods are used to explain
violations of the purchasing power parity (PPP) condition. Balassa (1964) and Samuelson(1964) have argued that different wage growth in nontradable sectors across countries is
attributable to the persistent deviation of real exchange rates from the PPP, known as
the Balassa-Samuelson puzzle. Furthermore, Backus and Smith (1993) state that, despite
progress in removing cross-border barriers, the poor relationship between real exchange
rates and consumption (the Backus-Smith (BS) puzzle) arises because nontradable goods
are not considered in economic theory and there is low substitution between tradable andnontradable goods. Nagayasu (2017) confirms that the BS puzzle is caused mainly by
the imperfect substitutability between tradable and nontradable goods, rather than theexchange rate fluctuation.
1

There are many studies using microdata in other countries. For example, Blundell et al. (1994)
and Crossley and Low (2011) studied household characteristics and time-varying nature in the study ofinter-temporal substitution, respectively, in the UK. Similarly, using the UK microdata, Attanasio and
Browning (1995) studied demographic effects on inter-temporal substitution.

3

2

Substitution between tradable and non-tradable goods

This section explains the theoretical definition of substitution following the analyticalframework often used in previous studies.2 That is, consumers maximize their utility,
which is a function of consumption. Closely following Amano and Wirjanto (1998), a
household (i) is assumed to maximize the following expected utility function (U (·)) thatis based on consumption (C).

E

"∞
X

#
β t U (CitT r , CitN T r )

(1)

t=0

where E is an expectations operator, and the consumption of tradable and nontradable goods are denoted as CtT r and CtN T r respectively. β ∈ (0, 1) is a subjective
discount factor, and subscript t denotes time (t = 1, ..., T ). To derive the EIS, Zeldes(1989) and Blundell et al. (2008) use the following constant-elasticity-of-substitution
utility function with a parameter of household-specific tastes, θit :U (CitT r , CitN T r ) =u(CitT r , CitN T r )1−γ
exp(θit )1−γ(2)

where γ (γ > 0) is the coefficient of relative risk aversion (RRA). 1/γ is the inter temporal elasticity of substitution between tradable and nontradable goods. Generally,
previous studies report a large γ (typically less than 10) and the inter-temporal elasticity
is not equal to one as predicted by a time-separable utility model (Constantinides 1990).
Moreover, we assume that the taste parameter comprises time and household-specificelements (ηt and δi ) as well as random components (ωit ∼ N (0, σω2 )).
θitT r = ηtT r + δiT r + ωitT r
θitN T r = ηtN T r + δiN T r + ωitN T r
Therefore, there is no need for taste variables to be identical for tradable and nontradable goods. Eq. (2) without θit is often used to describe a steady-state conditionin economic growth models, which makes this utility function very popular in macroeco2

The intra-temporal elasticity of substitution is hereinafter referred to simply as elasticity of substitution unless specified.

4

nomic analyses. Using the above mentioned notations, the consumption index becomesequal to:1u(CitT r , CitN T r ) = [∅ exp(θitT r )(CitT r )1−α + (1 − ∅) exp(θitN T r )(CitN T r )1−α ] 1−α(3)where α > 0. Parameter ∅ is a weight attached to tradable goods (∅ ∈ (0, 1)). This index
represents the utility function being additively separable into two types of goods, andbecomes a Cobb-Douglas-type function when α approaches one. This index is homothetic
and assumes no income effect. The non-homothetic index may be more plausible in a
general setting, but this classical assumption is maintained here because our analysis isbased on cross-sectional data and this assumption makes our results comparable withthose in previous studies. In these preference specifications, 1/α is the EIS (Ogaki andReinhart 1998, Amano and Wirjanto 1998), which is of interest here,3 and the parameterof substitution is theoretically positive.
Based on these equations, optimal consumption behavior can be stated by analyzing
the first-order condition, which implies that the relative price equals the ratio of marginal
rates of substitution.
∂U

Tr
pTitr
∅ exp(θitT r )(CitT r )−α
∂Cit
=
=
Tr
∂U
pN
(1 − ∅) exp(θitN T r )(CitN r )−αit∂C N T r(4)itThis equation can be expressed in the natural logarithmic form as Eq. (5), and shows thatthe absence of household characteristics results in the model misspecification. Critically,
Eq. (5) assumes a homogenous EIS even though taste factors are included.

ln

pTitr
Tr
pN
it




= ln

∅
1−∅



+ (θitT r − θitN T r ) + α ln

CitN T r
CitT r(5)

To estimate the homogeneous EIS, we re-express Eq. (5) in terms of consumption, as will
be discussed in Section 4. Moreover,we consider several combinations of social factorsthat are expected to affect tastes and the consumption composition, and the robustnessof our findings will be examined by considering financial wealth of households, which isabsent in the above mentioned theoretical model.
3

Using these two types of substitution, Amano and Wirjanto (1998) show the Edgeworth-Pareto
conditions.

