Monetary Distortions in the Consumption-Leisure Choice:
An Empirical Investigation

Youngsoo Bae
Department of Economics
410 Arps HallThe Ohio State University
1945 N. High Street
Columbus, Ohio 43210-1172
E-Mail: bae.35@osu.edu
Tel.: (614) 292-5461

Vikas Kakkar∗
Department of Economics and FinanceCity University of Hong Kong
Kowloon, Hong Kong
E-Mail: efvikas@cityu.edu.hk
Tel: (852) 2788-9707

Masao Ogaki∗
Department of Economics
410 Arps HallThe Ohio State University
1945 N. High Street
Columbus, Ohio 43210-1172
E-Mail: mogaki@econ.ohio-state.edu
Tel.: (614) 292-5842

July 2005∗ We gratefully acknowledge financial support from City University of Hong Kong’s Strategic Research Grant 7000907,
and thank Jack Hung for providing research assistance.

Monetary Distortions in the Consumption-Lesire Choice: An Empirical Investigation

Abstract:
In a wide class of monetary models with both cash and credit goods, the main welfare cost of inflationis that it distorts the choice between these two goods. In these models, distortions exist because therelevant measure of the relative price between cash and credit goods for consumers is the usual relative
price discounted by the nominal interest rate. Changes in the inflation rate therefore create distortions
by affecting the nominal interest rate. This paper proposes a new statistical method for detecting theexistence and magnitude of this distortion in a monetary model of the consumption-leisure choice. The
empirical analysis is motivated by deriving a long-run restriction between the stochastic and deterministic
trends of real consumption, the real wage rate and the gross nominal interest rate from the first-orderconditions of the representative agent’s optimization problem. Using nondurable- and food-consumption
as cash goods, and leisure as the credit good, this method is applied to a diverse group of 12 economies.
The evidence suggests that such distortions exist and tend to be statistically and economically significant
for most high- and medium-inflation economies, but not for low-inflation economies.

JEL Classification: E21 (Consumption), E41 (Demand for Money), C22 (Time-Series Models)1Introduction

In a wide class of monetary models with cash goods (goods purchased with money) and credit goods(goods purchased with credit), the main welfare cost of inflation is that it distorts the choice between
these two goods (see, e.g., Lucas (1984), Lucas and Stokey (1987), and Townsend (1987)). This classincludes many cash-in-advance models with one good and leisure in which leisure plays the role of acredit good (see, e.g., Schmitt-Grohe and Uribe (2000) and Ireland (2003)). In these models, distortions
exist because the relevant measure of the relative price between cash and credit goods for consumers isthe usual relative price discounted by the nominal interest rate. Changes in the inflation rate therefore
create distortions by affecting the nominal interest rate. This paper proposes a new statistical method for
detecting the existence and magnitude of this distortion in a monetary model of the consumption-leisurechoice.
In the monetary models cited above, money is held for transactions purposes, and the distortions arecaused for the following reason. As long as the nominal interest rate is positive, holding non-interestbearing money involves an opportunity cost. Consumers count this opportunity cost as an extra costfor purchasing cash goods but not for credit goods because money is held only for transactions involving
cash goods.
In our empirical work, we use nondurable- and food-consumption as cash goods and leisure as thecredit good. The empirical analysis is motivated by deriving a long-run restriction between the stochastic
and deterministic trends of real consumption, the real wage rate and the gross nominal interest rate fromthe first-order conditions of the representative agent’s optimization problem. We investigate a diverse
group of 12 economies. The evidence suggests that such distortions exist and tend to be statisticallyand economically significant for most high- and medium-inflation economies, but not for low-inflation
economies.
Empirical work by Hodrick, Kocherlakota, and Lucas (1991) and Braun (1994) also uses monetarymodels with cash and credit goods, but these authors do not investigate this particular form of distortion.
Many other aspects of monetary distortions have been studied in the empirical literature on monetary
economics. For example, Fisher (1981) estimates shoe leather costs (the costs in time and effort incurredby people and firms who are trying minimize their holdings of cash). Christiano, Eichenbaum andEvans (1996) try to detect evidence on the empirical plausibility of the “limited participation” models
of Christiano and Eichenbaum (1992, 1995), in which monetary distortions occur because some people
are not allowed to continuously participate in financial trades. More recently, Boyd, Levine and Smith(2001) examine the evidence in favor of theoretical models (Huybens and Smith, 1999) in which even3

predictable increases in inflation affect the financial sector’s performance adversely due to informational
asymmetries in credit markets.
In contrast, monetary distortions on the relative price of cash versus credit goods have only beenstudied in the theoretical literature, and have not been studied by other researchers in the empiricalliterature. Ogaki (1988) studied the relative price monetary distortion with U.S. time series data, using
food as the cash good and automobiles as the credit good. Because the inflation rate has been relatively
low in the United States, he found only mixed evidence of such distortions. A priori, it is expected thatstronger evidence will emerge from countries with higher inflation rates. Ogaki (1988) used cointegrating
regressions that are similar to the ones used here. The concept of cointegration proposed in Engle andGranger (1987) was relatively new in 1988, and better econometric procedures for cointegrated systems
have been developed in the last decade. Hence, the econometric procedure used in Ogaki (1988) is notsatisfactory for the purpose of our research.
Ogaki and Park (1998) proposed a cointegration approach to estimating preference parameters, which
can be readily used for our research. Ogaki and Park’s approach has been used by Ogaki (1992), Cooley
and Ogaki (1996) and Ogaki and Reinhart (1998), among others. The econometric procedure proposedby Ogaki and Park allows one to test the null hypothesis of stochastic cointegration and the deterministic
cointegration restriction, both of which are implied by our model. Stochastic cointegration means thatthe stochastic trends in the variables are eliminated when their linear combination is formed by a vector,
called the cointegrating vector. The deterministic cointegration restriction means that the cointegrating
vector also eliminates the deterministic trends, which arise from the drift terms of the variables.

