MEASURING INTERTEMPORAL SUBSTITUTION IN CONSUMPTION:
EVIDENCE FROM A VAT INCREASE IN JAPAN

David Cashin and Takashi Unayama*

Abstract—We estimate the intertemporal elasticity of substitution in con-
assunzione (IES) using a preannounced increase in Japan’s consumption tax
rate. Because this tax is highly comprehensive, the rate increase was
announced prior to its implementation, and because other factors that affect
the real interest rate were constant, the tax rate increase presents an ideal nat-
ural experiment to estimate the IES. A Japanese monthly household survey
is exploited to accurately categorize nondurables, and our empirical specifi-
cation addresses intratemporal substitution bias. We find that the IES is 0.21
and not significantly different from 0, but it is significantly less than 1.

IO.

introduzione

I N this paper, we estimate the intertemporal elasticity of

substitution in consumption (IES) using an increase in the
Japanese consumption tax rate as a natural experiment. IL
consumption tax, which is a value-added tax (VAT),
increased from 3% A 5% in April 1997. Unlike VAT in many
other countries, Japan has a single flat rate with a relatively
small number of exemptions. As expected, the tax burden
was borne fully by consumers in the form of higher prices.
Because nominal interest rates and the inflation rate were
constant around the implementation of the tax rate increase, Esso
can be treated as an exogenous change in the real interest rate,
which provides an ideal situation to estimate the IES.

Previous research on this topic (Hall, 1988; Attanasio &
Weber, 1993, 1995; Ogaki & Reinhart, 1998) has relied on an
instrumental variables approach to address the critical econo-
metric problem that the real interest rate is endogenous in the
standard log-linearized Euler equation for consumption.
Tuttavia, as Yogo (2004) notes, asset returns are notoriously
difficult to predict, and as a result, the available instruments
are weak. Weak instruments can lead to biased estimators
and finite sample distributions of test statistics that depart
greatly from their limiting distributions. This paper avoids
the problem of weak instruments by exploiting the natural
experiment presented by the consumption tax rate increase.

In addition to the novel research design, our data set
plays an important role in estimating the IES. We use the
Japanese Family Income and Expenditure Survey (JFIES),

Received for publication November 1, 2012. Revision accepted for pub-

lication January 5, 2015. Editor: Mark W. Watson,

* Cashin: Federal Reserve Board of Governors; Unayama: Hitotsubashi

University and RIETI.

We thank Joel Slemrod, James Hines, Chris House, Mel Stephens, Caro-
line Weber, anonymous referees, and seminar participants at the 2012
NBER Japan Project Meeting, Japan’s Ministry of Finance, IL 2011 Inter-
national Institute of Public Finance Congress, the University of Michigan,
and the University of Otago for helpful comments and suggestions. In addi-
zione, we thank Megumi Araki for her helpful assistance. We are also grate-
ful to the National Science Foundation, the Japan Society for the Promotion
of Science, and RIETI for funding part of this study. The views expressed
here are strictly our own and do not necessarily represent the position of
the Federal Reserve Board or the Federal Reserve System.

A supplemental appendix is available online at http://www.mitpress

journals.org/doi/suppl/10.1162/REST_a_00531.

a monthly household-level panel data set. Given our use of
microdata, our results are free from the aggregation bias
discussed in Attanasio and Weber (1993, 1995). Its high-
frequency (monthly) panel structure allows us to adopt the
conventional Euler equation approach and observe con-
sumption expenditure immediately before and after imple-
mentation of the tax rate increase.

Inoltre, because the JFIES is highly disaggregated by
item type, we can define nondurables appropriately. The defi-
nition in previous studies has included goods and services
that exhibit some degree of storability or durability. For
esempio, as Mankiw (1985) points out, footwear and clothing
are usually considered to be nondurables, but they should be
classified as durables. Attanasio and Weber (1993, 1995), IL
first to address this issue, exclude durables and semidurables
but pay little attention to storability. Storable goods can be
stockpiled during low-price periods for consumption in high-
price periods. Failing to account for this behavior could bias
the estimate of the IES upward. To avoid these biases, we
separate nonstorable nondurable goods and services (per esempio.,
eating out) from storable nondurable (per esempio., laundry detergent)
and durable (per esempio., automobiles) goods and services.

With multiple goods, we explicitly consider intratemporal
substitution between nondurables, storables, and durables by
constructing a model of consumer choice. As Ogaki and Rein-
hart (1998) demonstrate, failing to account for intratemporal
substitution can induce a biased estimate of the IES when pre-
ferences over nondurables and durables are nonseparable. In
general, the service flow from durables becomes higher prior
to a tax rate increase because the user cost of durables falls.
With nonseparable preferences, households substitute between
nondurables and durables. If we do not control for this, the esti-
mate of the IES will be biased, where the sign of the bias
depends on the structure of intratemporal preferences. IL
empirical specification derived below, consistent with our
modello, is robust to the possibility of intratemporal substitution.
Exploiting these advantages, our point estimate of the IES
È 0.21, which is significantly less than 1 but not significantly
different from 0. While the baseline regression uses the sam-
ple period between April 1992 and March 2002, the choice of
sample period has little impact on our results. Inoltre, IL
results are robust to sample selection criteria. Point estimates
from those robustness checks range between 0.17 E 0.36,
comparable to those in previous studies using macrodata such
as Hall (1988), Ogaki and Reinhart (1998), and Yogo (2004),
but less than those using microdata such as Attanasio and
Weber (1993, 1995), Vissing-Jorgensen (2002), and Gruber
(2013). We employ additional tests to check whether liquidity
constraints or data quality is responsible for the small IES but
find no evidence to support these assertions.

The Review of Economics and Statistics, May 2016, 98(2): 285–297
(cid:2) 2016 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 3.0
Unported (CC BY 3.0) licenza.
doi:10.1162/REST_a_00531

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286

THE REVIEW OF ECONOMICS AND STATISTICS

Our analysis also highlights the importance of allowing
nonseparable preferences over durables and nondurables
and suggests the two composite goods are strong comple-
menti. When we restrict preferences over durables and non-
durables to be separable, we obtain a point estimate of the
IES of 0.91, which is significantly larger than our baseline
estimate of 0.21 and similar to the estimates of Attanasio
and Weber (1993, 1995) and Vissing-Jorgensen (2002),
who also use microdata but restrict preferences to be separ-
able over durables and nondurables. Combining our empiri-
cal results with the Euler equation derived from the baseline
modello, we can go beyond our finding that preferences over
durables and nondurables are nonseparable and place an
upper bound on the elasticity of substitution between dur-
ables and nondurables. Specifically, our results imply that
the elasticity of substitution between durables and nondur-
ables is less than our IES estimate of 0.21. Così, durables
and nondurables are strong complements.

To the extent that our finding of a small IES is applicable
in other contexts, it suggests that policies that aim to dam-
pen volatility in household consumption expenditure
through changes in the real interest rate will not be effec-
tive. For the same reason, the deadweight loss from a prean-
nounced increase in a VAT and the taxation of interest
income is likely to be small.

The remainder of the paper is organized as follows. Sez-
tion II provides background on Japan’s April 1997 con-
sumption tax rate increase and evidence for our assertion
that the tax rate increase presents an ideal natural experi-
ment to estimate the IES. Section III introduces a represen-
tative agent model of household consumption to make pre-
dictions about household consumption in the months
following announcement of a Consumption Tax rate
increase. We then present an empirical specification consis-
tent with the model and discuss identification of the IES.
The data used in estimation and our results are presented in
section IV. Section V summarizes and discusses our results.