5

3

Data

Our analysis requires consumption and price data. Survey-based consumption data are
obtained from the Zenkoku Shohi Jittai Chosa (National Survey of Family Income andExpenditure, NSFIE) compiled by Japan’s Ministry of Internal Affairs and Communications (MIAC). This survey has been conducted every five years since 1959 to gather
detailed information about the consumption patterns of residents in Japan. In fact, the
NSFIE is the most comprehensive dataset of consumption data in Japan with a sample
size of about 50000 households for each year. Consumption consists of the consumptionof durable, semi-durable, and non-durable goods as well as services. Generally, durable
goods are those that are expected to last more than one year, and the distinction between
durable and semi-durable goods is made according to price. Following the traditional
approach (Balassa 1964), the first three are treated in this study as tradable goods andservices as nontradable goods.4 In addition to expenditures, the NSFIE contains information about income and social backgrounds such as age, gender and employment status.
The NSFIE is also comprehensive in terms of geographical coverage and includes about
5000 geographical units (cities, towns, and villages).
Cross-sectional household-level NSFIE data are disseminated to the public from theStatistics Bureau of Japan’s MIAC for four years (1989, 1994, 1999, and 2004). There isanother dataset, the Kakei Chousa (Family Income and Expenditure Survey, FIES), whichis conducted monthly, but its sample size is only about 9000 households, and furthermore
household-level data from this survey are not disseminated to the public. Thus, ourdataset covers the bubble period (through February 1991) and the post-bubble period(March 1991 onwards). During the bubble period, prices of financial and nonfinancial
assets rose in an unprecedented manner, and consumers perceived that such price increases
in financial assets and real estates were permanent. On the other hand, the post-bubble
period was an era of low economic growth and low inflation, and consumers did not havebright prospects for the future. Therefore, our sample periods are long enough to coversignificant shifts in consumers’ living environments that potentially become factors to
4This dataset has been used to analyze savings behavior in Japan by many researchers (e.g., Hayashi
2011, Kitamura et al. 2001). They provide detailed descriptions of this dataset and also point out the
deficiencies in it especially for the analysis of savings.

6

change consumption decisions.5
This survey is conducted during September-November each year for households of
two or more persons and during the October-November of each year for single-personhouseholds. Single-person households account for only a small fraction of our dataset(Table 1), and the average number of household members is around three, typically twoparents and a child (Figure 1). The largest household in our sample contains sevenmembers. Interestingly, large (more than five people) as well as two-person families tend
to reside in the countryside, while there is more likelihood of four-person families inmetropolitan areas (Tokyo, Osaka, and Nagoya regions). On the other hand, there are noclear regional differences in terms of the distribution of single-person families.
Household heads are typically aged around 45 to 49 years, and the majority (90%) are
male, and 40% of households live in one of the three metropolitan areas. Moreover, 70%of households have at least one member with a full-time job6 and a simple average annual
salary of 6.7 million yen, with savings of 11.4 million yen. Income profiles of households
are also presented in Figure 2 by time periods, age groups and generations (cohorts). It
shows that income distribution is skewed to the left, indicating that more consumers earn
less than the average income. Furthermore, consumers aged between 55–59 (Age7), which
is more or less in line with the retirement age in Japan, earned the highest.
It is interesting to note that income inequality widens along with age and cohort (Table2). The heads of household in the same cohort can be identified because age profiles arereported in 5-year intervals, and the survey is conducted every 5 years. Greater inequality
is usually found among the older people and generations, perhaps due to differences inwork experiences. Because older people generally possess more hands-on and relevant
experience, their income is expected to be high. However, not all people are promoted atwork as the amount of accumulation of job skills is rather specific to individual workers. As
a result, a society is normally less egalitarian in line with age and cohort. Nevertheless, byinternational standards, Japan has been considered as historically egalitarian. The Gini
coefficient for Japanese labors between 35 and 65 years old from 2009 to 2013 is reported
as 0.329 while that for U.S. labors it is reported as 0.453 (Aizawa et al. 2017). The
5

For these four years, annual inflation (YOY) was 2.3, 0.7, -0.3 and 0.0 percent, and the overnight
uncollateralized call money rate was 5.117, 2.196, 0.058 and 0.001%.
6
The distinction between full-time and part-time jobs is important because of job security and social
benefits aspects, which are often not available to part-time workers in Japan.

