gmm v1 artykul a

Economic Modelling 16 1999 293

]306

Modelling consumption: permanent-income

or rule-of-thumb behaviour?

Dimitris Hatzinikolaou

The Flinders Uni

ersity of South Australia, School of Economics, GPO Box 2100, Adelaide,

SA 5001, Australia

Accepted 9 December 1998

Abstract

A number of authors have recently estimated the percentage of aggregate consumption
accounted for by consumers who simply consume their current income in each period
instead of behaving according to the permanent-income-rational-expectations hypothesis.
The magnitude of this percentage has important policy implications. The existing models,
however, incorporate approximations that may destroy the consistency of its estimates. The
paper considers a model that does not share this problem. Using Greek annual aggregate
data, 1960

]1993, the model produces estimates of this percentage that are lower than those

produced by the existing models. Utility-loss calculations suggest that the differences may be
important.

JEL classifications: E21; E62; H31

Keywords: Life cycle permanent income hypothesis; Rational expectations; Rule-of-thumb consumption;

Greece

1. Introduction

A major policy implication of the life-cycle-permanent-income hypothesis under

rational expectations LC-PIH-RE , as formulated by Hall 1978 , is that short-run

fiscal policy designed to influence private consumption e.g. a temporary tax cut is

Current address: University of Ioannina, Department of Economics, PO Box 1186, 45110 Ioannina,

Greece. Tel.:

q30 651 97336; fax: q30 651 97340. Permanent address. Tel.: q61 8 8201 2987; fax: q61

8 8201 5071; e-mail: dimitris.hatzinikolaou@flinders.edu.au

0264-9993

9 9 9 3 9 8 0 0 0 4 4 - 3

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rEconomic Modelling 16 1999 293᎐306

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doomed to failure. The importance of this implication has stimulated a large
number of authors to test empirically the LC-PIH-RE. Most tests reject Hall’s
formulation, however, and a new literature has emerged in an attempt to find a
modification of the LC-PIH-RE that is compatible with the data.

A branch of this literature abandons the representative-consumer assumption

and argues that the population actually consists of two groups of consumers: the
life-cyclers, who maximize their expected lifetime utility subject to their expected
life-time resources, and the ‘rule-of-thumbers’, who simply consume their current
income. Rule-of-thumb behaviour can be explained partly by the presence of
liquidity constraints and partly by ‘myopia’, i.e. the failure of some consumers to
form rational expectations about their future income and make optimal choices. A

number of studies Campbell and Mankiw, 1989, 1990, 1991; Jappelli and Pagano,

1989; Vaidyanathan, 1993 have recently focused on the estimation of the ‘excess-
sensitivity parameter’, which might be interpreted as the percentage of aggregate
consumption accounted for by the rule-of-thumbers and is an indicator of the
degree to which the LC-PIH-RE is incompatible with the data. Thus, the closer
this percentage is to unity the greater is the empirical failure of the LC-PIH-RE
and the greater is the scope for short-run countercyclical fiscal policy designed to
influence private consumption, the largest component of aggregate demand. The
empirical models used in these studies are modified Euler equations for consump-
tion that attempt to capture the behaviour of both groups of consumers. These
models, however, incorporate approximations that might destroy the consistency of

the estimates for the sake of simplicity. But, as Deaton 1992, p. 177 notes, ‘no
amount of mathematical convenience can compensate for the loss of substance’.

After reviewing the existing models, this paper considers an alternative model

that is highly non-linear, but avoids using unnecessary approximations. Using
Greek annual aggregate data, 1960

᎐1993, it obtains estimates of the excess

sensitivity parameter from all models and finds that the estimates produced by the
alternative model are lower than those produced by the existing models. Utility-loss
calculations suggest that the differences may be important.

A motivation for the paper is the tightening of the non-interest terms of

consumer credit by the Bank of Greece in 1996 OECD, 1996, pp. 47, 112 .
Consumer credit in Greece had been restricted until early 1994, when it was
virtually liberalised, a policy that led to a rapid growth of consumer loans, e.g.

64.6% in 1994 Bank of Greece, 1995, p. 115 . In addition to curbing inflation, the
recent tightening aims at preventing consumers from becoming ‘overindebted’
Ž

Ethnos, 1996 , which implies that the proportion of ‘myopic’ consumers may be

significant.