To

test the sensitivity of our empirical results to the econometric procedure, we also use a more recently
developed Hausman-type cointegration test proposed in Choi, Hu and Ogaki (2005).
The rest of the paper is organized as follows. Section 2 describes the economic model. Section
3 presents the econometric model based on the model in Section 2. The econometric procedures are
explained in Section 4. Section 5 presents the empirical results. Concluding remarks are contained in
Section 6.

2

A Cash-In Advance Model of the Consumption-Leisure Choice

Consider the representative consumer who maximizes the lifetime utility function

U=

∞
X

β t u(Ct , Lt )

t=0

4

(1)

subject to appropriate budget constraints and cash-in-advance constraints for purchasing the consumption
good. Here β is a discount factor, Ct denotes consumption and Lt denotes leisure at time t. It is assumed
that the momentary utility function u is additively separable in consumption and leisure and has thefollowing functional formu(Ct , Lt ) =Ct1−α − 1
+ V (Lt ).
1−α

(2)

Here V is a continuously differentiable concave function and α is a preference parameter that can beinterpreted as the inverse of the intertemporal elasticity of substitution of consumption. The first ordercondition for the consumption-leisure choice can be summarized byWt
V ′ (Lt )=(1 + it )
Ct−α

(3)

where Wt is the real wage rate, it is the nominal interest rate and V ′ (Lt ) is the marginal utility of leisure.
Taking the logarithm of both sides of Equation (3) yieldsln(Ct ) =11ln(Wt ) − ln(1 + it ) − ln(V ′ (Lt )).
α
α

(4)

Equation (4) forms the basis of our econometric model.
The left-hand-side of Equation (3) is the relevant relative price for the consumption-leisure choicebecause the consumer is required to hold cash in order to purchase the consumption good in this model.
Since the opportunity cost of holding cash is the forgone interest payment, Equation (3) is obtained.

3

The Econometric Model

Since the seminal work of Nelson and Plosser (1982), it is well known that most macroeconomic timeseries are well approximated by unit-root nonstationary processes. Thus, ln(C), ln(W ), ln(1 + i) are
assumed to be unit root nonstationary. This assumption is consistent with the evidence documented in
Ogaki (1992) and Cooley and Ogaki (1996).1 Leisure is assumed to be strictly stationary. This implies
that ln(V ′ (Lt )) is strictly stationary, so Equation (4) gives the cointegrating regression:ln(Ct ) = b1 + b2 ln(Wt ) + b3 ln(1 + it ) + ut
1 The evidence presented in Subsection 5.2 of this paper is also consistent with this assumption.

5(5)

where b1 = E(ln(V ′ (Lt ))), b2 = 1/α, b3 = −1/α, and ut = ln(V ′ (Lt )) − b1 . In Equation (5), it is theinterest rate with the maturity date that exactly matches the holding period of money. However, theholding period of money is not known, and the data for that particular interest rate might not be available
even if the holding period of money were known. Therefore, we use available short-term interest rate datafor it in our cointegrating regression. Using this variable does not violate the cointegration implicationof the model as long as the measured interest rate is cointegrated with the interest rate in the model.
This assumption is plausible because all interest rates are cointegrated if risk and term premiums are
stationary.
The model implies that b2 = −b3 = 1/α. However, b3 in our cointegrating regression will be different
from −1/α if the measured interest rate is not cointegrated with the interest rate in the model with a(1, −1)′ cointegrating vector. For example, the cointegrating vector will be different from (1, −1)′ except
for the special case that the holding period is exactly equal to one year in our annual data.2 Hence we
do not interpret the estimated b3 as 1/α and do not impose the restriction b2 = b3 in our empirical work.
In addition, if the consumer decides to change the holding period of money as the short-term nominalinterest rate changes, then our assumption of the constant holding period of money is violated. Even inthis case, Equation (5) as a cointegrating regression may be a good approximation because the short-term
nominal interest rate will be a good measure of transaction costs in equilibrium. However, there is no
reason to believe that the restriction b2 = b3 should hold in this case.