7inequality results from differences in education and marital status in Japan, and education
and working hours in the United States. Occupations and positions in companies are inturn influenced by educational attainment and work experience.
Figure 3 plots the proportion of services in the total consumption according to keygrouping variables, and suggests heterogeneity in consumption composition. For instance,
small families tend to spend proportionally more on services, and there is a notable difference in consumption patterns between single-person households and families. Furthermore, the very poor and rich households tend to consume services proportionally less thanthe middle-income groups. A large portion of the consumption of the poor is in necessary
goods for living, which are often considered non-durable goods. The wealthy households
purchase enough services and spend more on expensive economic goods. Similarly, households in urban areas and female households spend more on services, reflecting the factthat more services are available in larger cities.
In addition to consumption data, we obtain price data from the CPI compiled by the
MIAC (see Table 1). To maintain consistency with the consumption data, and given theparticular months of the year during which the NSFIE is conducted, we use the price data
for August.7 In this manner, we attempt to mitigate the potential endogeneity problem inour specification, which was overcome by the use of cointegration techniques in previous
time series analyses. Due to lack of detailed residential information of households in the
NSFIE, we use the CPI of Tokyo to represent prices in the metropolitan areas, and thenational average as a proxy for prices in other regions.8

4

Intra-temporal substitution

4.1

The standard specification of EIS (Model 1)

Initially, we estimate the classical EIS specification (Amano and Wirjanto 1998), thereby
assuming the constant RRA across households and no taste shift variables (θitT r − θitN T r ).
However, unlike some previous studies, it is more natural to express Eq. (5) in terms
of prices in a highly competitive market, in which prices are often given to consumers.
7

The general results remain unchanged when the CPI for September is used.
Our results may suffer because of a lack of variation in regional prices, but this problem is mitigatedby our analysis of price ratio as opposed to price level.
88Furthermore, because our data are cross-sectional, the subscript t disappears from ourestimation model. We name this specification Model 1.
ln

CiN T r
CiT r



 

 Tr 
∅1p1ln+ ln Ni T r
=−
α
1−∅
α
pi

(6)

This equation shows the magnitude of changes in consumption patterns (i.e., from tradable
to nontradable goods or vice versa) in response to price differences. Therefore, parameter1/α measures the extent to which consumption patterns have changed due to increases
in relative prices. When α > 0, an increase in the prices of tradable goods leads to a
decline in their consumption and/or a rise in that of nontradable goods. Random shocks
to preferences frequently considered in time series analysis, are assumed to be captured
in a fixed effects term in cross-sectional analyses.
In a more compact form that is directly linked with statistical analysis, Eq. (6) canbe expressed as:ỹ = ax̃ + u
where ỹ = yi − N −1

PN

i=1 yi and x̃ = xi − N

−1

(7)

PN

i=1 xi represent relative consumption andthe price ratio, respectively. This data transformation results in E(ỹ) = E(x̃) = E(u) =0. The residual u is normally distributed with a constant variance (σ 2 ). We estimate thisequation using the Bayesian estimation approach (the random-walk Metropolis-Hastings
sampling method) that allows us to impose easily a non-negativity parameter constraint
on the EIS.
In order to obtain posterior distributions of parameters, Model 1 assumes the priordistributions (a ∼Uniform(0,100) and σ 2 ∼ IG(0.01, 0.01)), and several statistics arecalculated in order to summarize the posterior. We can evaluate a parameter size by
examining the posterior mean, median, 95% credible interval, and standard deviationof the marginal posterior distributions. In addition, the Monte Carlo standard error(MCSE) is presented to show the accuracy of the posterior mean estimates; the small
MCSE indicates good sampling. The difference in the mean and medium values indicatesthe asymmetry in the posterior distributions.
Table 3 summarizes these statistics of the EIS for a variety of household groups.

9The estimation with iterations of 10000 and burn-in of 3000 suggests that the EIS is5.433 without considering social indicators. This is slightly higher than the EIS reported
in Cashin and McDermott (2003). Their estimates, using macroeconomic data for fiveadvanced countries (Australia, Canada, NZ, the UK, and the US), range from 0.6 to
3.5. However, such estimates may not be very accurate as they may be sensitive to thehousehold characteristics. Previous studies on consumption point out that consumption
behavior is heterogeneous among consumers, and thus the consumption composition is
likely to differ according to consumers’ characteristics such as family size (e.g., Irvine1978). Therefore, we estimate the elasticity using Eq. (7) by consumer type in terms ofresidential location, gender, employment status, and family size.
Indeed, the EIS appears to differ among households. It is reported to be higher in themetropolitan areas and for males. Furthermore, the level of substitution is higher for thosein employment. This result may be contrary to the expectation that poor people are moresensitive to prices, but is consistent with prior academic studies (Havranek et al. 2015) on
inter-temporal substitution. They interpret this result as suggesting that non-employedpersons purchase only really necessary goods and thus may be living already below thesubsistence levels at which relative prices are less relevant to their consumption decisions.
On the other hand, wealthy consumers tend to purchase relatively more luxurious goods
that are not necessities and thus have potential alternatives. More significant discrepancies
in the EIS are reported between single-person households and those with two or more
persons. Our finding of heterogeneous EIS among different households here implies thatsocial factors need to be included in the EIS estimation.