II. The Consumption Tax Rate Increase: An Ideal
Natural Experiment to Estimate the IES

Japanese government made it clear that it expected the bur-
den of the Consumption Tax would be borne fully by consu-
mers.2 Accordingly, changes in consumer prices should be
proportional to changes in the Consumption Tax rate. In
other words, given a nominal interest rate, an increase in the
Consumption Tax rate lowers the real interest rate through a
proportional price increase across goods and services.

The Consumption Tax was introduced in 1989 at a rate
Di 3%, and it was increased to 5% in April 1997. IL 1997
increase was originally proposed as a part of the Murayama
tax reform, which passed through the Japanese Diet in late
1994.3 Because the primary purpose of the reform was to
continue the shift from direct to indirect taxation, the con-
sumption tax rate increase was coupled with immediate cuts
in income tax rates. In that sense, the tax increase was com-
pensated.

Although the Murayama reform package set a target date
of April 1997 for the Consumption Tax rate increase, it was
unclear whether the increase would actually be implemen-
ted then. This is because the reform legislation also stated
that the increase would be imposed only if the economy
had sufficiently recovered from a prolonged recession
(1991–1993) and subsequent years of feeble growth. Hav-
ing judged the economy to have sufficiently recovered, IL
ruling Liberal Democratic Party (LDP) decided to raise the
tax rate as scheduled. The bill to raise the Consumption Tax
rate passed through the upper house on June 25, 1996, E
the tax rate increase was scheduled to become effective on
April 1, 1997.

Even after this passage, it was not clear that the Con-
sumption Tax rate increase would be implemented in April,
as it was the central issue in October 1996 elections to the
lower house of the Diet, with the LDP promising to imple-
ment the tax rate increase as planned while the opposition
promised to shelve it. The LDP narrowly won the election,
and on December 26, 1996, the government submitted the
fiscal year 1997 budget, finally deciding to increase the
Consumption Tax rate to 5% on April 1, 1997.

B. The Consumption Tax Rate Increase as a

Natural Experiment

UN. Japan’s Consumption Tax and the April 1997

Rate Increase

Japan’s Consumption Tax is a value-added tax (VAT).
Unlike VAT in many other countries, the consumption tax
has a single flat rate with a relatively small number of
exemptions.1 In addition, as documented by Ishi (2001), IL

To estimate the IES, variation in the real interest rate, IL
price of current consumption relative to future consump-
zione, is necessary. Because the real interest rate is defined
as the nominal
interest rate minus the inflation rate, UN
change in the inflation rate will induce the necessary varia-
zione. Di conseguenza, the April 1997 Consumption Tax rate

1 Exemptions include transfer or lease of land, transfer of securities,
transfer of means of payment, interest on loans and insurance premiums,
transfer of postal and revenue stamps, fees for government services, inter-
national postal money orders, foreign exchange, medical care under the
medical insurance law, social welfare services specified by the social wel-
fare services law, midwifery service, burial and crematory service, trans-
fer or lease of goods for physically handicapped persons, tuition, entrance
fees, facilities fees, examination fees of schools designated by the Articles
of the School Education Law, transfer of school textbooks, and the lease
of housing units.

2 When the consumption tax was introduced in 1989, the government
took several steps to ensure this outcome. Primo, the Special Council on
the Transition was formed to promote enforcement of the tax across agen-
cies. Secondo, the government carried out an extensive advertising cam-
paign to allay the public’s fear of price hikes and restrain overcharging by
traders. A telephone service was also set up so consumers could report
complaints about prices. Finalmente,
the Economic Planning Agency
increased the budget for the price monitoring system. The situation was
nearly identical in 1997.

3 For the political process, see Ishi (2001) and Takahashi (1999).

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MEASURING INTERTEMPORAL SUBSTITUTION IN CONSUMPTION

287

FIGURE 1.—PERCENTAGE CHANGE IN NONSTORABLE, NONDURABLE PRICES

FIGURE 2.—AVERAGE INTEREST RATES ON SHORT-TERM LOANS AND DISCOUNTS

The figure presents the month-to-month percentage change in unadjusted and seasonally adjusted non-
storable, nondurable prices. To remove seasonality, we regress the monthly percentage price change in
nonstorable, nondurable goods and services on month dummies. The residuals are added to the constant
term from the regression to obtain a seasonally adjusted monthly percentage price change. The dashed
vertical line in the figure is April 1997, the month the consumption tax rate increase was implemented.

The figure presents the average contracted interest rate on short-term loans and discounts. These are
the average interest rates applied to a contract of less than one year between commercial banks and len-
ders. The data come from the Bank of Japan.

increase, which represented an exogenous increase in the
future price level during a period in which nominal interest
rates were stable, presents an ideal natural experiment to
estimate the IES, which we discuss below.

Primo, the tax rate increase can be regarded as an exogen-
ous change in consumer prices. Not only is it the case that
the tax system is exogenous to individual households, but it
is also true that the impact of the tax rate increase is inde-
pendent of consumer behavior. This is because the VAT by
and large applies to expenditures regardless of the charac-
teristics of the consumer, the point of purchase, or the type
of goods purchased. Figura 1 shows the month-to-month
percentage change in the consumer price index for nonstor-
able, nondurable goods and services, the component of con-
sumption expenditure that we use to estimate the IES.
While inflation was negligible in most months prior to and
following implementation of the tax rate increase, the price
level increased by 2.39% between March and April 1997,
consistent with full forward shifting of the Consumption
Tax onto consumers at the time of implementation.4 The
figure also suggests that there was not a significant seasonal
component to price changes around the time of the tax rate
increase. Consequently, the optimal response to the Con-
sumption Tax rate increase is unlikely to be confounded by
seasonality in prices. Di conseguenza, we can focus on a one-
time price change and rule out the influence of an additional
factor (cioè., variation in pretax prices due to transitory or
seasonal components) that affects the real interest rate.

We can also rule out the influence of the nominal interest
rate on the real interest rate. Figura 2 presents the average
contracted interest rates on short-term loans and discounts,
which are the average interest rates applied to a contract of
less than one year between a commercial bank and lender.
The average interest rate fell precipitously throughout 1995

4 Carroll et al. (2010) find that full forward shifting at the time of a con-

sumption tax rate increase is the norm across most countries.

but remained relatively constant thereafter. This suggests
that households would not change their nominal interest
rate expectations in the months surrounding implementation
of the Consumption Tax rate increase. In other words,
households should not have expected any changes in nom-
inal interest rates by the central bank that would offset or
augment the intertemporal substitution incentives.

These facts imply that

the tax rate increase can be
regarded as an exogenous change in the real interest rate,
which allows for consistent estimation of the intertemporal
substitution response using ordinary least squares (OLS).
Previous studies of intertemporal substitution have relied
on an instrumental variables approach to address the well-
documented endogeneity between the real interest rate and
consumption growth. The standard approach has been to
instrument for the contemporaneous real interest rate with
lagged interest rates. Tuttavia, there are several potential
issues with the instruments that have been employed. Primo,
as Yogo (2004) notes, it is notoriously difficult to predict
the real interest rate, and therefore some of the previous stu-
dies in this literature (especially those using aggregate data)
suffer from the weak instrument problem. Weak instru-
ments lead to estimates of the IES biased in the direction of
OLS, which itself is likely to suffer from a downward bias.5
Even if the weak instrument problem is overcome, there
still exists the potential for correlation between the lagged

5 Two-stage least squares (2SLS) estimators using weak instruments are
biased in the direction of OLS for the following reason. Suppose the
structural equation is given by yi ¼ bxi þ gi and the first-stage equation
by xi ¼ pzi þ ni. If p is truly 0 due to weak instruments, then any varia-
tion in the predicted value of xi, ^xi will come from ni. It follows that the
variation in ^xi is no different from the variation in xi, and the OLS and IV
estimates are estimating the same quantity on average. For more informa-
zione, see Pischke (2010).