2. Basic definitions

To fix ideas, begin by defining the basic variables. First, let N , N , and N be

1 t

2 t

the numbers of life-cycle, of rule-of-thumb, and of all workers in the economy,

respectively N

s N q N . Second, let C , C , and C be life-cycle, rule-of-

1 t

2 t

1 t

2 t

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D. Hatzinikolaou

rEconomic Modelling 16 1999 293᎐306

295

thumb, and aggregate consumption C

s C q C . Third, let C s C rN ,

1 t

2 t

1 t

s C

rN , and C s C

rN be life-cycle, rule-of-thumb, and aggregate con-

2 t

sumption per worker. Thus, the identity C

s C

q C

can be written in per-worker

1 t

2 t

terms as C

s 1 y

␭ C q ␭C , where ␭ s N rN assumed to be constant over

1 t

2 t

time . Finally, let Y

and Y

be rule-of-thumb and aggregate disposable income.

2 t

In per-worker terms, let Y

s Y

rN and Y s Y

rN . By the definition of

2 t

rule-of-thumb consumption, we have C

s Y . In this paper, we assume that

2 t

disposable income per rule-of-thumb worker equals aggregate disposable income
per worker, i.e. Y

s Y , so that C s Y . This holds if the fraction of aggregate

2 t

disposable income that accrues to the rule-of-thumbers is exactly equal to

␭, i.e. if

␭Y

2 t

3. Previous models

Assuming quadratic separable preferences and constant real interest rates,

Jappelli and Pagano 1989 derive the following modified Euler equation, which
allows for rule-of-thumb behaviour:

Ž .

s a q a C

␭ Y y a Y

q e .

1 t

They estimate

␭ for each of the seven countries in their sample by using aggregate

data and by applying non-linear instrumental variables NLIV as well as full-infor-

mation maximum likelihood FIML . As instruments, they use a linear trend and
the first lag of consumption, of disposable income, of government expenditure, and
of exports. However, using the le

els of these variables, which may be non-sta-

tionary; lagging them only once; assuming that preferences are separable in
consumption and other goods; and that the real interest rate is constant may
destroy the consistency and the asymptotic normality of the estimates.

Ž .

Adding and subtracting the quantity C

␭Y

to Eq. 1 and then rearrang-

.Ž

ing gives

⌬C s a q a y 1 C

␭Y

␭⌬Y q e , where ⌬ is the differ-

Ž .

ence operator, e.g.

⌬C s C y C . This equation is equivalent to Eq. 1 . Note,

however, that if C and Y are cointegrated unit-root processes, then it is a

non-linear error correction model ECM . By letting u be the residual from the

regression of C on a constant and on Y

the cointegrating regression ,

␭ can be

estimated by applying linear instrumental variables LIV to the following equa-
tion, using as instruments stationary variables lagged at least twice:

Ž .

⌬C s b q b u

␭⌬Y q e .

Using aggregate data for 59 countries, Vaidyanathan 1993 estimates

␭ using Eq.

Ž .

2 as well as restricted and unrestricted versions of Eq. 1 .

Campbell and Mankiw 1991 , among others, also assume that C

s Y , thus assuming Y s Y .

2 t

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Since consumption and income seem to evolve as log-linear rather than as

linear stochastic processes and since it is desirable to allow for variable real

interest rates, Campbell and Mankiw 1989, 1990, 1991 prefer the model

Ž .

⌬log C s

␮ q ␪ log 1 q r q ␭⌬log Y q ⑀ ,

where r is a real interest rate and

␪ is the elasticity of intertemporal substitution.

Using aggregate data for a group of industrialised countries, they estimate variants
of this equation using LIV, emphasising that the instruments must be stationary

Ž .

variables lagged at least twice. Eq. 3 is a modification of the log-linearised Euler
equation that is derived by assuming separable preferences represented by a

standard constant-relative-risk-aversion

CRRA utility function. In their 1990

paper, which uses US data only, Campbell and Mankiw allow for non-separable

preferences by replacing log 1

q r with ⌬log X , where X s labour supply, or

government expenditure, or stock of consumer durables. These experiments con-

Ž .

firm their earlier conclusion, however, that their simple model, i.e. Eq. 3 , ‘will be
hard to beat as a description of the aggregate data on consumption, income, and

interest rates’ Campbell and Mankiw, 1989, p. 212 .

Despite its popularity, the log-linearisation of a Euler equation may not be an

innocuous transformation, however, because it will destroy the consistency of the

estimates if the untransformed Euler equation is the correct model Gallant, 1987,

p. 427 . Also, it requires the restrictive assumption that C and r be jointly

conditionally lognormal and homoskedastic see Deaton, 1992, p. 64 . Finally, as

Campbell and Mankiw 1991, p. 729 note, the interpretation of

␭ as the fraction of

rule-of-thumb consumers is not exact in their log-linear model.