4.2

The EIS and social factors (Model 2)

Recognizing the importance of social factors in consumption decisions, we re-estimate the
EIS based on Eq. (8) that adds social backgrounds of households (Θi = θiT r − θiN T r ) as
explanatory variables in Model 1. This specification is in line with previous studies (e.g.,
Zeldes 1989, Blundell et al. 2008) and is equivalent to allowing household-specific terms
in the cross-sectional analysis, and is referred to as Model 2.
ln

CiN T r
CiT r



 


 Tr 
1
∅
1
p
=−
ln
+ Θi + ln Ni T r
α
1−∅
α
pi
10

(8)

where Θi is specified as a function of social factors for each household i.
Θi =a + bGenderi + cF amily sizei + dAgei + eAge2i + f W orkers in f amilyi + ui
The choice of these social variables is similar to that of Zeldes (1989) who considers
family size, age and squared age of household heads, but we also use other variables
such as Gender and Workers in the family. Notably, we consider differences in taste
among genders and also the unique characteristics of families with more than one workers(Workers in family), typically households of two-parent working families that have beensteadily increasing over the years, reaching 10 million in 2007. Since the average annual
salary of such households is around 7 million yen in total, individual workers in twoparent working families are often relatively poor, and they may find it difficult to live ona single source of income. Among social indicators, age is important in the analysis of theJapanese economy because demographic changes have accelerated over recent decades;
while the birth rate remains low (1.46), Japanese longevity is one of the highest in theworld: 80.79 for males and 87.05 for females in 2015. As a result, Japan has become
one of the most aging countries in the world, and this phenomenon has created social
problems such as a decreasing labor force and inadequate social care funding. To tackle
these issues, the typical retirement age has been gradually increasing from 55 years in
the 1970s and 1980s to 60 years in 2016, even for those employed by large corporations.
Furthermore, the government is encouraging firms to increase the retirement age further
to 65 years by introducing the Law of Stabilization of Employment of Older Persons in2013.
Generally, consumption decisions are considered to be closely related to life stages.
The life cycle hypothesis (Modigliani 1966) asserts that young people save for their retirement, and they dis-save for living when they become pensioners. Skinner (1988) has
demonstrated that due to uncertainty in future interest rates and earnings, precautionarysaving accounts for more than half of total life time saving. Although his paper focusedon savings, it has strong implications for household decisions as consumption is the otherside of the coin, and the (dis-)saving behaviors is consistent with smoothing consumption
in response to expected changes in their future income. Their efforts to smooth consumption and maximize utility are also reflected in the intra- and inter-temporal elasticity of11substitution.
Because Eq. (8) is a linear equation, we maintain the same prior distribution for theparameters as those used in Table 3; however, additional parameters (a, b, c, d, e,andf )of explanatory variables related to social factors are assumed to follow the normal distribution (Normal(0,10000)) as there is no strong theoretical predicted sign for theseparameters. In other words,

a, b, c, d, e, f ∼ N (0, 10000)
EIS ∼ U nif orm(0, 100)σ 2 ∼ IG(0.01, 0.01)

Table 4 summarizes the results from the specification with and without time dummies(1994, 1999 and 2004). Ceteris paribus, our results suggest that, females, and small andyoung families tend to spend proportionally more on services. Furthermore, when there
are more than two people working in a family, there is a tendency for the household toconsume proportionally more tradable goods. Because 95% credible intervals of theseparameters do not cross zero, we can interpret these parameters as statistically significant, thereby implying the rejection of the null hypothesis of a homogenous consumption
composition among household groups.
The EIS is also reported to differ among models with different compositions of social
factors; however, when both social factors and time dummies are included in the specification, the EIS estimates are consistently close to zero. Then, which EIS is the mostreliable? For this purpose, we choose the best model on the basis of the Deviance Information Criterion (DIC) estimated by the Markov Chain Monte Carlo method (MCMC).
The DIC is widely used in Baynesian analyses to describe the model accuracy, and similar
to the information criteria for time series (e.g., Akaike information criterion), the smallvalue of this criterion indicates that the model is a best fit to the data.9 The deviancefor observed data y is −2 log p(y|ϑBayes ), where ϑBayes is the posterior mean and p(.) is
9

The DIC is probably the most standard criterion, and, despite potential problems, has yielded the
expected positive statistics in our analysis.

12the log predictive density and is theoretically positive and less than one. Then, the DIC
is often calculated as:
DIC = −2 log p(y|ϑBayes ) + 2pDIC
where pDIC is the effective number of parameters. We check which variable is the bestfor grouping our observations.
According to the DIC, the model comprising time dummies and the social indicators,
which includes Gender, Family size, Age, Age2 , and Workers in family, has the smallest
value of the DIC (Table 5). Therefore, the EIS of 0.004 seems to be most supported by
the data, and the medium value also shows a similar EIS. Figure 4 presents convergenceof EIS estimates and ensures their statistical reliability. Thus, together with Cashin andUnayama (2016) who report evidence of the insignificant elasticity of inter-temporal substitution, our study suggests a marginal importance of price mechanisms in Japan during
our sample period. Given the significant parameter size for household characteristics in
Eq. (8), social backgrounds of households are more influential over consumer decisions
than prices. To check the robustness of our elasticity estimates, we shall next calculate
the EIS between non-durables and services as well as among cohorts. Furthermore, theEIS will be investigated taking into account financial backgrounds of households.