Using OLS, Gruber (2013) obtains an estimate of the IES of (cid:2)0.55,
which is significantly less than his estimates when instrumenting for the
after-tax real interest rate. Vissing-Jorgensen (2002) finds that estimates
of the IES converge toward 0 as the number of instruments is increased.
This is because the weak instrument problem is increasing in the degree
of overidentification.

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THE REVIEW OF ECONOMICS AND STATISTICS

FIGURE 3.—NUMBER OF ARTICLES MENTIONING THE CONSUMPTION TAX

FIGURE 4.—PRICE RATIOS RELATIVE TO NONSTORABLE NONDURABLES

Fonte: Authors’ calculations. Circulation numbers for the Nihon Keizai Shimbun and Yomiuri Shim-

bun are from Japan’s Audit Bureau of Circulations.

interest rates and consumption growth, which is discussed
by Gruber
(2013). Inoltre, Attanasio and Weber
(1993, 1995) show that studies using lagged instruments
and aggregate nondurable expenditure data suffer from a
downward bias in estimates of the IES known as aggrega-
tion bias.6 This study avoids these issues by using an exo-
genous institutional price change.

While exogenous variation in the real interest rate is a
necessary condition for estimating the IES, it must also be
the case that households are aware of the change. While we
cannot provide direct evidence on household awareness of
the consumption tax rate increase, we can provide indirect
evidence by examining news coverage prior to implementa-
zione. Figura 3 reports the number of articles that mention the
phrase consumption tax in the Nihon Keizai Shimbun,
Japan’s leading business newspaper, with a circulation of
Sopra 3 million (In 2010), and the Yomiuri Shimbun, a leading
nonbusiness newspaper, with a circulation of over 10 million
(In 2010).7 There was a steady upward trend that began just
prior to enactment of the June 1996 legislation. Coverage
peaked in the Yomiuri Shimbun in October 1996, Quale
coincided with elections to the lower house of the Diet.
Overall coverage in both papers was consistently high in the
months following the election but prior to the tax change,
with nearly 300 articles in the Nihon Keizai Shimbun
mentioning the consumption tax in March 1997. Questo
suggests that households were aware of the tax rate increase
and might therefore engage in intertemporal substitution
behavior.

The news coverage also suggests that households may
have been aware of the effects of the Murayama reform
package as a whole. Figura 3 shows that coverage initially

6 Attanasio and Weber (2010) sum up aggregation bias as follows:
‘‘The aggregate consumption growth rate is computed by taking logs of
the mean of individual consumption, whereas [the log-linearized Euler
equation] implies that means of the logs should be taken instead. . . . IL
difference between these two terms is highly serially correlated, così
invalidating lagged consumption growth as an instrument.’’

7 Circulation numbers come from Japan’s Audit Bureau of Circulations.

The figure presents the ratio of seasonally adjusted durable and storable nondurable prices to nonstor-
able nondurable prices. To remove seasonality, we regress the consumer price indices for durable, stor-
able nondurable, and nonstorable nondurable goods and services on month dummies. The residuals are
added to the constant in the regression to obtain seasonally adjusted price indices. To calculate the ratios,
we divide the seasonally adjusted durable and storable nondurable price by the seasonally adjusted non-
storable nondurable price in each month. The dashed vertical line in the figure is April 1997, the month
of implementation.

peaked in September 1994, which coincided with the pas-
sage of the Murayama reform. Accordingly, households
may have known the package was intended to be revenue
neutral over the long run. This in turn implies that the
income effect associated with the tax rate increase would be
piccolo, and thus, we need not pay much attention to separate
identification of the intertemporal substitution and income
effects.8

Finalmente, the relative pretax price of goods and services
did not change around the time of the consumption tax rate
increase. Figura 4 shows the price of durables and storable
nondurables relative to nonstorable nondurables around the
time of the consumption tax rate increase. As the figure
demonstrates, there was little change in the relative price of
these goods. This fact allows us to make the simplifying
assumption of constant relative pretax prices in the model
presented in section III. Di conseguenza, we need only concern
ourselves with the possibility of intratemporal substitution
between durables and nonstorable nondurables resulting
from the reduction in the user cost of durables just prior to
the Consumption Tax rate increase, which we discuss
further in Section IIIA.

To summarize, we argue that the April 1997 consump-
tion tax rate increase presents an ideal natural experiment
to estimate the IES for the following reasons: the tax rate
increase can be regarded as an exogenous change in the
real interest rate, the real interest rate was relatively stable
prior to and following implementation, the tax rate increase
was predictable and consumer awareness was high, E
relative pretax prices were constant among taxable goods
and services.

8 That said, our empirical specification does attempt to identify the
combined income and intertemporal substitution effects in the months
immediately following announcement of
the consumption tax rate
increase.

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MEASURING INTERTEMPORAL SUBSTITUTION IN CONSUMPTION

289

III. A Consumption Tax Rate Increase and the
Intertemporal Elasticity of Substitution

UN. The Model

In this section, we construct a model to demonstrate the
impact of a Consumption Tax rate increase on both house-
hold consumption and expenditure. A household consumes
three types of taxable goods and services: nonstorable non-
durables (N), storable nondurables (S), and durables (D).9
Household i maximizes its lifetime utility function, U, IL
discounted sum of the instantaneous utility, tu. Suppose the
utility function at time s is

Us ¼

X1

t¼s

bt(cid:2)S

(cid:2)

R
R (cid:2) 1

(cid:3)

H
ut

io
R(cid:2)1
;
R (cid:2) 1

where b is the subjective discount factor, s is the IES, E
ut is the instantaneous utility. Unlike previous studies, we
use a deterministic setting because we focus on short-run
dynamics around the time of the consumption tax rate
increase.

Following Ogaki and Reinhart (1998), the intratemporal
utility function is assumed to take the CES form for N, S,
and D,

ut ¼ u CN

T ; CS

T ; Dt

(cid:4)

H
(cid:5) ¼ CN

T

2(cid:2)1

2 þ aCS
T

2(cid:2)1

2 þ bDt

io 2

2(cid:2)1

2(cid:2)1
2

;

t and CS

where CN
t are consumption of N and S, rispettivamente;
Dt is the stock of D held at the end of period t; [ is the intra-
temporal elasticity of substitution; and a and b are some
positive numbers that determine the weights attached to S
and D.10 It is worth noting that the utility function becomes
additively separable in N, S, and D if s ¼ [.

The CES specification assumes that preferences are
homothetic. Pakos (2011) finds instead that preferences are
nonhomothetic. Specifically, durables are luxuries and non-
durables are necessities. If this is the case, ignoring nonho-
motheticity can lead to an estimate of the IES that is biased
in su (see also Okubo, 2008). Nevertheless, we believe it
is reasonable to maintain the simplifying assumption of
homotheticity, since income effects should not be present
on implementation of the Consumption Tax rate increase.11

9 In online appendix A, we construct a model that allows nonseparable
preferences over taxable and tax-exempt goods and services and derive
testable implications regarding additive separability. The null hypothesis
of additive separability is not rejected by the data. Based on this result,
we ignore tax-exempt goods and services throughout our analysis.

10 Because we are focusing on short-run dynamics, our model ignores
the labor/leisure choice, effectively assuming that labor supply is fixed
during the period of interest. This is made more plausible by the fact that
we restrict our sample to households who do not change jobs during their
time in the sample. Crossley, Basso, and Wakefield (2009), who investigate
a VAT rate change in the United Kingdom, also ignored the labor supply
decision.

11 Income effects associated with the Consumption Tax rate increase
should appear on announcement of the tax rate increase, whereas identifi-
cation of the IES relies on changes in expenditure on implementation of
the Consumption Tax rate increase.