4. An alternative model

Consider a life-cycler whose one-period utility function is

␥

␣

␤

␣y␤

Ž .

s C L G

y 1 r

␥ , ␥ / 0,

1 t

where L

s leisure per worker and G s government expenditure per worker,

assumed to be exogenous and to take on the same values for both groups of

consumers so there is no need to distinguish between L

and L , for example .

1 t

2 t

The assumption of exogeneity of L is based on the empirical observation that

hours of work are determined institutionally see Hatzinikolaou and Ahking, 1995,

Ž .

p. 1118 . The utility function 4 has already been used in the literature e.g.

Hatzinikolaou and Ahking, 1995 . It has the following characteristics. First, it
implies that the consumer considers a geometric weighted average of C , L, and G,

with weights

␣, ␤, and 1 y ␣ y ␤. Second, it reduces to other utility functions by

placing various restrictions on its parameters. For example, if

␥ s 0, it reduces to

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logarithmic utility; and if

␣ s 1 and ␤ s 0, it reduces to the standard CRRA

utility function, which has been widely used in the empirical literature see, e.g.
Mankiw, 1981; Hansen and Singleton, 1982; Campbell and Mankiw, 1989, 1990,

1991 . Third, if

␣ ) 0, ␤ ) 0, and 1 y ␣ y ␤ ) 0, it is strictly increasing in C , L,

and G non-satiation ; and if

␣ ) 0 and 1 y ␣␥ ) 0, it is strictly concave in the

choice variable C . Fourth, if

␥ ) 0 ␥ - 0 , in addition to the non-satiation

restrictions, it implies that C , L, and G are pairwise Edgeworth complements

substitutes . Finally, it leads to an estimating equation whose variables are likely

to be stationary, an empirically attractive property.

Under time separability, the first-order condition Euler equation for consump-

tion is

q r

␣␥y1

␤␥

␣y␤ ␥

Ž .

s 1,

1 t

␦

where

␦ is a subjective discount rate ␦ ) 0 and E is a mathematical expectation

conditional on information available at the beginning of time t.

The following

steps lead to an estimating equation that allows for rule-of-thumb behaviour. First,
define l

s L rL , g

s G rG , y

s Y rY , and apc s C rY . Sec-

Ž .

ond, remove E from 5 , add a prediction error, e

, to its right-hand side, and

solve the resulting equation for C

to obtain C

s k

C , where k

is a

1 t

q1 1t

non-linear function of l

, g

, e

, and r . Third, multiply C

s k

1 t

q1 1t

␭ ; add the quantity k

␭ C y Y y ␭ C

y Y

, which is zero, since

2 t

s Y ; use C s 1 y

␭ C q ␭C and the definition of k ; and rearrange, to

2 t

1 t

2 t

obtain

q r

␣␥y1 ␤␥

Ž1

␣y␤ .␥

Ž .

apc

␭ r apc y ␭

y 1 s e

q1 tq1

␦

Ž .

The variants of Eq. 3 considered by Campbell and Mankiw 1990 should, in

Ž .

principle, be special cases of the log-linearised version of 6 that uses log 1

q e

f e . However, again, the meaning of

␭ in these variants is different. To see

why, consider Eq.

of Campbell and Mankiw

1991 , which in fact uses

Ž1

␭. ␭

s C

instead of using C

s 1 y

␭ C q ␭Y .

1 t

5. Econometric methodology

Ž . Ž .

Ž .

Eqs. 1

᎐ 3 and 6 are estimated by the generalised method of moments

GMM , which exploits the orthogonality conditions between the error term and

Two goods are Edgeworth complements substitutes if the marginal utility of one increases decreases

as the quantity consumed of the other increases.

Ž .

Setting up the problem completely and interpreting Eq. 5 is a standard exercise see, e.g. Hatzinikolaou

and Ahking, 1995 . Assuming Ricardian equivalence and applying Hall’s, 1978, p. 986 perturbation

Ž .

argument, Eqs. 5 and 6 are derived in an appendix, which is available upon request. A non-Ricardian
model leads to the same Euler equation.

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298

the variables in the information set. The results are then evaluated by constructing
several specification tests. The methods are briefly described here by referring to

Ž .

Eq. 6 .

Let

␪ be a K = 1 parameter vector and z an M = 1 vector of instruments. For

Ž .