5

Further analyses

5.1

Elasticity between non-durables and services

Our definition of tradable goods consists of durable, semi-durable, and non-durable goods.
It is well known that consumers do not purchase durable goods as often as non-durable
goods because durables last longer than non-durables. Therefore, consumer decisions topurchase durable and semi-durable goods may not be as sensitive to price changes as nondurable ones. Indeed, most consumption studies distinguish between durable and nondurable goods, and they focus on the latter because prices of non-durables are expected
to react to economic shocks more in ways that are more consistent with economic theory.
Thus, we estimate the EIS between non-durable goods and services based on Model 2.
The results with or without time dummies are summarized in Table 6, and there

13are two messages in this table. First, like the EIS analysis of tradables and services,females and small families tend to consume services relatively more than non-durable
goods, ceteris paribus. Similarly, there is a tendency for older people to spend more on
tradable goods when time dummies are included. Second, the EIS between non-durables
and services is reported to be slightly higher than the EIS between tradables and services.
This is an expected outcome since durable and semi-durable goods, which are less sensitive
to prices, are removed from this analysis. However, such discrepancies between the EISs
are marginal, since the EIS between services and the non-durable (0.001 and 0.014) stays
within the 95% credible interval of the EIS between services and tradable goods (i.e.,
between 0.000 and 0.015 in Table 4). The EIS between non-durable goods and services inJapan is thus close to zero and is even lower than the EIS (=0.18) between non-durables
and service flowing from the stocks of durable goods in the USA (Pakos 2011).

5.2

Cohort effects

Next, we estimate the EIS between tradable goods and services according to the cohort.
Here, in order to make the estimation feasible, households in the same cohort groups
are identified by combining two cohorts in Table 1; for example, the youngest cohort(Cohort0+1) is created by combining Cohort 0 and Cohort 1 in the same year. As aresult, we have six cohort groups in this analysis. Otherwise, the same specifications
and prior distributions in Table 4 would be again employed in this subsection. Table 7
reports that younger cohorts are relatively more sensitive to prices; their EIS is higher
than that of older cohorts. But, again, differences in the EIS among cohorts are generally
insignificant, given that the EIS of the youngest cohort (0.021) often stays within the 95%
credible interval of older cohorts.

5.3

Income effects

So far, we have assumed that income effects are nil in our estimation; however, theseeffects are often reported to have significant impacts on substitution (e.g., Pakos 2011).
Pakos argued that the income effects are particularly related to durable goods that canbe regarded as non-necessities. Therefore, we investigate the EIS between tradables andservices in the non-homothetic context. But since we have only cross-sectional data and14

cannot trace consumption decisions of identical households over time, our theoreticalmodel is not suitable for showing how the households change consumption patterns in
response to increases in their own income. Rather, income effects should be interpreted
here as to what extent the EIS changes when households with different financial wealth are
examined. In order to address this question, we use two types of financial information (i.e.,annual salary and savings) and classify households into 10 categories based on quantilesof financial data (see Table 1). Then, assuming income effects are insignificant amonghouseholds in the same category, we estimate Model 2 for each group of income andsavings.
Table 8 suggests that there are differences in the EIS among household groups of different financial positions. The models classified by annual salary (Income0 to 9) showthat the EIS ranges from 0.010 to 0.188. The highest EIS is obtained from the third least
wealthy household group, and the lowest EIS is from the third wealthiest household group.
The lower middle income groups tend to have a higher EIS than the other income groups.
This is consistent with conventional expectations, but it differs slightly from Havranek
et al. (2015), who assumed a linear relationship between inter-temporal substitution andfinancial wealth and concluded that substitution increases along with financial wealth.
Our results imply that the least wealthy households do not change consumption composition much because most of their consumption are necessities; the EIS of the wealthy
households is low as they can afford price changes.
We can draw a similar conclusion from EIS estimates among different savings groups.
Again, there are variations in these EIS estimates. High EIS is reported for the lower
middle savings groups, and low EIS is reported for the most and least wealthy savings
groups. A similar non-linear relationship between the EIS and financial position is also
confirmed by household wealth (Wealth) defined as the total of annual salary and savings.
This comprehensive definition of wealth is closely related to the concept of permanent
income, in which savings act as a buffer to smooth consumption. Unlike in cohort analysis,the EIS differences are significant because the mean values of EIS go beyond the 95%
credible intervals of other groups on many occasions. This confirms the significant income
effects in the EIS estimation.
Finally, we note that aggregation bias exists even in household data analyses, although15

it is often discussed in the context of macroeconomic analysis. The aggregation bias
exists in our cohort analysis but is less pronounced in the income effect analysis, inwhich households are disaggregated in more detail (i.e., 10 groups). This can be seen bycomparing the results in Tables 4, 7, and 8, all of which are obtained from Model 2 andthus, household data. These tables show that the EIS estimates from the disaggregate
analysis in which households are classified for example by financial standing, are greaterthan the ones from the whole household samples. The classification method to grouphouseholds (i.e., by annual salary, savings, and wealth) does not influence this outcome.
It has been discussed that this aggregation bias arises from an a priori assumption ofhomogeneous parameters in aggregate data analysis (e.g., Attanasio and Weber 1993),
and this explanation still appears valid in household-level analyses. However, the factthat the EIS is very small remains unchanged and thus, our results pose a question about
the role of a price mechanism in the allocation of services and tradable goods in Japan.