4

The Econometric Procedure

If the monetary distortion exists, the model implies that b3 is negative in Equation (5). Hence, the main
purpose of this paper is to see if the data support this prediction of the model. We can apply Ordinary
Least Squares (OLS) directly to Equation (5), and this estimator is called static OLS in the cointegration
literature. Even though the static OLS estimator is super consistent, it is not attractive for our purpose because it is not asymptotically efficient. It is also difficult to conduct inference on the statisticalsignificance of b3 with static OLS because it has a nonstandard distribution. Hence we utilize two asymptotically efficient estimators – Park’s (1992) Canonical Cointegrating Regression (CCR) estimator3 andStock and Watson’s (1993) dynamic OLS estimator. The static OLS estimator is not efficient because
2 For example, if the deviation from the expectation theory of the term structure of interest rates is stationary, thenthe cointegrating vector is (1, 1)′ if the true holding period of money is one month and a one-year interest rate and anannualized one-month interest rates are used.
3 Monte Carlo experiments in Park and Ogaki (1991) show that they have better small sample properties than Johansen’s(1991) estimators even when the Gaussian VAR structure assumed by Johansen is true. Further details regarding CCR-based
estimation and testing can be found in Ogaki (1993a, 1993b).

6

strict exogeneity is violated. The CCR estimator corrects for endogeneity by a nonparametric method.
The dynamic OLS estimator corrects for endogeneity by a parametric method of adding leads and lagsof the first difference of the regressor.

The parametric method would work better if the parametriccorrection is a good approximation, whereas the nonparametric method is more robust.
We also test for cointegration. Since the model implies cointegration, it is desirable to test the null
hypothesis of cointegration to control the probability of rejecting a valid economic model. Although estimation methods that have no cointegration as their null hypothesis are commonly used in the literature,these methods have low power and may fail to reject the null hypothesis with high probability even whenthe model is actually consistent with the data.
With the CCR procedure, we use Park’s (1990) variable addition test to test the null hypothesis ofcointegration. With this procedure, we can test the null hypothesis of stochastic cointegration and thenull hypothesis of the deterministic cointegration restriction.4

In the DOLS framework, we use Choi,

Hu, and Ogaki’s (2005) recently developed Hausman-type cointegration test to test the null hypothesisof cointegration.
While the DOLS estimator is well known, the Hausman-type cointegration test is not. Therefore, themain idea of the Hausman-type cointegration test is explained briefly in this subsection. Consider thefollowing dynamic regression where yt is an I(1) variable, xt is a 2-dimensional vector of I(1) variables,
and k stands for the order of leads and lags.

yt = β ′ xt +

2 X
k
X

(γi,j ∆xi,t−j ) + et .

(6)

i=1 j=1

The leads and lags of the first difference of the regressors are added in this regression in order to correct
for the endogeneity problem. Following Stock and Watson (1993), we assume that the endogeneity
correction of adding leads and lags perfectly eliminates the endogeneity problem in that et is strictly
exogenous with respect to the regressors in Equation (6) in this paper.5
Now, if the error term et is I(0), then this is a dynamic cointegrating regression. As shown by Stockand Watson (1993), the OLS estimator for this regression is super-consistent and asymptotically efficientunder their regularity conditions.
On the other hand, if the error term et is I(1), then Equation (6) is a spurious regression, and the
Dynamic OLS is inconsistent for the coefficient β as shown in Choi et al. (2005). The Hausman-type
cointegration test utilizes these properties to discriminate between the situation in which et is I(0) and4 See Ogaki and Park (1998) for definitions of these terminologies and a description of the testing procedure.
5 It is assumed here that the endogeneity correction is complete only for ease of exposition. This assumption can berelaxed under some regularity conditions as shown by Saikkonen (1991).

7

that in which et is I(1). In order to understand the idea of this test, it is useful to start with an analysisof the DOLS estimator by the Gauss-Markov Theorem, using Ogaki and Choi’s (2001) framework. For
this purpose, we consider a special case in which et is serially uncorrelated. In this case, Ogaki and Choi’s
conditional probability version of the Gauss-Markov Theorem applies,6 and the OLS applied to Equation(6) is the Best Linear Unbiased Estimator (BLUE) given the realization of the regressors.
Now consider the case in which et is a random walk. Then all the assumptions of the conditional
probability version of the Gauss-Markov Theorem hold except for the spherical variance assumption. In
this case, the OLS applied to Equation (6) is unbiased (since we are assuming strict exogeneity), but is
not efficient. In this case, we can apply the Generalized Least Squares (GLS) to Equation (6) to obtain
the BLUE. Applying GLS to Equation (6) basically means that we apply OLS after taking the firstdifference of Equation (6):∆yt = β ′ ∆xt +

2 X
k
X

(γi,j ∆2 xi,t−j ) + ∆et .

(7)

i=1 j=1

Choi et al. (2005) call this estimator the GLS corrected estimator.
In more general cases in which the error is serially correlated, Choi et al. (2005) note that asymptotic
theory shows that (a) the DOLS estimator is asymptotically efficient if et is I(0), (b) the GLS corrected
estimator is consistent, but is not as efficient as the DOLS estimator if et is I(0), (c) the DOLS estimatoris inconsistent if et is I(1), and (d) the GLS corrected estimator is consistent if et is I(1).
These observations naturally lead to the idea of testing for cointegration by comparing the DOLS
estimates and the GLS corrected estimates for β. Let the Hausman-type cointegration be defined by′HT = T βbdgls − βbdols Vbβ−1 βbdgls − βbdols(8)

where T stands for the sample size, βbdols stands for DOLS estimator in level regression, βbdgls stands

for GLS corrected estimator in differenced regression, and Vbβ stands for a consistent estimator for the√asymptotic variance of T (βbdgls − β). Under the null hypothesis that the error term is I(0), both

estimators βbdols and βbdgls are consistent and, therefore, they should be ‘close’ to each other. The test

statistic, HT , has an asymptotic chi-square distribution with 2 degrees of freedom. On the other hand,under the alternative hypothesis that the error term is I(1), the level regression will be spurious and,
therefore, only the differenced regression will be consistent. Therefore, the estimates from these two
6 We implicitly assume that the error has finite second moments and that the design matrix is of full column rank given
the realization of the regressors.