Eq. 6 ,

␪ s

␣, ␤, ␥, ␦, ␭ . Under the joint hypothesis of rational expectations

and of a correctly specified model, the error term e

has zero mean, is serially

uncorrelated, and is uncorrelated with any information known at the beginning of
time t, when expectations are formed. Thus, permissible instruments are relevant

variables dated t

q 1 y h, where h G 2. See also Hall, 1988, p. 348; and Campbell

and Mankiw, 1990, p. 268. The joint hypothesis implies the orthogonality condi-

Ž .

tions E z

s 0 whose sample counterpart is denoted here by g ␪ s

q1yh tq1

rT ⌺

, where T is the number of observations that are available for

sh tq1yh tq1

estimation after the construction of growth rates and of lagged variables. Assuming

that M

G K a necessary condition for identification , estimation of ␪ and testing

Ž .

of the joint hypothesis are based on g

␪ . In particular, GMM chooses ␪ to

Ž .

minimize the quadratic form q

␪ s g ␪ S g ␪ , where S is an M = M symmet-

ric weighting matrix. In order to achieve positive semidefiniteness of the matrix S

and to obtain autocorrelation-consistent standard errors, the definition of S is that

of Newey and West 1987, 1994 , which sets the value of the ‘lag truncation

w Ž

w x

parameter’ equal to 4 T

r100

, where ‘ . ’ means ‘integer part of’.

The instrument vector used here is z

s constant, c

, l

, g

q1yh

, w

, where c

s C rC is one plus the rate of growth in

q1yh

consumption, w

s W rW is one plus the rate of growth in a real wage, and

is an ex-post real interest rate. Tauchen 1986 and Davidson and MacKinnon
Ž

1993, pp. 222 and 604 point out that in small samples efficiency gains from using

more instruments are obtained at the cost of a greater bias in the estimates. In the
light of this result, the values of h and M are chosen to be as small as possible so
as to ensure parameter identification while minimizing the bias. Thus, for Eqs.
Ž . Ž .

Ž .

᎐ 3 , the choice h s 2 is used so M s 7 and T s 31 ; whereas for Eq. 6 , the

choices h

s 2, 3 so M s 13 and T s 30 and h s 2, 3, 4 so M s 19 and T s 29

are also used, since choosing h

s 2 does not lead to statistically significant

estimates. The value of the ‘lag truncation parameter’ is set equal to 3, since

w Ž

4 30

r100

s 3.

To evaluate the models statistically, the following tests are carried out. First, the

hypothesis that e

is serially uncorrelated is tested against the alternative

hypothesis of ith order serial correlation by estimating Gauss-Newton regressions

and by calculating the values of an F-statistic, denoted by F

see Davidson and

ARi

Ž .

As an example, here is how F

for Eq. 6 is constructed. Let R be the series of the GMM residuals;

AR 2

R1 and R2 be the first two lags of R, where the lost observations are set to zero so the series R1 and

R2 also have T observations ; R1H and R2H be the fitted values from the ordinary least squares OLS
regressions of R1 and R2 on the instruments z; and XDH, XAH, XBH, XGH, and XLAH be the fitted

Ž .

values from the OLS regressions of the derivatives of the non-linear part of 6 with respect to

␪

evaluated at

␪ on z. The statistic F

is calculated as the F-test for the hypothesis that the

AR 2

coefficients of R1H and R2H in the OLS regression of R against XDH, XAH, XBH, XGH, XLAH,

R1H, and R2H without a constant are zero.

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MacKinnon 1993, Sections 7.7 and 10.10 . Note that when h

s 2 M s 7 is

chosen and the value of F

is significant, then the validity of the instruments is

AR2

questionable, since the error term may be correlated with the instruments. For the

Ž .

same reason, when Eq. 6 is estimated with h

s 2, 3 M s 13 the statistic F

AR3

used as an additional test; and when it is estimated with h

s 2, 3, 4 M s 19 the

statistics F

and F

are also used. Second, the validity of the instruments is

AR3

AR4

checked by regressing the GMM residuals against the instruments and by calculat-

ing the adjusted R , denoted by R

, and the marginal level of significance or

⭈z

p-value of the F-statistic for the hypothesis that all the slope coefficients in these
regressions are zero. Third, since M

) K, the joint hypothesis is tested by using the

well-known test of overidentifying restrictions, also an instrument-validity test.

Ž .