6

Summary

Using a survey-based Japanese household data, we estimated the EIS between tradable
and nontradable goods and revealed several interesting differences in the consumption
patterns of households with different social backgrounds. In particular, we find the EIS
as very low in Japan based on several models and show that the EIS is substantiallyoverestimated without consideration of household characteristics and time dimensions.
Indeed, when these factors are taken into account, the EIS becomes very close to zero,
thereby questioning a role of a price mechanism in Japan. The insignificant role of prices
in household decisions is confirmed by taking into account cohort and income effects aswell as examining the EIS between services and non-durable goods.
This result signals the direction of future research on international economics. As
discussed in the introductory section, this study sheds light on the Backus-Smith puzzle:
the weak relationship between exchange rates (relative prices) and the consumption ratio
results from the low EIS between tradables and nontradables. Our estimates for intratemporal substitution suggest that the EIS between tradables and nontradables differs
according to financial standing of households: the lower middle groups tend to have a16

higher EIS. But more importantly, our empirical evidence implies that services cannot
often be considered as substitutes for tradable goods even among these families. The low
rate of substitution between them, regardless of financial standing of households, justifies
Backus and Smith (1993) explaining a violation of the PPP and poses a question about
the price mechanism, which is a center of economics. Moreover, given the fact that social
factors are found to be very important elements in household decisions on consumption
allocation, researchers seem to have relied too heavily on the EIS to explain a violationof the purchasing power parity condition.

17

Appendix
The NSFIE does not collect information of non-Japanese households and students due
to difficulties in collecting information of their income and expenditures. Otherwise, in
principle, all households in the NSFIE are used for the analysis. However, those who do
not possess all (dependent and independent) variables in our specifications, are excluded
from this study, and household heads considered in this study are those who are morethan and including 20 years old. In this survey, the annual salary of more than 25million
yen is recorded as 25 million, and similarly the savings of more than 95 million yen isrecorded as 95 million. NSFIE data is available for purchase from the Statistics Center,
the Ministry of Internal Affairs and Communication (MIAC), and is not transferable tothird parties following the regulation of the MIAC.

18

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21

22

0.750731
67482591144.092

Employment status
Annual salary
Savings

0

0

11

14

Max
1
1
1
1
1
7
1

0

0

Savings group

Workers in family

Notes: Note: The sample periods are 1989, 1994, 1999 and 2004.

0

1

9

9

0.432591
014005816 10000 2.50E+07
1470.187
09500

2.681678

2.806542

Min
0
0
0
0
0
1
0

Income group192,599
192,599
144,8025.26673

Generation(cohort) group 187,639

192,599 6.741333

Age group

Mean Std. Dev.
0.076866 0.171349
0.171345
0.18873
0.434025 0.198527
0.317764
0.20056
0.105343 0.306996
3.303283 1.422743
0.401264 0.490156

Obs
192,014
192,014
192,014
192,014
192,599
192,599
192,599

Variables
Durable goods
Semidurable goods
Nondurable goods
Services
GenderNo. of family members
Metropolitan area

Comments
A fraction out of total consumption
A fraction out of total consumption
A fraction out of total consumption
A fraction out of total consumption
Female=1, Male=0
PeopleMetropolitan=1, Otherwise=0
Age 20-24=0
Age 25-29=1
Age 30-34=2:
Age 80-84=13
Age +85=14
Generation of Age group =0 in 1989=0
Generation of Age group=1 in 1989 =1:
Generation of Age group=11 in 1989 =11
Employed=1, Otherwise=0
Yen0000 Yen
Income0 if Salary < 2640000
Income1 if 2640000 ≤Salary < 3560000
Income2 if 3560000 ≤Salary <4320000
Income3 if 4320000 ≤Salary <5090000
Income4 if 5090000 ≤Salary <5950000
Income5 if 5950000 ≤Salary <6850000
Income6 if 6850000 ≤Salary <7970000
Income7 if 7970000 ≤Salary < 9400000
Income8 if 9400000 ≤Salary <1.18e+07
Income9 if Salary≥1.18e+07
Saving0 if savings <430000
Saving1 if 430000 ≤savings <1970000
Saving2 if 1970000 ≤savings <3440000
Saving3 if 3440000 ≤savings <5000000
Saving4 if 5000000 ≤savings <6900000
Saving5 if 6900000 ≤savings <9300000
Saving6 if 9300000 ≤savings <12700000
Savin7 if 12700000 ≤savings <18330000
Saving8 if 18330000 ≤savings<29840000
Saving9 if savings≥29800000
Workers=0 if non household head is
employed, otherwise Workers=1