8

estimators will be very different with a large probability. The test statistic, HT , diverges in this case.

5

Empirical Results

5.1

Data

Data on real consumption, the real wage rate and the nominal interest rate are required to estimate
equation (5). Since the model assumes that money is required to purchase the consumption good, it ismore appropriate to use data on those components of consumption that are likely to be purchased bycash, rather than the aggregate consumption expenditure. Cooley and Ogaki (1996) also recommendthat at least a component of the aggregate consumption expenditure should be omitted. In this paper,
the nondurable- and food-consumption components are used as proxies for the cash good.
We try to select economies with a wide range of inflation experiences for which the relevant consumption data are available. While such consumption data are readily available for developed countries, it isgenerally not possible to obtain a sufficiently long time-series for most developing countries. Our dataset,comprising a total of 12 countries, is therefore skewed towards the developed economies.7 The primarysources of data are the National Accounts of OECD Countries, the International Financial Statistics
published by the IMF, and the United Nations Statistical Yearbook. Further details regarding the data
are provided in the Appendix.
Table 1 presents the summary statistics of the inflation history of these countries over the past twoor three decades. The average inflation rate varies from a low of 4.5% for Japan to a high of 90.4% forIsrael. The “High” and “Low” columns indicate the variability of the inflation rate as measured by its
range.8 Consistent with the well documented stylized facts in the empirical literature on inflation, higher
inflation rates also tend to be associated with a greater variability in the inflation rate. The countries
are classified into 3 groups of high- (greater than 10%), medium- (between 5 and 10%) and low- (below
5%) inflation economies to study how the existence and severity of the monetary distortion vary with the
inflation rate.

5.2

Trend Properties of the Data

Prior to estimating the cointegrating regressions between real consumption, real wage rates and thegross nominal rates, it is necessary to assess the evidence for the two assumptions that are being made7 The 12 countries are Canada, France, Greece, Hong Kong, India, Israel, Italy, Japan, Philippines, Spain, UK and USA.
8 The range of the inflation rate is defined as the difference between the highest and lowest inflation rates over the sample

period.

9

regarding the trend properties of the data. The first assumption is that all three variables are unit-root
nonstationary, which is a pre-requisite for estimating a cointegrating regression. The second assumption
is that the two independent variables, the real wage rate and the gross nominal interest rate, are notstochastically cointegrated with each other. If the second assumption is violated, one can still estimate a
modified version of Equation (5), but the two parameters of the model can no longer be identified.
Table 2 reports the results of testing the null hypothesis of a unit root, against the alternative oftrend-stationarity, based on the Said-Dickey (1984) and the Phillips-Perron (1988) t-ratio tests.9 At least
one of the two tests fails to reject the null of a unit root for most of the variables. Exceptions are thenondurable-consumption for Greece (α = 10%), the Philippine nominal interest rate (α = 10%), Indian
food-consumption and real wage rate (α = 1%), and Japanese nondurable-consumption (α = 5%). These
results are consistent with Ogaki (1992) and Cooley and Ogaki (1996), who also find evidence in favor of
the unit-root hypothesis for food- and nondurable-consumption and the real wage rate.
Table 3 reports the results of the tests for the null hypothesis of no stochastic cointegration between
the real wage rate and the gross nominal interest rate. In addition to the Said-Dickey t-ratio test,
Park’s (1990) I(1, 5) test is also employed. Both tests are based on residuals from an OLS cointegrating
regression between the real wage rate and the gross nominal interest rate that includes a time trend. The
I(1, 5) test does not reject the null hypothesis for any of the countries at conventional significance levels.
However, for three countries (France, India and Japan), the Said-Dickey test is significant (α = 1%) anddoes not agree with the I(1, 5) test.
Overall, the two assumptions regarding the trend properties of the variables are supported empirically.

5.3

Cointegration Results

Having established that the underlying assumptions are plausible, we proceed to test the empirical validityof equation (5), which embodies the long-run restriction between the stochastic and deterministic trends
of real nondurable/food-consumption, the real wage rate and the gross nominal interest rate implied by
the model.
Table 4 reports the results of estimating equation (5) using the CCR procedure with nondurableconsumption as the cash good. The first panel reports the results for the group of high-inflation countries.
For all four countries, the coefficient of the real wage rate, which measures the intertemporal elasticity
of substitution, has the theoretically correct positive sign and is statistically significant at conventionalsignificance levels. The focus of this paper is on the coefficient of the interest rate. It also has the
9 The Said-Dickey test is also popularly known as the Augmented Dickey-Fuller test.