The relevant statistic is defined as J

s T = q ␪ and is asymptotically distributed

␹

. Newey 1985 shows, however, that the statistic J often fails to reject a

y K

misspecified model, because it has little power against some local alternatives, so it
can lead to the acceptance of GMM estimates that are in fact inconsistent. In

particular, it may easily fail to detect parameter instability Newey, 1985, pp.

239

᎐240 .

Thus, as a fourth test, a likelihood-ratio LR type statistic is constructed to test

the hypothesis of structural stability. The test is discussed in Ghysels and Hall
Ž

Ž .

1990, pp. 127

᎐128 and can be implemented as follows. Again, refer to Eq. 6 , but

Ž . Ž .

Ž .

note that Eqs. 1

᎐ 3 must be written in the form of 6 , i.e. with the error term as

the only variable on the right-hand side, before applying the test to them. Suppose
that we want to test for a structural break in period t . Let D be a dummy variable

defined as D

s 0 for t - t and D s 1 for t G t . Also, let T and T denote the

number of observations available for estimation in the first and in the second

subsample T

q T s T . Parameter instability, if any, is assumed to occur in the

Ž .

second subsample. First, use the instrument vector z to estimate 6 with the first
T observations only and let J be the value of the statistic J obtained from this

Ž .

estimation. Second, construct two equations, one by multiplying Eq.

.Ž

rT 1 y D and the other by multiplying it by T rT D , and use z to estimate

them as a system. Let J

be the value of J from this estimation. The statistic

s J y J is asymptotically distributed as

␹

and can be used to test for

t 0

structural stability. All estimates and tests are derived using the econometric
computer programme RATS, version 4.2.

6. The data

The sources of the data are given in Appendix A. The empirical definitions of

the variables are as follows. First, C

s national private consumption expenditure

on non-durables, services, and semidurable goods, divided by the consumer price

Note that testing for a zero-mean error term in each equation is part of the test of overidentifying

restrictions, since the instrument set includes a constant.

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D. Hatzinikolaou

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300

index CPI and by total employment N . Second, leisure per worker is measured
as L

s 5840 y 50 = HR , where HR s hours of work per week in manufacturing,

assuming that the time endowment per worker per year is 5840

s 365 = 16 hours

and that the average worker works 50 weeks per year. Third, G

s central govern-

ment expenditure, excluding payments for amortization and interest on the public
debt, social security,

and transfers to the rest of the world, divided by CPI and by

N. Fourth, Y

s income of households, including private non-financial unincor-

porated enterprises, less direct taxes and social-security contributions, divided by
CPI and by N. Fifth, W

s weighted average compensation per hour of male and

female wage earners in all manufacturing firms employing 10 or more persons,

Ž .

deflated by CPI. Sixth, the ex-post real interest rate

is the rate offered by

commercial banks for 3

᎐12 month demand, time, and regular savings deposits in

Ž .

drachmas less the CPI inflation rate

␲ . Seventh, the ex-ante real interest rate r

is the nominal interest rate just defined less expected inflation

␲ .

A series for

␲

is constructed recursively by regressing

␲ on lagged variables

e.g. the rate of growth in money supply, in labour productivity, in the US

dollar

᎐drachma exchange rate, and in import prices in US$ and by taking

one-step-ahead forecasts.

To produce each value of

␲

, the sample is updated and

also possibly the regressor set, so that the forecasting regression fits the data well
and passes a series of diagnostic tests at the 5% level of significance. The series

␲

fails one test of rationality at the 5% level, namely the forecast error

␲ y ␲

fails to be a white-noise process, but passes that test at the 1% level and passes all

other tests of rationality at the 5% level see Lovell, 1986 .

Finally, reliable data on N are available only for 1961 census year and from

1966 onward. The values of N for 1960 and 1962

᎐1965 are obtained by regressing

⌬ N on a constant and on emigration, using data for the period 1966᎐1989. This

regression assumes that the massive emigration from Greece in the 1960s was the
reason for the negative trend in N in that decade.

A possible structural break might have occurred in 1981, when the socialists won

a national election. Since the share of central government expenditure in GDP
grew from approximately 23% in 1980 to approximately 46% in 1993 and since

Ž . Ž .

government expenditure is absent from Eqs. 1

᎐ 3 , a structural-stability test is

carried out by choosing t

s 1981.

7. Results

Ž . Ž .

Table 1 reports the results from the estimation and testing of Eqs. 1

᎐ 3 and

Ž .

6 . Each column reports parameter estimates, their t-ratios, an estimate of loss of

Social security benefits are excluded from the definition of government spending in order to avoid

Ž .

double counting in 4 . If they are included, the empirical results remain virtually unchanged, however.