In maximizing its lifetime utility, the household faces
three constraints: the intertemporal budget constraint and
laws of motion for the stock of S and D. The intertemporal
budget constraint is given by

ÞAt(cid:2)1 þ Yt (cid:2) pN
At ¼ 1 þ it
ð
(cid:6)
(cid:4)
t XD
t þ u XD
(cid:2) pD
T

T (cid:2) pS

t XS
t CN
T
(cid:7) (cid:2) h Stð Þ for t ¼ s (cid:3) (cid:3) (cid:3) 1;

(cid:5)

where At is financial wealth held at the end of period t; it is
T , pS
the nominal interest rate in period t; Yt is income; pN
T ,
t are the prices of N, S, and D, rispettivamente; XS
and pD
t and
XD
t are gross expenditures on S and D, rispettivamente; and St
is the stock of S held at the end of period t. The functions y
and u represent costs associated with the storage of S and
purchase of D, which we discuss below. Finalmente, we take
As(cid:2)1, Ds(cid:2)1, and Ss(cid:2)1 as given.

As we discussed in the previous section, it was expected
that the Consumption Tax rate increase would be fully
passed onto consumers in the form of higher prices at the
time of implementation (hereafter, period T). Inoltre,
nominal interest rates and the pretax price level were stable
around implementation. Di conseguenza, we can safely make the
following two simplifications to the intertemporal budget
constraint:

8
>>>< >>>:

1:

t ¼ pN; pS
pN

t ¼ pS; pD

t ¼ pD

pN
t ¼ 1 þ s
ð

ÞpN; pS

before and at period T (cid:2) 1
t ¼ 1 þ s
ð
in and after period T:

ÞpS; pD

t ¼ 1 þ s
ð

ÞpD

2: it ¼ i 8 T;

where t is the inflation rate due to the tax rate increase. In
our case, t ¼ 0.0239 because the CPI for N increased by
2.39% from March to April 1997.

The function y accounts for the cost of holding a stock of
storables, S.12 This consists of costs from stock shortages as
well as storage costs. Per esempio, if a household runs out
of storable nondurable goods such as toothpaste, there is a
time cost associated with making a trip to the store to pur-
chase an additional
tube. Alternatively, stockpiling S
requires the use of storage space that could be used for
other purposes. These scenarios suggest that there exists a
bliss point for the stock of S, S(cid:4), which means that
h0ðSi;tÞ (cid:5) 0 if Si;T (cid:5) S(cid:4) and h0ðSi;tÞ > 0 if Si;t > S(cid:4).

u accounts for costs associated with the purchase of D.
The purchase of a durable good is an infrequent event, E
more effort is required than for a nondurable purchase. Questo
may include collecting catalogs, identifying key specs, E
shopping around to get a better price. Assuming that the

12 Previous studies have shown empirically that demand is affected by
the storability of a good (Hendel & Nevo, 2004, 2006). In particular,
households weigh the benefits of purchasing storable goods at a lower
price against the cost of holding additional inventory.

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THE REVIEW OF ECONOMICS AND STATISTICS

opportunity cost of a household’s time spent shopping is
increasing, convex, and proportional to the amount spent on
durable goods, it follows that ui is increasing and convex in
its argument, questo è, u0 > 0 and u00 > 0.

Finalmente, the evolution of the stocks of S and D is given by

St ¼ 1 (cid:2) ds
ð

ÞSt(cid:2)1 (cid:2) CS

t þ XS
T

for t ¼ s (cid:3) (cid:3) (cid:3) 1

E

(cid:4)
Dt ¼ 1 (cid:2) dD

(cid:5)Dt(cid:2)1 þ XD

T

for t ¼ s (cid:3) (cid:3) (cid:3) 1;

where dS and dD are the depreciation rates of S and D,
respectively.13

B. Optimal Consumption Path and the Intertemporal

Elasticity of Substitution

Solving the household’s optimization problem, we obtain

the following first-order conditions:

@Ut=@CN
T
@Ut(cid:2)1=@CN

T(cid:2)1

¼

¼

(cid:9)(cid:2)1

R

(cid:8)

(cid:8)

(cid:9) R(cid:2)2

Ft
Ft(cid:2)1
1
B 1 þ i

(cid:8)
rð2(cid:2)1Þ CN
T
CN
T(cid:2)1
(cid:9) pN
(cid:9)
(cid:8)
T
;
pN
Þ
T(cid:2)1

ð

(cid:8)

t ¼ CN
CS
T

(cid:8) (cid:9)

(cid:8) (cid:9) pS
pN

1
UN

(cid:9)(cid:2)2

;

t þ h0 Stð Þ ¼
pS

1 (cid:2) dS
1 þ i

;

Dt ¼ CN
T

(cid:8) (cid:9)
pD
H
pN
(cid:9)

(cid:8)
1
B
1 (cid:2) dD
1 þ i

(cid:8)

(cid:2)

Dove

(cid:2)
1 þ u0

(cid:3)

(cid:5)

(cid:4)
XD
T

1 þ Ctþ1s
ð

(cid:2)
Þ 1 þ u0

(cid:4)
XD
tþ1

(cid:3)(cid:10)(cid:9)(cid:2)2
(cid:5)

;

(4)

Ft ¼ 1 þ a

2

(cid:8) (cid:9)2(cid:2)1
CS
T
CN
T

þ b

2

(cid:8) (cid:9)2(cid:2)1
Dt
CN
T

E

Ct ¼

(cid:11)

1 if t ¼ T
0 if t 6¼ T:

Equazione (1) gives the standard Euler equation, Quale

can be rewritten as

13 In the case that dS and dD are equal to 1, S and D effectively become

nondurables.

CN
T
CN

T(cid:2)1

¼ b 1 þ i
ð

½

(cid:6)R 1 þ Cts
Þ

ð

(cid:8)
Þ(cid:2)r Ft
Ft(cid:2)1

(cid:9)R(cid:2)2

2(cid:2)1

:

Then, taking the logarithm of both sides and using the gen-
Þ ffi x for small x, the consump-
eral approximation ln 1 þ x
tion changes can be denoted as

ð

DlnCN

t ¼ j þ

R(cid:2) 2
2 (cid:2)1

DlnFt (cid:2) rCts

(5)

T (cid:2) lnCN

t ¼ lnCN

where DlnCN

T(cid:2)1 and DlnFt ¼ lnFt (cid:2) lnFt(cid:2)1:
This shows that once we assume that preferences over N,
S, and D are additively separable (cioè., s ¼ [), the IES, S,
can be estimated simply by dividing the change in log con-
sumption growth of N at the time of implementation by the
size of the tax rate increase, T. Tuttavia, as Ogaki and Rein-
hart (1998) point out, if preferences over N, S, and D are in
fact nonseparable (cioè., s = [), this simple approach could
yield a biased estimator. To address this issue, we add
regressors to allow for nonseparable preferences in the
empirical specification described below.

(1)

(2)

(3)

C. Empirical Specification

To estimate the IES, we use an empirical specification
that is consistent with the model and is able to separately
identify the IES from intratemporal substitution effects.
According to the model presented above, the intratemporal
substitution effects, or changes in ln Ft, will appear symme-
trically in the months prior to and following implementa-
zione. D'altra parte, the intertemporal substitution effect
is present only at the time of implementation. This is key to
identifying the IES.

With this in mind, the following specification can iden-

tify the IES,

DlnCN

sì;m ¼ controls þ

X

aN
sì;mDDy;m þc1997;AprD1997;Apr;

sì;mð

Þ2I

where DDy;m is the first difference of month dummies for
the period I and D1997,Apr is a dummy for April 1997.