10

theoretically predicted negative sign and is statistically significant for all four countries. The point
estimates of the interest rate coefficient for Greece and Spain imply that a 1% permanent increase ininflation reduces nondurable-consumption by more than 2% in the long run. The corresponding reduction
in nondurable-consumption for the Philippines and Israel is more modest, at 0.9% and 0.2% respectively.
With the exception of the H(1, 3) statistic for the Philippines, which is significant at the 1% level, the H(1,2) and H(1, 3) test statistics do not reject the null hypothesis of stochastic cointegration at conventionalsignificance levels for these 4 countries. The deterministic cointegration restriction is satisfied for all four
countries (α = 1%). This is strong evidence in favor of the model.
The second panel of Table 4 reports analogous results for the medium-inflation group of countries.
The intertemporal elasticity of substitution has the expected positive sign and is statistically significant
for all countries except India, for which it is significantly negative (α = 5%). Possible explanations forthe incorrect sign for India are the trend stationarity of the real wage rate and nondurable-consumption,or stochastic cointegration between the real wage rate and the nominal interest rate, which makes thecoefficients unidentified. The interest rate coefficient has the predicted negative sign and is statisticallysignificant for France, Hong Kong and Italy (α = 5%). It is negative but insignificant for India, andsignificant but positive for the UK. The H(1, 2) and H(1, 3) test statistics decisively reject the null
hypothesis of no stochastic cointegration for Hong Kong, and are also significant for the UK (α = 5%).
They are not significant for France, India and Italy (α = 5%). The deterministic cointegration restriction
is strongly rejected for Hong Kong, but not for other countries (α = 1%). Overall, the results for the
medium-inflation group are somewhat mixed, with only France and Italy finding clear empirical support.
The last panel of Table 4 reports the results for the group of low-inflation countries. The intertemporalelasticity of substitution is significant and positive only for Japan (α = 5%). The interest rate coefficient
has the incorrect positive sign and is statistically significant for all three countries (α = 1%). The H(1,2) and H(1, 3) statistics are not significant for any of the three countries, and the H(0, 1) statistic issignificant only for the US (α = 1%). In contrast to the high- and medium-inflation groups, there is noevidence of monetary distortions for group of low-inflation economies.
Table 5 reports the results of estimating equation (5) using the CCR procedure with food as the cash
good. The first panel reports the results for the high-inflation group of countries. The intertemporalelasticity of substitution is correctly signed and statistically significant for all countries except Israel
at conventional significance levels. The interest rate coefficient has the expected negative sign and issignificant for all 4 countries. The null hypothesis of stochastic cointegration is rejected for Spain (α = 1%)
by the H(1, 2) and H(1, 3) statistics, but not for Greece, Israel and the Philippines (α = 5%). The

11

deterministic cointegration restriction is not rejected for any country at the 1% level of significance.
These results are similar to those for nondurable-consumption, and support the model’s key predictionof monetary distortions.
The second panel of Table 5 reports the results for medium-inflation countries. With the exceptionof India, the intertemporal elasticity of substitution for all other countries is estimated with the correct
positive sign and is also statistically significant (α = 5%). As mentioned earlier, the incorrect sign for
India might be caused by trend-stationarity of some of the variables or due to an identification problem.
The coefficient of the interest rate has the correct sign for all 5 countries, but is statistically significant
only for Hong Kong and Italy (α = 5%). The H(1, 2) and H(1, 3) statistics do not reject the null
hypothesis of stochastic cointegration for any of the countries (α = 5%). The deterministic cointegration
restriction is also not rejected by the H(0, 1) statistic. Overall, these results support the existence ofmonetary distortions, but the magnitude of the distortions is smaller and less significant compared to thehigh-inflation economies.
The last panel of Table 5 reports the results of estimating equation (5) for the low-inflation group ofcountries. The intertemporal elasticity of substitution has the correct sign and is statistically significant
for Canada and Japan (α = 5%). However, it is significantly negative for the U.S. (α = 5%). Theinterest rate coefficient is incorrectly signed for all 3 countries and is statistically significant (α = 10%).
The H(1, 2) and H(1, 3) statistics reject the null hypothesis of stochastic cointegration for Japan, but
not for Canada and the U.S. (α = 5%). The H(0, 1) statistic rejects the deterministic cointegration
restriction for the U.S., but not for Canada and Japan (α = 5%). These results are similar to those for
nondurable-consumption in that the monetary distortions predicted by the model cannot be detected.
Our results with the dynamic OLS procedure are presented in Tables 6 and 7, with nondurable andfood consumption as the cash good, respectively. For most of the countries, the results are qualitatively
similar to those from the CCR procedure. One notable exception is the result for Greece: the coefficientfor the interest rate has the theoretically incorrect positive sign, and it is statistically significant in Tables
6 and 7. There was evidence against the deterministic cointegration for Greece in Tables 4 and 5. It is
possible that the dynamic OLS estimator did not work well because of the failure of the deterministic
cointegration restriction. Another notable difference is that the evidence for monetary distortions is notstatistically significant for either cash good for France and Hong Kong. The Hausman-type test finds
some evidence against cointegration only for Canada and United States.
To summarize, for all high-inflation economies, the evidence indicates that statistically significant
monetary distortions exist for both of the cash goods for three of the four countries. The results for Greece