Most studies either assume that the real interest rate is constant, e.g. Hall 1978 , or use an ex-post

real interest rate, e.g. Mankiw 1981 . An exception is Hall 1988 , which uses an ex-ante real rate.

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Table 1

Ž . Ž .

Ž .

GMM estimation of Eqs. 1

᎐ 3 and 6 ᎏ unrestricted and restricted

Ž .

Equation

Restrictions None

None

␣ s 1, ␤ s 0

␭ s 0

UUU

␣

᎐

0.29

0.38

0.26

᎐

0.37

0.59

1.66

2.60

2.20

UUU

␤

᎐

0.52

0.47

0.57

᎐

0.48

0.62

1.63

5.30

2.46

UUU

␥

᎐

0.94

1.03

1.62

0.52

1.18

0.40

1.47

3.37

4.04

2.18

␦

᎐

y0.006 y0.001

0.006

y0.006

0.001

y0.42

y0.15

2.06

y1.08

0.16

UUU

␭

0.39

0.52

0.71

0.34

0.27

0.19

0.36

᎐

3.91

4.50

7.33

1.21

1.96

2.89

3.26

Utility loss

0.12

0.28

30.71

0.09

0.07

0.05

0.10

᎐

0.80

0.82

0.63

0.25

0.50

0.88

0.28

0.43

AR 1

0.82

0.63

0.86

0.29

0.80

0.98

0.54

0.71

AR 2

᎐

0.84

0.70

0.68

0.82

AR 3

y0.17

y0.16

y0.22

y0.12

y0.41

y0.94

y0.34

y0.41

e . z

0.94

0.92

0.99

0.82

0.98

0.99

0.95

0.98

0.55

0.31

0.96

0.19

0.84

0.93

0.91

0.83

0.42

0.53

0.71

0.64

0.49

0.69

0.39

0.43

1981

Note.

UUU

significant at the 1% level;

significant at the 5% level;

significant at the 10% level. The

numbers in parentheses are t-ratios; those in brackets are p-values.

utility if a consumer behaves as a rule-of-thumber rather than as a life-cycler see

the next section , and information on the diagnostic tests. Since the focus of the
paper is the magnitude of the parameter

␭, the table does not report estimates of

Ž . Ž .

the other parameters of Eqs. 1

᎐ 3 , but reports estimates of all of the parameters

Ž .

of Eq. 6 , since the latter is under evaluation.

Before discussing the results, the following comments are in order. First, given

the small size of the sample, it is difficult to test the stationarity assumption
Ž

Ž . Ž .

Ž .

required by GMM . For the variables of Eqs. 2 , 3 and 6 , stationarity seems to

be defensible, however. In particular, the variables used for the estimation of Eq.
Ž .

6 have no obvious trends and the unit-root hypothesis can be rejected at the 5%

level for c, l, g, y, w, r, and

, though only at the 10% level for apc.

Second, the

The unit-root hypothesis for the variables c, l, g, y, and w is tested with augmented Dickey-Fuller

tests. These tests also suggest that the variables c, g, y, and w may have a mild negative trend. For r
and

, that hypothesis is tested by regressing each variable on its first lag only and by using the critical

values of the top part of Fuller’s Table 8.5.2 Fuller, 1976, p. 373 . A constant and a time trend are not
significant, but in the case of

, unless they are excluded the hypothesis cannot be rejected. Finally, in

the case of apc, a constant is included, so a critical value is obtained from the middle part of Fuller’s
table.

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D. Hatzinikolaou

rEconomic Modelling 16 1999 293᎐306

302

tests on the parameters assume that each estimate is a random drawing from a
normal distribution, but for non-linear models and for small samples convergence
to the normal distribution may be problematic.

The basic results can be summarized as follows. First, the four models perform

reasonably well, since parameter estimates lie in the expected range

and the

diagnostic tests provide no evidence of misspecification for any of the equations.

Ž .

Note, in particular, that the estimates of the parameters of Eq. 6 , unrestricted as
well as restricted, satisfy the non-satiation and concavity restrictions and suggest
that consumption, leisure, and government expenditure are Edgeworth comple-
ments. Second, unless we impose restrictions on the parameters, choosing M

s 7

Ž .

for Eq. 6 causes an identification problem, reflected in the failure of all of its
estimates to be statistically significant. Also, choosing M

s 13 leads to estimates of

␣ and ␤ that are significant only at the 10% level.

Without imposing any

restrictions, only when M

s 19 are all estimates significant at the 5% level. Third,

whenever statistically significant and unrestricted, the estimates of

␭ obtained from

Ž .