Our main coefficient of interest is c1997;Apr, which corre-
sponds to (cid:2)rs. Since t is known to be 0.0239, as discussed
above, the IES, S, can be identified as (cid:2)c1997;Apr=s. IL
sì;m’s correspond to r(cid:2)2
aN
2(cid:2)1 DlnFy;M, which capture the intra-
temporal substitution effects. Unless preferences are addi-
tively separable (cioè., s ¼ [), at a minimum, aN
1997;Mar
should be nonzero and statistically significant, since the
user cost of durables fell in this month. In more general
cases where durable adjustment costs are present (cioè.,
u 6¼ 0), aN
sì;m may be nonzero in other months surrounding
implementation as well, since changes in Ft will be nonzero
in months other than March 1997 (cioè., the set I may contain
months in addition to March 1997).

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291

TABLE 1.—BOUNDING [ USING ESTIMATES OF aN

1997;Mar AND s

^r

< 1 > 1

^aN
1997;Mar

> 0
< 0 1 > r >2
1 >2> r or 2> 1 > r

r >2> 1 or r > 1 >2
2> r > 1

While our empirical specification can exactly identify the
IES, the intratemporal elasticity of substitution, [, is not
directly identified. Tuttavia, based on our model, bounds
on the value of [ can be given. By the definition of Ft, we
know that Ft is an increasing function of Dt=CN
if [ > 1,
T
and vice versa. Inoltre, D1997;Mar=CN
1997;Mar should be
greater than D1997;Feb=CN
1997;Feb due to the lower user cost of
durables in March. Così, it follows that D ln F1997;Mar > 0 if
[ > 1 and D ln F1997;Mar < 0 if [ < 1. On the other hand, it is mathematically obvious that the term r(cid:2)2 2(cid:2)1 > 0 if s > [ >
1 or s < [ < 1 while r(cid:2)2 2(cid:2)1 < 0 if [ < s < 1 or [ > 1 > s.
Accordingly, once we estimate s and aN
1997;Mar; we can
place a bound on [, as shown in table 1. To demonstrate,
suppose we find that ^r < 1 and ^aN 1997;Mar > 0 (the actual
case we will find below); then we can conclude that [ < s < 1. Since aN 2(cid:2)1 DlnF1997;Mar, it is positive when r(cid:2)2 2(cid:2)1 < 0 and DInF1997;Mar < 0: Consequently, we know that either r >2> 1 O 2< r < 1 should be satisfied. However, the former condition, r >2> 1, cannot be satisfied with an
estimate of s less than 1; Perciò, the theoretical upper
bound of [ should be the estimated s, ^r.

2(cid:2)1 > 0 and DInF1997;Mar > 0, or r(cid:2)2

1997;Mar corresponds to r(cid:2)2

In addition to the dummies of interest, we add controls
for factors affecting consumption that were excluded from
the theoretical model, such as seasonality, demographics,
and unobservables. The actual regression equation is

DlnCN

io;sì;m ¼ c þ DZmdm þ DXi;sì;m/þ
þ c1996;OctD1996;Oct þ c1996;NovD1996;Nov
þ c1996;DecDDec þ c1997;AprD1997;Apr
i DDy;m þ mN
aN
þ

io;sì;M;

X

(6)

sì;mð

Þ2I

where DZm is the first difference of a vector of month dum-
mies. Consequently, dm represents the seasonal effects.
DXi;sì;m is a vector of (potentially) time-varying household-
specific characteristics, which includes the number of
household members;
the number of working household
members; the number of household members under age 18;
the number of household members above age 65; and inter-
view dummies, which control for ‘‘survey fatigue,’’ the ten-
dency of households to report lower expenditure in later
interviews. It is worth noting that household-specific fixed
effects (or non-time-varying characteristics) are already
controlled for by taking the first difference.

The dummies for October, novembre, and December
1996 (D1996;Oct, D1996;Nov, and D1996;Dec, rispettivamente) are
included to determine whether there was any effect on con-
sumption associated with announcement of the tax rate
increase. The effect is the sum of the income effect and the
intertemporal substitution effect. As we discussed in section
II,
the announcement of the tax rate increase occurred
sometime between October and December 1996; così, it is
preferable to include not a single month but all three month
dummies. The signs of the coefficients associated with each
dummy are, Tuttavia, ambiguous. The income effect should
be negative because the rate increase represents a negative
income shock, while the intertemporal substitution effect
should be positive, reflecting households’ incentive to
increase their consumption during the periods between
announcement and implementation, when the price level
was relatively low. Di conseguenza, the sign of the coefficients
depends on which effect dominated the other.14

Finalmente, mN

io;sì;m is an error term that accounts for unobserva-
bles affecting household consumption of N. Standard errors
are robust to serial correlation within households over time.

IV. Empirical Evidence

UN. Data

We use data from the Japanese Family Income and Expen-
diture Survey (JFIES) to estimate the IES.15 The JFIES is a
rotating panel survey in which households are interviewed
for six consecutive months and approximately 8,000 house-
holds are interviewed each month.16

Our estimates make use of JFIES data from the period
between April 1992 and March 2002, a symmetric five-year
window around the April 1997 rate increase. We choose to
exclude the bubble years before April 1992 because house-
hold expenditures prior to 1992 grew at a much faster pace
than they did after the bursting of the economic bubble in
1991; they remained more or less flat after that. Our sample
period ends in March 2002, which coincided with the
beginning of another boom.

We limit the sample to households that complete all six
interviews, but nearly all households can be used as the
response rate of the JFIES is quite high. Although data for
agricultural households are available in the JFIES after

14 There is also a literature that suggests that the income effect asso-
ciated with a tax change is absent until the tax change is implemented.
Vedere, Per esempio, Watanabe, Watanabe, and Watanabe (2001) and Mer-
tens and Ravn (2012). If this were the case, our estimate of the IES would
be biased upward, as the decline in expenditure from March to April
would capture not only intertemporal substitution but also the negative
income effect.

15 See Stephens and Unayama (2011, 2012) for more information

regarding the JFIES design and content.

16 Until 2002, single-person and agricultural households were excluded
from the JFIES. As of the 2009 JFIES, single-person households com-
posed 11.8% of the population and were responsible for 18.1% of expen-
ditures, while agricultural households accounted for 2% of the population
E 2.1% of expenditures.

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THE REVIEW OF ECONOMICS AND STATISTICS

Variable

Age of head
Number of household members
Number of household members under age 15
Number of household members aged 65 or over
Number of working members
Yearly income
Total expenditure
Excluding tax-exempted items
Nonstorable nondurables (N)
Storable nondurables (S)
Durables (D)

Number of observations
Number of households

TABLE 2.—SUMMARY STATISTICS

Mean

51.5
3.38
0.68
0.47
1.52
7,113
317
221
120
52
47

SD

13.7
1.24
0.98
0.75
0.95
4,652
266
195
78
32
138

Yearly household income and monthly household expenditures are listed in thousands of yen, con 2005 serving as the base year.

Minimum

Maximum

17
2
0
0
0
0
20
15
7
0.58
0

646,900
129,380

99
11
7
4
7
97,043
14,346
9,255
5,523
3,790
7,678

1999, we drop them to maintain consistency over the sam-
ple period. Also, we use male-headed households and those
whose head does not change his job because March is the
end of the fiscal year in Japan, when we observe many job
changes that may cause systematic changes in consumption
around the time of the consumption tax rate increase. IL
sample restrictions leave us with 646,900 observations from
129,380 households. Tavolo 2 presents summary statistics
for our sample.

The JFIES expenditure data are highly disaggregated by
item type, which allows us to accurately categorize goods
and services. It is critical for our purpose to distinguish not
only between taxable and tax-exempt goods and services
but also between N, S, and D. To construct expenditure on
N, we first exclude expenditures on goods and services that
were not subject to the consumption tax. As shown in table
2, expenditure on taxed items was 70% of total expenditure,
while most
tax-exempt expenditure consists of rent for
housing and education (per esempio., tuition for school), which we
would not expect to respond to a tax rate increase in the
short run.