12are consistent with this with the CCR procedure, but inconsistent with the dynamic OLS procedure.
Some of our estimates of the elasticity of consumption of the cash goods with respect to the nominalinterest rate exceeds 1 in absolute value for these countries, and are likely to translate into economicallysignificant welfare costs. The evidence for monetary distortions for the medium-inflation economies isrelatively mixed, with significant distortions evident for France, Italy and Hong Kong for at least one of the
cash goods with the CCR procedure, but only for Italy with the dynamic OLS procedure. There is little
evidence for the existence of monetary distortions for India and the UK. The empirical results from the
CCR procedure provide stronger support for the model for both high- and mdium-inflation countries. Thismay be because the lag length needed for the parametric correction in the DOLS procedure is constrainedin our relatively small samples. In sharp contrast to the medium- and high-inflation economies, virtuallyno evidence of monetary distortions is apparent for the low-inflation economies with either cash good andeconometric procedure.

6

Conclusions

This paper studies the existence and magnitude of monetary distortions in a model of the consumptionleisure choice. Using nondurable- and food-consumption as cash goods, and leisure as the credit good,
we document evidence of statistically and economically significant distortions for economies that haveexperienced double-digit or high single-digit inflation. There appears to exist a threshold level of therate of inflation, approximately equal to 5%, below which such distortions cannot be observed. A naturalextension of this work would be investigating the existence of these monetary distortions with alternative
credit goods, such as durable goods. It is hoped that these results enhance our understanding of thewelfare costs of predictable inflation.

13

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16

Appendix
This Appendix describes the sources of the data in detail. For Hong Kong, India, Israel, Philippines
and Spain, data on total real nondurable consumption expenditure and total real food expenditure wereobtained from the United Nations Statistical Yearbook (UNSY ). Nondurable consumption expenditurecomprised three categories; (a) Food, beverages and tobacco, (b) clothing and footwear, and (c) Medical
and health expenses. For the G-6 economies, the relevant consumption data were taken from the OECD’s
National Income Accounts, whereas for Greece they were taken from Data Stream. Aggregate consumption data were converted to per capita terms using population data from the International Financial
Statistics (IFS ) for all 12 countries.
It was not possible to obtain the same nominal interest rate series for all countries. For the U.S. andCanada, we used the six month Treasury bill rate; for France and Japan, the lending rate; for UK, thedeposit rate; for Hong Kong, the prime rate; for India, Italy, Philippines and Spain the discount rate;
and for Israel, the overall cost of unindexed credit. With the exception of Hong Kong and the U.S., thenominal interest rate for all countries was taken from the IFS. HK’s nominal interest rate series was takenfrom Data Stream, whereas that for the U.S. came from the Economic Report of the President.
Where possible, a real wage rate index for the manufacturing sector was used. No real wage data wereavailable for India, Israel and the Philippines. Nominal wage data for these countries was taken from the
UNSY, and deflated by the CPI (from the IFS ) to yield the real wage rate. The real wage rate index forHong Kong was taken from the HK government’s Census and Statistics Department, whereas that for
Spain came from Data Stream. Real wage rate indices (for the manufacturing sector) for Canada, France,
Italy, Japan and the UK were taken from Data Stream, whereas for the U.S. we used the real wage rate
for private nonagricultural industries from the Economic Report of the President.

17

Table 1: Summary Statistics of the Annual Inflation Rate
Country/ Sample

AverageHigh

Low

High-Inflation Countries
GRC

11.22123.826-0.00490.404373.820

10.94013.49246.673-0.32511.28024.5404.570(1961-1995)
ISR(1979-1994)
PHL(1980-1993)
SPN(1975-1994)

Medium-Inflation Countries
FRA

6.315

13.749

0.749

8.295

11.600

3.440

7.602

13.870-7.6309.748

21.277

2.043

7.217

24.2351.564(1973-1998)
HKG(1982-1994)
IND(1975-1991)
ITL(1970-1997)
UK(1961-1997)

Low-Inflation Countries
CAN

4.820

12.462

0.185

4.572

23.122-0.0924.634

13.5091.075(1961-1998)
JPN(1970-1997)
US(1961-1998)*

Countries with average annual inflation rate greater than 10% are classified as “HighInflation”, those with average annual inflation rate between 5% and 10% are classified as“Medium-Inflation”, and those with average annual inflation rate less than 5% are classified
as “Low-Inflation” economies.
18

Table 2: Trend Properties of the Data: Unit Root Tests
Country

Nondurable
SD/ADF a

PP b

Food
SD/ADF a

Real Wage Rate
PP b

SD/ADF a

Interest Rate

PP b

SD/ADF a

PP b

High-Inflation Countries
GRC-3.437∗-3.452∗-1.821-1.997-0.817-0.859-0.6710.410

ISR-1.736-1.830-1.861-2.010-1.939-2.057-2.595-2.603PHL-1.093-1.460-2.063-1.737-1.875-1.922-3.386∗∗-3.296∗SPN-2.273-1.105-2.173-1.870-3.299∗-0.056-1.153-0.937