Table 1: Descriptive summary and explanations of survey data

Table 2: Inequality within age and generation groups
Household group
Age0
Age1
Age2
Age3
Age4
Age5
Age6
Age7
Age8
Age9
Age10
Age11
Age12
Age13
Age14

Gini coefficient
0.275
0.218
0.217
0.219
0.225
0.236
0.247
0.270
0.303
0.347
0.351
0.362
0.379
0.408
0.430

Household group
Cohort0
Cohort1
Cohort2
Cohort3
Cohort4
Cohort5
Cohort6
Cohort7
Cohort8
Cohort9
Cohort10
Cohort11

Gini Coefficient
0.239
0.242
0.246
0.251
0.259
0.274
0.299
0.330
0.345
0.354
0.383
0.405

Notes: The inequality statistics are Gini coefficient. The higher values indicate
more serious inequality. Based on four year observations. Household groups aredefined in Table 1.

23

24

Notes: Based on Model 1. The MSCE stands for the Monte Carlo standard error.

Mean Std Dev MCSE Median 95% cred interval
obs
Full
5.433
0.045
0.001
5.432 5.344
5.522 161414
σ2
1.260
0.004
0.000
1.260 1.251
1.268
Metro
5.808
0.069
0.001
5.807 5.674
5.945 62810
σ2
1.148
0.006
0.000
1.148 1.136
1.161
Nonmetro
5.201
0.058
0.001
5.200 5.087
5.317 98604
σ2
1.330
0.006
0.000
1.330 1.319
1.342
Female
3.735
0.134
0.002
3.735 3.471
3.998 16599
σ2
1.141
0.012
0.000
1.141 1.117
1.166
Male
5.627
0.047
0.001
5.626 5.533
5.721 144815
σ2
1.272
0.005
0.000
1.272 1.263
1.281
Employed
5.608
0.057
0.001
5.607 5.496
5.719 117049
1.363
0.006
0.000
1.363 1.352
1.374
σ2Unemployed
5.061
0.071
0.001
5.061 4.924
5.201 44365
σ2
0.987
0.007
0.000
0.987 0.975
1.000Single person households 0.892
0.149
0.002
0.892 0.601
1.183 10829
σ2
0.982
0.013
0.000
0.982 0.956
1.008
Family
5.778
0.047
0.001
5.777 5.685
5.871 150585
σ2
1.273
0.005
0.000
1.273 1.264
1.282

Table 3: The substitution elasticity between tradable and nontradable goods based on micro
data

25
0.040
0.008
0.002
0.002
0.000
0.005
0.004

0.001
0.000
0.000
0.000
0.000
0.000
0.000

5.725 5.648
0.028 0.012-0.042 -0.046-0.110 -0.114
0.007 0.007-0.034 -0.044
1.002 0.996

5.803 0.004
0.045 0.019-0.038 -0.040-0.106 -0.158
0.008 0.010-0.023 -0.024
1.009 0.739

Note: Based on Model 2. Time dummies are for 1994, 1999, and 2004.

Elasticity
5.725
Gender0.028
Family size
-0.042Age-0.110Age2
0.007
Workers in family -0.034
σ2
1.002

Elasticity
GenderFamily size
Age
Age2
σ2
0.004
0.013
0.002
0.002
0.000
0.005
0.003

0.000
0.004
0.000
0.000
0.000
0.001
0.000

0.003 0.000
0.018 -0.004-0.040 -0.043-0.158 -0.163
0.010 0.009-0.024 -0.033
0.739 0.734

0.015
0.044
-0.037-0.1540.010-0.0140.744

Mean Std. Dev. MCSE Median 95% Cred. Interval Mean Std. Dev. MCSE Median 95% Cred. Interval
No time dummyTime dummies
5.724
0.041
0.001
5.723 5.646
5.804 0.003
0.003
0.000
0.002 0.000
0.011
0.033
0.008
0.000
0.033 0.017
0.049 0.051
0.006
0.000
0.051 0.040
0.062-0.0460.002
0.000-0.046 -0.050-0.042 -0.037
0.002
0.000
-0.037 -0.041-0.034-0.1130.002
0.000-0.113 -0.117-0.108 -0.167
0.002
0.000
-0.167 -0.171-0.163
0.007
0.000
0.000
0.007 0.007
0.008 0.010
0.000
0.000
0.010 0.010
0.010
1.003
0.003
0.000
1.003 0.996
1.009 0.740
0.003
0.000
0.740 0.735
0.745

Table 4: Intra-temporal substitution

Table 5: Deviance information criterion
Model
Gender, Family size, Age, Age2
Gender, Family size, Age, Age2 , Workers in family

No time dummy Time dummies
474358.6423573.3
474321.9423443.4

Notes: Based on Model 2.