In the next step, we divide goods and services that were
subject to the tax into three subcategories: D, S, and N. Noi
define N as goods and services that are neither storable nor
durable; questo è, they depreciate relatively quickly over time
when not in use, and when in use, they are fully consumed.
Di conseguenza, this category contains goods and services for
which the timing of consumption and expenditure roughly
coincides. Per esempio, fresh fruit, if not eaten, will spoil,
and it
is fully consumed with use. This category also
includes services such as taxi service, which is consumed at
the point of purchase.

We define S as those goods and services that depreciate
slowly over time if not used and fully if used. It follows that
these goods can be stockpiled for future consumption; con-
sequently, consumption and expenditure do not necessarily
coincide. Per esempio, laundry detergent can be stored for
long periods of time with little to no effect on its ability to
clean clothing, but once it is put into use, whatever amount
was used has been fully consumed. This category also

includes rail service, due to the fact that many Japanese
households purchase passes that are good for train travel for
several months. Così, one might expect that a household
would purchase a pass good for several months during a
low-price period and use the pass during a relatively high-
price period.

We define D as goods and services that depreciate rela-
tively slowly over time if not used and do not depreciate
fully with use. Consequently, consumption and expenditure
do not coincide for durables. This category includes tradi-
tional durables such as refrigerators and automobiles, COME
well as goods such as clothing that are classified as semi-
durables in the JFIES. Inoltre, we include a select
group of services such as home repair and tailoring, from
which consumers derive benefits long after the service is
provided.17

We then deflate monthly expenditures on N, S, and D
using tax-inclusive consumer price indices specific to our
categories.18 We are left with real monthly expenditures for
Japanese households from April 1992 through March 2002.
Tavolo 2 shows that more than half of taxable expenditure is
on N, while expenditures on S and D are similar. While it is
known that D may be underreported in the JFIES, this is not
the case for our dependent variable, N (see Unayama,
2011). Consequently, we are relatively unconcerned with
selection issues for nondurable goods and services.

Figura 5 displays plots of unadjusted and seasonally
adjusted real monthly household expenditure on N, S, E
D in 1996 E 1997. Note that once expenditures on N are
seasonally adjusted, as is the case in our empirical specifi-
cation presented in section IIIC, there appears to be rela-
tively little variation in N before and after implementation
of the Consumption Tax increase, while expenditures on S
and D exhibit a large spike in March 1997, followed by
somewhat lower expenditure after the tax increase.

17 See table 2 in the online appendix for our complete categorization of

N, S, and D.

18 In particular, we construct Laspeyres price indices for each of our
four categories using item-specific price indices and expenditure shares in
1990 for each of these items as the weights.

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MEASURING INTERTEMPORAL SUBSTITUTION IN CONSUMPTION

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FIGURE 5.—JFIES AVERAGE MONTHLY HOUSEHOLD EXPENDITURE, 1996–1997

The figure displays plots of unadjusted and seasonally adjusted real monthly household expenditures
(in thousands of yen) on nonstorable nondurable (N), storable nondurable (S), and durable goods and ser-
vices in 1996 E 1997. The bottom figure, which displays seasonally adjusted household expenditures,
plots the residuals plus the constant term from a regression of real monthly household expenditure on
month dummies, where April serves as the base month. The dashed vertical line represents implementa-
tion of the consumption tax increase in April 1997.

B. Empirical Results

Tavolo 3 presents our estimates for the entire sample based
on the specification given in equation (6). Regression (1)
includes only a dummy for April 1997. In effect, it ignores
announcement and intratemporal substitution effects. Noi
find that expenditure on N fell significantly between March
and April 1997. IL 2.16% decline in expenditure implies
that the intertemporal elasticity of substitution is 0.91. IL
estimate of the IES remains unchanged in regression (2),
which allows for announcement effects, but still these esti-
mates ignore intratemporal substitution.

Regression (3), our baseline specification, adds a first-
differenced March 1997 dummy intended to capture any
intratemporal substitution that resulted from the fall in the
user cost of durables in that month. Inclusion of this
dummy reduces the coefficient associated with the April
1997 dummy from (cid:2)2.16 A (cid:2)0.51. The implied IES is
0.21, which is significantly less than 1 but not significantly

different from 0. The coefficient associated with the first-
differenced March 1997 dummy, aN
1997;Mar, is positive and
significantly different from 0.