Medium-Inflation Countries
FRA-2.235-2.294-2.541-2.698-4.358∗-2.205-0.477-0.810HKG-5.470∗∗∗-2.661-2.312-2.158-1.760-1.436-2.949-2.416IND-1.100-4.371∗∗-5.783∗∗∗-6.606∗∗∗-9.865∗∗∗-12.562∗∗∗-2.687-2.664ITL-0.624-0.584-0.2110.240-0.189-0.307-0.535-0.208UK∗∗-2.583-1.424-1.547-2.141-2.225-1.879-1.831-3.788Low-Inflation CountriesaCAN-1.710-1.508-1.772-1.696-1.561-1.049-1.736-1.724JPN-4.336∗∗-3.654∗∗-2.069-1.932-3.807∗∗-5.498∗∗∗-2.679-1.814US-2.367-2.360-1.655-1.597-3.073-2.748-2.529-1.882

SD/ADF denotes the Said-Dickey/Augmented Dickey-Fuller t-ratio test for the null hypothesis of a unit
root against the alternative of trend-stationarity. The test was performed by starting with three lags andreducing the number of lags until the last lag is significant at the five-percent level. The critical values
used incorporate finite sample adjustments based on MacKinnon (1992).

b

Denotes the Phillips-Perron t-ratio test for the null hypothesis of a unit root against the alternative oftrend-stationarity.

c*, **, and *** denote significance at the 10%, 5% and 1% levels,respectively.

19

Table 3: Trend Properties of the Data: Tests for the Null Hypothesis of No Stochastic Cointegration Between Real Wage Rate and Gross Nominal Interest Rate
CountryI(1, 5)aSD/ADFb

High-Inflation Countries
GRC

4.254

-3.060ISR

1.100-2.553PHL

3.087-1.819SPN

222.420-2.753Medium-Inflation Countries
FRA

2.821

-7.547***HKG

12.774-2.204IND

8.301-6.320***

ITL

6.259

-2.970UK

10.730-2.915Low-Inflation Countries

a

CAN

1.171

-2.702JPN

7.400-4.874***

US

0.974

-2.349I(1, 5) denotes Park’s (1990) test for the null hypothesis of no cointegration. The 1%, 5%
and 10% critical values are 0.1027, 0.2506 and 0.4984, respectively.

b

SD/ADF denotes the Said-Dickey/Augmented Dickey-Fuller t-ratio test for the null hypothesis of no stochastic cointegration. The critical values used incorporate finite sample
adjustments based on MacKinnon (1992).

c*, **, and *** denote significance at the 10%, 5% and 1% levels, respectively.

20

Table 4: Canonical Cointegrating Regressions for Real Per Capita Nondurable Consumption
Country/Sampleln(Wt )aln(1 + it )aH(0,1)b

H(1,2)b

H(1,3)b

High-Inflation Countries
GRC

0.691

-2.063

4.528

1.267

1.393

(1970-1995)(0.173)(0.733)(0.033)(0.260)(0.498)

ISR

0.932

-0.191

5.196

0.116

3.063

(1979-1994)(0.294)(0.054)(0.023)(0.733)(0.216)

PHL

0.274

-0.925

1.609

2.921

9.845

(1980-1993)(0.055)(0.300)(0.205)(0.087)(0.007)

SPN

0.173

-2.331

1.735

0.129

1.469

(1975-1994)(0.032)(0.511)(0.188)(0.719)(0.480)Medium-Inflation Countries
FRA

0.962

-1.257

0.507

0.038

4.806

(1973-1998)(0.055)(0.252)(0.477)(0.846)(0.090)

HKG

2.473

-0.73833.62513.053151.734(1982-1994)(0.068)(0.113)(0.000)(0.000)(0.000)IND-0.518-0.615

1.469

2.424

3.373

(1975-1991)(0.048)(0.424)(0.225)(0.119)(0.185)

ITL

0.489

-0.477

0.258

3.449

3.806

(1970-1997)(0.051)(0.233)(0.611)(0.063)(0.149)

UK

0.173

1.139

0.001

4.553

8.677

(1961-1997)(0.035)(0.241)(0.977)(0.033)(0.013)Low-Inflation Countries
CAN

0.067

1.988

0.184

2.143

3.769

(1961-1998)(0.088)(0.470)(0.668)(0.143)(0.152)

JPN

0.410

1.715

1.708

0.721

2.208

(1970-1997)(0.024)(0.249)(0.191)(0.396)(0.332)

US-0.048

1.847

6.880

0.000

0.179

(1961-1998)(0.474)(0.924)(0.009)(0.993)(0.914)aStandard errors are in parenthesis.

b

H(0,1) tests the deterministic cointegration restriction, whereas H(1, 2) and H(1,3) test thenull hypothesis of stochastic cointegration. P-values are in parenthesis.
21

Table 5: Canonical Cointegrating Regressions for Real Per Capita Food Consumption
Country/Sampleln(Wt )aln(1 + it )aH(0,1)b

H(1,2)b

H(1,3)b

High-Inflation Countries
GRC

0.890

-2.65910.832

1.828

3.276

(1962-1995)(0.209)(1.031)(0.001)(0.176)(0.348)

ISR

0.137

-0.143

3.062

0.155

4.090

(1979-1994)(0.265)(0.053)(0.080)(0.694)(0.130)

PHL

0.210

-0.347

1.199

2.659

5.241

(1980-1993)(0.046)(0.270)(0.274)(0.103)(0.073)