Table 6: Intra-temporal substitution between non-durables and services
Mean
No time dummy
Elasticity
0.001
Gender0.087
Family size
-0.058Age
0.028
2-0.005Age
Workers in family -0.047
σ2
0.693
Time dummies
Elasticity
0.014
Gender0.067
Family size
-0.056Age-0.017Age2-0.003
Workers in family -0.041
σ2
0.678

Std DevMCSE

Median95% cred interval

0.001
0.007
0.002
0.002
0.000
0.005
0.002

0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.001 0.000
0.087 0.074-0.058 -0.061
0.028 0.024-0.005 -0.006-0.047 -0.055
0.693 0.688

0.003
0.101
-0.0550.031-0.005-0.037
0.698

0.014
0.007
0.002
0.002
0.000
0.005
0.002

0.001
0.001
0.000
0.000
0.000
0.001
0.000

0.009
0.067
-0.056-0.018-0.003-0.041
0.678

0.051
0.080
-0.053-0.012-0.002-0.033
0.683

0.000
0.053
-0.060-0.022-0.003-0.051
0.674

Notes: Based on Model 2.

Table 7: Intra-temporal substitution between tradables and services, by cohorts
Household group
Cohort0+1
Cohort2+3
Cohort4+5
Cohort6+7
Cohort8+9
Cohort10+11

Mean Std Dev
0.021 0.020
0.015 0.014
0.006 0.006
0.005 0.005
0.008 0.008
0.006 0.006

MCSE
0.001
0.001
0.000
0.000
0.000
0.001

Median 95% cred interval
0.014
0.001 0.076
0.011
0.000 0.052
0.004
0.000 0.023
0.004
0.000 0.019
0.005
0.000 0.028
0.005
0.000 0.025

Notes: Note: Based on Model 2. Two cohorts are grouped together. Cohort 0+1
indicates a generation combined Cohort 0 with Cohort 1, defined in Table 1. Timedummies and social indicators such as Gender, Age, Age2 , and Workers in family areincluded.

26

Table 8: Intra-temporal substitution between tradables and services, by financial positions
Household group
Income0
Income1
Income2
Income3
Income4
Income5
Income6
Income7
Income8
Income9
Saving0
Saving1
Saving2
Saving3
Saving4
Saving5
Saving6
Saving7
Saving8
Saving9
Wealth0
Wealth1
Wealth2
Wealth3
Wealth4
Wealth5
Wealth6
Wealth7
Wealth8
Wealth9

Mean
0.051
0.078
0.188
0.157
0.089
0.072
0.054
0.010
0.030
0.022
0.036
0.322
0.211
0.070
0.091
0.038
0.057
0.039
0.028
0.021
0.166
0.222
0.122
0.113
0.057
0.060
0.012
0.019
0.042
0.054

Std Dev
0.049
0.074
0.152
0.125
0.083
0.067
0.050
0.010
0.029
0.021
0.036
0.198
0.169
0.067
0.087
0.037
0.051
0.036
0.027
0.021
0.132
0.163
0.116
0.100
0.058
0.060
0.013
0.018
0.042
0.049

MCSE
0.002
0.003
0.013
0.016
0.004
0.003
0.002
0.000
0.001
0.001
0.001
0.020
0.014
0.005
0.004
0.001
0.002
0.002
0.001
0.001
0.012
0.017
0.010
0.005
0.003
0.003
0.001
0.001
0.002
0.003

Median
0.035
0.055
0.152
0.129
0.063
0.052
0.039
0.007
0.021
0.015
0.024
0.309
0.167
0.051
0.063
0.026
0.042
0.028
0.020
0.015
0.131
0.189
0.088
0.085
0.038
0.041
0.008
0.013
0.029
0.040

95% cred interval
0.001 0.184
0.002 0.277
0.007 0.566
0.006 0.461
0.003 0.311
0.003 0.248
0.002 0.180
0.000 0.038
0.001 0.109
0.000 0.079
0.001 0.132
0.021 0.728
0.010 0.651
0.002 0.261
0.003 0.320
0.001 0.139
0.002 0.187
0.001 0.133
0.001 0.098
0.000 0.079
0.005 0.493
0.010 0.597
0.004 0.431
0.003 0.377
0.002 0.222
0.001 0.218
0.000 0.046
0.001 0.067
0.001 0.151
0.002 0.182

Notes: Based on Model 2. Household groups are defined in Table 1, and the number
attached to variables indicates a quantile.Time dummies and social indicators such as
Gender, Age, Age2 , and Workers in family are included.

27

Figure 1: Consumers by family size, age group, and generation

Notes: Household groups are defined in Table 1.

28

Figure 2: Average salary

Notes: Household groups are defined in Table 1.

29

Figure 3: The proportion of services by groups

Notes: Household groups are defined in Table 1.

30

Figure 4: Intra-temporal substitution

Notes: Based on Model 2.

31