Eq. 6 range from 0.19 to 0.27, so they are lower than those obtained from Eqs.
Ž . Ž .

᎐ 3 , which range from 0.39 to 0.71, and those reported by Jappelli and Pagano

1989 , 0.54 NLIV and 0.60 FIML .

Based on the information of Table 1, however, it is not possible to decide which

estimate of

␭ is more reliable; and further testing does not lead to conclusive

evidence, either. The following observations might be suggestive, however. First, as

Ž .

the last column of Table 1 shows, when the restriction

␭ s 0 is imposed on Eq. 6 ,

the diagnostic tests do not provide evidence of misspecification, which suggests that
the value of

␭ may be low. Non-rejection of the model might simply reflect the low

power of the tests, however, a consequence of the small sample size. Second, the

Ž .

coefficient of log 1

q r in Eq. 3 ,

␪ s 0.20, has a t-ratio of 2.34. In addition, if r

Ž .

is treated as constant in Eq. 6 , there is evidence of misspecification. Thus,

Ž .

treating r as a constant in Eqs. 1 and 2 might cause the estimates to be

inconsistent. Treating it as a variable in these equations has little effect on the

Ž .

results, however. Third, the results from Eq. 6 provide some evidence that the

Ž .

In the case of the unrestricted Eq. 6 , the estimate of

␦ is negative when M s 7 and when M s 13,

but is statistically insignificant. When M

s 19, it has the correct sign positive and is significant.

Note the following results, which are not reported in Table 1. First, although the data provide some

Ž .

evidence that C and Y are cointegrated, the error-correcting term in Eq. 2 fails to be statistically
significant. Second, the possibility of a structural break in 1974 was also considered for the reasons

explained in Hatzinikolaou and Ahking 1995, footnote 10 ; but, again, no evidence of structural

Ž .

instability was found for any of the equations. Third, when Eq. 6 is estimated with M

s 19, the

p-value of the statistic F

is 0.49.

AR 4

Note that

␣, ␤, and ␭ are expected to be positive. Thus, for example, a t-ratio of 1.66 for the

hypothesis H :

␣ s 0, is significant at the 10% level, since the alternative hypothesis is H : ␣ ) 0. Note

also that it is possible to obtain estimates that are significant at the 5% level when M

s 13 by imposing

restrictions that are supported by the data, e.g.

␤ s 2␣.

Using consumption expenditure which includes spending on durable goods , Vaidyanathan 1993

produces several estimates of

␭, claims that they are similar, and reports the one that has the smallest

standard error, without making clear which model generates it. For Greece, that estimate is 0.36.

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D. Hatzinikolaou

rEconomic Modelling 16 1999 293᎐306

303

variables L and G may be important,

so excluding them might lead to inconsis-

Ž .

tent estimates. When these two variables are excluded from Eq. 6 , by imposing
the restrictions

␣ s 1 and ␤ s 0, there is still no strong evidence of misspecifica-

tion, but the estimates of

␭ are larger than in the unrestricted regressions. In

particular, when M

s 13, we get

␭ s 0.36 see the second-to-last column of Table

1 ; and when M

s 7, we get

␭ s 0.49 with a t-ratio of 5.58 this regression is not

reported in the table because it produces insignificant estimates of

␥ and ␦ . This

finding casts some doubt on the reliability of high estimates of

␭. In addition,

Ž .

despite the significance of L and G in Eq. 6 , the variables

⌬log L and ⌬log G

Ž .

are insignificant in Eq. 3 ; and their presence causes the estimate of

␭ to be

somewhat lower, namely 0.64. This finding suggests that the log-linearisation of the
Euler equation might not be an innocuous transformation.

Finally, note that a low estimate of the percentage of rule-of-thumb consumers is

consistent with the high net household saving rate in Greece relative to other

OECD countries as well as with the possibility to borrow from relatives thanks to

strong family ties , which reduces the severity of liquidity constraints for many
consumers.

8. Utility loss of rule-of-thumb behaviour

Do the differences in the estimates of

␭ matter? If yes, then the choice of model

becomes crucial. An answer can be derived from utility-loss calculations.

Fol-

lowing Campbell and Mankiw 1991, pp. 747

᎐749 , it is possible to measure

approximately the utility loss to a rule-of-thumber, who chooses C

s Y in each

2 t

period instead of choosing the optimal level of consumption, C

, the level chosen

by a life-cycler i.e. C

s C . The monetary value of the loss in each period,

1 t

expressed as a percentage of C

, is approximately given by

y C

2 t

Ž .