SPN

0.090

-0.960

0.000

9.534

9.645

(1975-1994)(0.015)(0.216)(0.999)(0.002)(0.008)

Medium-Inflation Countries
FRA

0.576

-0.117

0.295

1.843

5.285

(1973-1998)(0.054)(0.231)(0.587)(0.175)(0.071)

HKG

0.589

-0.216

0.178

0.253

5.912

(1982-1994)(0.019)(0.042)(0.673)(0.615)(0.052)IND-0.344-0.243

0.697

2.216

3.429

(1975-1991)(0.047)(0.393)(0.406)(0.136)(0.180)

ITL

0.833

-1.312

0.045

0.275

1.898

(1970-1997)(0.056)(0.258)(0.832)(0.600)(0.387)UK

0.802-0.063

2.821

3.260

3.548

(1961-1997)(0.019)(0.106)(0.093)(0.071)(0.170)

Low-Inflation Countries
CAN

0.658

0.376

0.271

1.419

1.566

(1961-1998)(0.036)(0.110)(0.603)(0.233)(0.457)

JPN

0.698

0.735

2.217

5.044

15.441(1970-1997)(0.024)(0.252)(0.136)(0.025)(0.000)US-2.060

3.326

7.343

0.083

3.097

(1961-1998)(0.941)(1.756)(0.007)(0.773)(0.213)aStandard errors are in parenthesis.

b

H(0,1) tests the deterministic cointegration restriction, whereas H(1, 2) and H(1,3) test thenull hypothesis of stochastic cointegration. P-values are in parenthesis.
22

Table 6: Hausman-type Cointegration Test for Real Per Capita Nondurable Consumption
Country

DOLSb

Lead & Lagaln(Wt )

Hausmanln(1 + it )Test

-0.00631.80051.4512(0.1118)(0.6710)0.4718-0.1090(0.5576)(0.0574)

0.3871-1.0402(0.0481)(0.3653)0.3145-2.2321(0.0179)(0.1488)

High-Inflation Countries
GRC

2(1962-1995)
ISR

1(1979-1994)
PHL

1(1980-1993)
SPN

2(1975-1994)

0.50610.19950.2951

Medium-Inflation Countries
FRA

2(1973-1998)
HKG

0(1982-1994)
IND

1(1975-1991)
ITL

2(1970-1997)
UK

2(1961-1997)

1.2862-0.6140(0.7642)(1.7822)2.2564-0.7280(0.2371)(0.9424)-0.3427

6.9375(0.0516)(1.3000)

0.5605-1.0582(0.2011)(0.2953)

0.78910.1339(0.0281)(0.1754)1.22441.38480.02872.01230.2154Low-Inflation Countries
CAN

2(1961-1998)
JPN

2(1970-1997)
US(1961-1998)a2

0.26101.0502(0.1144)(0.3839)0.70870.5126(0.2514)(2.4783)-0.4206-1.1938(0.5445)(1.5429)

6.0997∗∗0.385316.3383∗∗∗

Lead and lag lengths of Hausman-type Cointegration test is selected by the BIC method with maximum length is set to 2.

bStandard errors, calculated by the Newey-West HAC estimator with bandwidth parameter of 2, arein parenthesis.

c

Critical value of χ2 (2) are 4.61, 5.99 and 9.21 for 10%, 5% and 1% significance levels. *, ** and ***denote the rejection at 10%, 5% and 1% significance levels.

23

Table 7: Hausman-type Cointegration Test for Real Per Capita Food Consumption
Country

DOLSb

Lead & Lagaln(Wt )

Hausmanln(1 + it )Test

0.05672.37330.9985(0.0489)(0.2933)

0.6355-0.0540(0.3388)(0.0348)0.3712-0.9749(0.0502)(0.3807)0.2427-0.1609(0.0087)(0.0720)High-Inflation Countries
GRC

2(1962-1995)
ISR

1(1979-1994)
PHL

1(1980-1993)
SPN

2(1975-1994)

0.45110.19350.3105

Medium-Inflation Countries
FRA

2(1973-1998)
HKG

0(1982-1994)
IND

1(1975-1991)
ITL

2(1970-1997)
UK

2(1961-1997)

0.3397-0.8032(0.6831)(1.5929)0.6198-0.2821(0.0619)(0.2461)-0.2687

6.3242(0.0634)(1.5970)0.2088-0.1522(0.1381)(0.2028)

0.15551.0196(0.0600)(0.3747)0.51770.35600.04091.46271.2702

Low-Inflation Countries
CAN

2(1961-1998)
JPN

2(1970-1997)
US(1961-1998)a2-0.2875

0.8585(0.1340)(0.4497)

0.39010.9048(0.1050)(1.0356)-0.0756-0.8063(0.3527)(0.9996)

5.7401∗0.31588.4532∗∗

Lead and lag lengths of Hausman-type Cointegration test is selected by the BIC method with maximum length is set to 2.

bStandard errors, calculated by the Newey-West HAC estimator with bandwidth parameter of 2, arein parenthesis.

c

Critical value of χ2 (2) are 4.61, 5.99 and 9.21 for 10%, 5% and 1% significance levels. *, ** and ***denote the rejection at 10%, 5% and 1% significance levels.

24