Given our interpretation of aN

sì;m in section IIIC and IES
(S) estimate of 0.21, it follows that preferences over dur-
ables and nondurables are nonseparable and that the two
composite goods are strong complements (cioè., [ < s ¼ 0.21). Intuitively, this result is derived from the fact that the fall in the user cost of durables in March 1997 was accom- panied by an increase in both durable and nondurable expenditures, while nondurable expenditures in other months prior to and following the tax rate increase exhib- ited little variation. The result is consistent with the findings of Pakos (2011) and Cashin (2016), but conflicts with the results of Ogaki and Reinhart (1998), who find an elasticity of substitution between durables and nondurables that exceeds 1.19 To develop a better sense of the strength of our comple- mentarity result, we also examine the contemporaneous cor- relation between the first difference of the logarithm of monthly durable and nonstorable nondurable expenditures over our entire sample period. Figure 4 shows that the price of durables (relative to nondurables) fell throughout our sample period. Given this fact, a positive contemporaneous correlation would be consistent with complementarities. Indeed, we find a positive and highly significant contem- poraneous correlation (0.10) between durable and nondur- able expenditures, which further strengthens our finding that durables and nondurables are strong complements.20 To consider the possibility that the intratemporal substi- tution effects persisted beyond March and April 1997 as a result of durable adjustment costs, regression (4) of table 3 includes additional first-differenced month dummies. In this case, the estimate of the IES is slightly larger than in the baseline estimate (0.30), while we cannot reject the null that all first-differenced month dummies are 0. Table 4 presents regression estimates intended to test the robustness of our results. Because seasonal effects may change over time, a longer sample period could yield an incorrect estimate of the IES. While we use the symmetric five-year window from 1992 through 2002 in the baseline, regression (1) uses a four-year window (1993–2001) and 19 Pakos (2011) demonstrates that Ogaki and Reinhart’s result may be biased due to the assumption of homothetic preferences. Given homo- thetic preferences where durables are luxuries and nondurables are neces- sities, growth in the durable consumption share over time that has accom- panied a fall in durable prices is incorrectly attributed to the substitution effect rather than the income effect. 20 Another story, which is consistent with our result, but unrelated to complementarities between durables and nondurables, is that nondurables serve as an input to the durable purchase technology (e.g., consuming gasoline and eating out when purchasing a new television from an elec- tronics store). Identification of the IES is robust to either story. The differ- ence is the interpretation of the first-differenced March 1997 dummy. Under the complementarity story, the dummy captures complementarities between the service flow from the durable stock and nondurable con- sumption, while under the other story, it captures the additional nondur- able purchases that must be made in order to facilitate the increase in dur- able purchases. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 9 8 2 2 8 5 1 9 7 4 6 2 5 / r e s t _ a _ 0 0 5 3 1 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 294 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 3.—ESTIMATES OF THE INTERTEMPORAL ELASTICITY OF SUBSTITUTION (IES) DEPENDENT VARIABLE: NONSTORABLE NONDURABLES (DlnCN i;y;m (cid:8) 100) (1) (2) (3) (4) Coefficient SE Coefficient SE Coefficient SE Coefficient SE First difference of month dummies DDFeb,1997 DDMar,1997 DDApr,1997 DDMay,1997 DDJun,1997 p-value for F-test for all DD ¼ 0 Month dummies DOct,1996 (a) DNov,1996 (b) DDec,1996 (c) DApr,1997 (d) F-test: (a) þ (b) þ (c) ¼ 0 ( p-value) Implied IES (¼|(d)| divided by 2.39) [95% CI] Sample period Sample restrictions Observations 1.66** 0.82 NA NA 0.042** (cid:2)2.16*** 0.78 NA 0.91 [0.27, 1.55] (cid:2)0.93 1.21 (cid:2)0.05 (cid:2)2.16*** 0.78 0.76 0.79 0.78 (cid:2)0.93 1.21 (cid:2)0.05 (cid:2)0.51 0.78 0.76 0.79 0.84 0.23 (0.80) 0.91 [0.27, 1.55] 0.23 (0.80) 0.21 [(cid:2)0.48, 0.90] 0.23 (0.65) 0.30 [(cid:2)0.65, 1.24] 1992–2002 Yes 646,900 (cid:2)1.10 0.56 (cid:2)0.89 (cid:2)1.54* 0.06 0.139 (cid:2)0.93 1.21 (cid:2)0.05 (cid:2)0.71 0.78 0.91 0.94 0.90 0.78 0.78 0.76 0.79 1.15 This table presents estimates from a regression based on equation (6). The dependent variable is the first difference of the logarithm of monthly household expenditures on nonstorable nondurable goods and ser- vices. Standard errors are robust to serial correlation within households over time. All columns report OLS regressions, which include, in addition to variables in the table, the first difference of month dummies, age of household head, and the first difference of the following variables: indicators for each interview, the number of household members, working members, members under age 18, and members over the age of 65. Significant at *10%, **5%, ***1%. TABLE 4.—ROBUSTNESS TESTS: DIFFERENT SAMPLES Dependent Variable: Non-storable Non-durables (DlnCN i;y;m (cid:3) 100) (1) Coefficient 1.75** (cid:2)1.03 1.60** 0.03 (cid:2)0.41 SE 0.83 0.79 0.78 0.80 0.86 0.59 (.407) 0.17 [(cid:2)0.53, 0.87] 1993–2001 Yes 526,612 (2) Coefficient 1.54* (cid:2)0.38 1.33* 0.13 (cid:2)0.71 SE 0.85 0.81 0.79 0.82 0.88 1.08 (0.266) 0.30 [(cid:2)0.43, 1.03] 1994–2000 Yes 394,673 (3) Coefficient 1.79** (cid:2)0.94 1.60** 0.10 (cid:2)0.86 SE 0.74 0.73 0.71 0.72 0.78 0.42 (.650) 0.36 [(cid:2)0.27, 0.99] 1992–2002 No 764,895 First difference of month dummies DDMarch,1997 Month dummies DOct,1996 (a) DNov,1996 (b) DDec,1996 (c) DApr,1997 (d) F-test: (a) þ (b) þ (c) ¼ 0 ( p-value) Implied IES (¼|(d)| divided by 2.39) [95% CI] Sample period Sample restriction Observations This table presents estimates from a regression based on equation (6). The dependent variable is the first difference of the logarithm of monthly household expenditures on nonstorable nondurable goods and ser- vices. Standard errors are robust to serial correlation within households over time. All columns report OLS regressions, which include, in addition to variables in the table, the first difference of month dummies, age of household head, and the first difference of the following variables: indicators for each interview and the number of household members, working members, members under age 18, and members over the age of 65. Significant at *10%, **5%, ***1%. regression (2) a three-year window (1994–2000). The resulting IES estimates (0.17 and 0.30, respectively) are similar to the baseline estimate. Regression (3) removes all sample selection criteria (e.g., male-headed household, par- ticipated in all six interviews). The implied IES is the lar- gest of all our regressions (0.36), but still small and signifi- cantly less than 1. Our results are comparable to the results in previous stu- dies that use macrodata. Hall (1988) summarizes his results by saying that ‘‘the value may even be zero and is probably not above .2’’ (p. 350). Ogaki and Reinhart (1998) conclude that the point estimates fall in a ‘‘range of 0.32 to 0.45’’ when allowing for nonseparable preference (p. 1095); moreover, Yogo (2004) reports the 95% confidence inter- vals [(cid:2)0.56, 0.45] using Japanese data between 1970 and 1998 (Yogo, 2004, table 3). In contrast, studies based on survey data have found lar- ger estimates of the IES. Attanasio & Weber (2010) sum- marize their results (Attanasio & Weber, 1993, 1995) as fol- lows: lower estimates of the IES based on macrodata can be explained by aggregation bias; once this bias is taken into account, the IES estimate increases to approximately 0.8 (Attanasio & Weber 2010). Similarly, Vissing-Jorgensen (2002) obtain point estimates of the IES in the range of 0.8 to 1.0 when accounting for limited asset market participa- tion. Gruber (2013) obtains an even larger IES estimate of 2 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 9 8 2 2 8 5 1 9 7 4 6 2 5 / r e s t _ a _ 0 0 5 3 1 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 MEASURING INTERTEMPORAL SUBSTITUTION IN CONSUMPTION 295 TABLE 5.—HETEROGENEITY ACROSS HOUSEHOLD TYPES Dependent Variable: Nonstorable Nondurables (DlnCN i;y;m (cid:8) 100) (1) (2) (3) (4) Coefficient SE Coefficient SE Coefficient SE Coefficient SE First difference of month dummies DDMar,1997 Month dummies DOct,1996 (a) DNov,1996 (b) DDec,1996 (c) DApr,1997 (d) 1.19 (cid:2)0.82 0.99 (cid:2)0.13 (cid:2)0.57 0.89 0.85 0.81 0.86 0.93 3.95** (cid:2)1.37 2.28 (cid:2)0.27 (cid:2)0.36 2.00 2.00 2.22 2.05 1.94 1.48 (cid:2)1.88 1.18 0.39 (cid:2)0.36 1.11 1.10 1.06 1.10 1.17 1.70 0.25 1.28 (cid:2)0.74 (cid:2)0.80 1.21 1.09 1.10 1.13 1.22 F-test: (a) þ (b) þ (c) ¼ 0 ( p-value) Implied IES (¼|(d)| divided by 2.39) [95% CI] Sample period Sample group Observations 0.04 (0.97) 0.24 [(cid:2)0.53, 1.01] 1992–2002 Working 539,073 0.36 (0.62) 0.15 [(cid:2)1.45, 1.75] 1992–2002 No job 107,827 0.23 (0.81) 0.15 [(cid:2)0.81, 1.11] 1992–2002 Higher income 311,837 0.23 (0.55) 0.34 [(cid:2)0.67, 1.34] 1992–2002 Lower income 335,063 This table presents estimates from a regression based on equation (6). The dependent variable is the first difference of the logarithm of monthly household expenditures on nonstorable, nondurable goods and ser- vices. Standard errors are robust to serial correlation within households over time. All columns report OLS regressions, which include, in addition to variables in the table, the first difference of month dummies, age of household head, and the first difference of the following variables: indicators for each interview; the number of household members, working members, members under age 18, and members over the age of 65. Significant at *10%, **5%, ***1%. when using cross-sectional variation in capital income tax rates as a source of identifying variation. We believe that our estimates are preferable to previous estimates because we use microdata, a natural experiment approach, an appropriate categorization of nondurables, and a specification that is robust to nonseparable preferences between durables and nondurables. The use of microdata implies that our result is free from aggregation bias. Exploiting a natural experiment allows us to avoid the pro- blem of weak instruments and the potential for correlation between lagged instruments and contemporaneous con- sumption growth.21 Restricting the analysis to nonstorable nondurable goods and services mitigates the concern that we are capturing an expenditure elasticity rather than the intended consumption elasticity. Finally, as evidenced by the results from regressions (2) and (3) in table 3, allowing for nonseparable preferences has a significant impact on our estimate of the IES. It is possible that our small estimate of the IES is attribu- table to liquidity constraints. Because liquidity-constrained consumers are less able to smooth consumption across peri- ods, the estimated IES could be smaller if many households faced a binding constraint around the time of the consump- tion tax rate increase. To test for this possibility, we sepa- rate the sample into groups that are more likely to be liquid- ity constrained and groups that are relatively less likely to be constrained. First, we separate working and nonworking households. While the nonworking group includes unem- ployed households, most are retired.22 Because retired households can expect little to no income growth, they are 21 As in this paper, Engelhardt and Kumar (2009) use microdata and an approach that exploits a natural experiment to find the IES is 0.74. Unlike other papers (including this one), however, the IES is not derived from the Euler equation, and as a result, it is difficult to compare to our esti- mates. 22 More than 90% of nonworking households are aged 60 or older. much less likely to be liquidity constrained. As regressions (1) and (2) in table 5 show, the difference in the estimated IES between working and nonworking is small. A more conventional method to test for liquidity constraints is to divide households into higher- and lower-income groups. The results in regressions (3) and (4) indicate that the IES is slightly larger for lower-income households. Overall, the results in table 5 suggest that liquidity constraints are not responsible for our small IES estimate. Data quality is another possible explanation why con- sumption of N was insensitive to the tax rate increase. If households incorrectly report their expenditures every month, the real changes would be attenuated by measure- ment error, causing our estimate of the IES to be biased toward 0. To evaluate this, we regress the first difference of the logarithms of S and (1 þ D) on the same set of vari- ables.23 Expenditures on S and D should change around implementation much more than expenditure on N. This is because S and D are subject not only to intertemporal sub- stitution in consumption, but also arbitrage effects. Regres- sions (2) and (3) in table 6, which employ the same specifi- cation used for N, given in equation (6), show that expenditures on S and D in March 1997 increased signifi- cantly. While it is difficult to interpret these coefficients, the results demonstrate that changes in expenditure are accurately reported, suggesting that data quality issues do not preclude us from finding a response to the Consumption Tax rate increase. Finally, we consider the announcement effects. Specifi- cally, we are interested in their sum. We find that the sum is slightly positive, but does not differ significantly from 0 in 23 A small percentage of households report 0 monthly expenditure on durables, and as a result, we must take the logarithm of 1 þ D. Results do not significantly change if we omit households with 0 durable expendi- tures from the analysis. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 9 8 2 2 8 5 1 9 7 4 6 2 5 / r e s t _ a _ 0 0 5 3 1 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 296 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 6.—ARBITRAGE EFFECTS FOR STORABLES AND DURABLES (1)a ((4) in Table 3) (2) (3) Nonstorable Nondurables (DlnCN i;y;m (cid:8) 100) Storable Nondurables (DlnXS i;y;m (cid:8) 100) Durables (DlnXD i;y;m (cid:8) 100) First Difference of month dummies DDFeb,1997 DDMar,1997 DDApr,1997 DDMay,1997 DDJun,1997 p-value for F-test for all DD ¼ 0 Month dummies DOct,1996 DNov,1996 DDec,1996 DApr,1997 Sample period Sample restriction Observations SE 0.78 0.91 0.94 0.90 0.78 0.78 0.76 0.79 1.15 Coefficient (cid:2)1.10 0.56 (cid:2)0.89 (cid:2)1.54* 0.06 (cid:2)0.93 1.21 (cid:2)0.05 (cid:2)0.71 0.139 1992–2002 Yes 646,900 SE 0.87 0.97 1.01 0.91 0.83 0.85 0.88 0.94 1.28 Coefficient 0.01 10.06*** (cid:2)3.80*** (cid:2)0.73 1.21 0.00*** 1.13 (cid:2)1.91** 1.58* (cid:2)2.43* 1992–2002 Yes 646,900 Coefficient SE 3.40 3.71 3.72 3.24 2.94 3.13 2.95 3.03 4.72 7.16 21.89*** (cid:2)0.35 2.07 6.93** 0.00*** 0.78 (cid:2)4.02 3.41 (cid:2)8.13* 1992–2002 Yes 646,906 This table presents estimates from a regression based on equation (6). The dependent variable is the first difference of the logarithm of monthly household expenditures on nonstorable nondurables (column 1), stor- able nondurables (column 2), and durables (column 3). Standard errors are robust to serial correlation within households over time. All columns report OLS regressions, which include, in addition to variables in the table, the first difference of month dummies, age of household head, and the first difference of the following variables: indicators for each interview; the number of household members, working members, members under age 18, and members over the age of 65. Significant at *10%, **5%, ***1%. a This refers to column 4 in table 3. all regressions presented in tables 3, 4, and 5. As discussed in section IIIC, this implies that the positive intertemporal substitution effect cancels out any negative income effect that may have resulted from announcement of the consump- tion tax rate increase. V. Summary and Discussion This study examines intertemporal substitution in con- sumption using a preannounced increase in Japan’s con- sumption tax rate from 3% to 5%. Because the Japanese consumption tax is highly comprehensive, the tax rate increase was announced prior to its implementation, and other factors that affect the real interest rate were con- stant, it presents an ideal natural experiment to estimate the IES. A Japanese monthly household survey is ex- ploited to accurately categorize nondurables. Our research design and the use of microdata allow us to avoid the pro- blems of weak instruments and aggregation bias. Further- more, our empirical specification is robust to intratem- poral substitution between durables and nondurables. Given the exogenous change in the real interest rate, our detailed data, and flexible empirical specification, we find that the IES is small. The baseline point estimate is 0.21 and does not differ significantly from 0, but is signifi- cantly less than 1.24 From a broader policy standpoint, two implications emerge from our result. First, recent work by Correia et al. (2013) demonstrates that when nominal interest rates are at the zero lower bound, a reduction in the VAT can be used 24 The results of Pakos (2011) and Okubo (2008) suggest that our esti- mate of the IES would be even smaller had we allowed for nonhomothetic preferences. to mimic an interest rate cut. However, our result suggests that the stimulus provided by such a policy may be rela- tively limited.25 Second, previous authors (Kaplow, 2008; Auerbach & Kotlikoff, 1987; Auerbach, Kotlikoff, & Skinner, 1983) have raised concerns over the efficiency costs of prean- nounced increases in consumption tax rates. They posit that the longer the length of time between announcement and implementation of a consumption tax rate increase, the lar- ger will be the welfare losses due to the acceleration of con- sumption in the period prior to implementation. However, our result suggests that the welfare losses of preannounce- ment are small.26 While we find that consumption is insensitive to the real interest rate, the same is not necessarily true for expendi- ture. Durability and storability allow households to change the timing of their expenditure without changing the timing of consumption. Our future work will examine these effects associated with Japan’s consumption tax rate increase. In doing so, we will be able to fully characterize the consump- 25 For a borrowing-constrained household, consumption should increase throughout the entire period of the rate decrease. Crossley et al. (2009) point out that the fraction of constrained households likely increases dur- ing downturns. If this is true, a rate decrease may provide stimulus not because of the intertemporal substitution effects but rather an income effect for constrained households. 26 This finding is reinforced by the results in Cashin (2011), which examines the intertemporal substitution and arbitrage effects of three separate increases in the goods and services tax rate in New Zealand. In all three cases, the length of time between announcement and implemen- tation differed, but in all three cases, the expenditure response was con- fined to the month prior to implementation, which indicates the response was driven by largely unavoidable arbitrage effects rather than intertem- poral substitution in consumption. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 9 8 2 2 8 5 1 9 7 4 6 2 5 / r e s t _ a _ 0 0 5 3 1 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 MEASURING INTERTEMPORAL SUBSTITUTION IN CONSUMPTION 297 tion and expenditure response to a change in the real inter- est rate. 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