␳

where

␳ s yu C

ru , u s

⭸ ur⭸ C , and u s ⭸

⭸ C

, which are evalu-

C C

2 t

C C

2 t

ated at C . As was shown earlier, C

s 1 y

␭ C q ␭C ; and since C s C and

1 t

2 t

1 t

..Ž

s Y , it follows that C s 1r 1 y

␭ C y ␭Y and C y C rC s 1 y

2 t

. Ž

Ž .

apc

r apc y

␭ . Thus, the sample counterpart of the quantity in 7 is

1 1

y apc

Ž .

␳

2 T

apc

␭

The hypothesis H :

␤ s 0 can be rejected in three out of four regressions; whereas the hypothesis

H : 1

␣ y ␤ s 0 can be rejected only when M s 19, in which case the p-value of the Wald test is

0.0008.

I am grateful to an anonymous referee for making this suggestion.

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)

D. Hatzinikolaou

rEconomic Modelling 16 1999 293᎐306

304

If the utility function is quadratic then

␳ depends on the level of ‘bliss

consumption’, which may be difficult to estimate, see Cochrane 1989, pp. 327

᎐328 .

Ž .

Alternatively, if utility is given by Eq. 4 , then

␳ s 1 y ␣␥. Thus, using the

˜˜

estimates

␣ s 0.26 and ␥ s 1.62, we get ␳ s 0.58.

Ž .

The utility-loss calculations reported in Table 1 are derived from quantity 8

␳ s 0.58 using and the various values of ␭. Note that this measure of loss of utility

corresponds to measure L of Campbell and Mankiw 1991 , but avoids using the

approximations used in the last line of their Eq. 22 . Also, note that it is an

increasing function of

␭, since apc ) ␭ for all values of t and of ␭ considered

here. Thus, although the loss of utility is small for the estimates of

␭ generated by

the alternative model e.g. only 0.05% of optimal consumption when

␭ s 0.19 , it is

significant for some of the estimates of

␭ obtained from the other models. In

particular, for

␭ s 0.71 the loss is almost 31%, which is a serious loss of utility.

9. Summary and conclusion

The focus of the paper has been the estimation of the percentage of rule-of-

thumb consumers-workers using Greek aggregate data and four different models,
three of which already exist in the literature. For Greece, the existing estimates of
this percentage range from 0.36 to 0.60. The existing models incorporate approxi-
mations that might destroy the consistency of the estimates, however. The paper
considers an alternative model that avoids using unnecessary approximations.
Here, the estimates of this percentage obtained from the existing models range
from 0.39 to 0.71; whereas those from the unrestricted alternative model, whenever
they are statistically significant, are lower, ranging from 0.19 to 0.27. The paper
does not produce conclusive empirical support for the alternative model, but
provides reasons why its estimates may be more reliable.

Different estimates of the percentage of rule-of-thumb consumers lead, of

course, to different policy conclusions. For example, temporary tax cuts will be
much less effective in stimulating consumption if this percentage is only 0.19 than
if it is 0.71. As another example, the recent tightening of consumer credit in
Greece, which is expected to raise this percentage, may cause only a small decline
in utility if the tightening raises it from 0.20 to 0.30, but may cause a serious
decline in utility if it raises it to 0.70.

Acknowledgements

I am grateful to two anonymous referees of this journal and to my colleague

Peter Wagstaff for their comments and suggestions, which improved the paper
significantly. The usual disclaimer applies.

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D. Hatzinikolaou

rEconomic Modelling 16 1999 293᎐306

305

Appendix A: Data sources

The data are available from the author upon request. Their sources are as

follows: household income, direct taxes, social security contributions, consumption,

saving, government expenditure, transfers to the rest of the world OECD, Natio-

nal Accounts, vols. I and II ; CPI, GDP, interest rate, exchange rate, money supply,

import prices in US dollars International Financial Statistics, series 64, 99b, 60l,

ahx, 34, 75d ; total employment OECD, 1987, 1991, 1992, Report of the Governor

of the Bank of Greece, Statistical Yearbook of Greece ; emigration United

Nations, Demographic Yearbook ; hours of work, wage rate International Labor

Office, Yearbook of Labor Statistics ; interest payments on the public debt, price

level of imported machinery and transportation equipment in drachmas Bank of

Greece, 1992, Economic Bulletin of the Bank of Greece ; productivity of labour
Ž

Summers and Heston, 1991 .

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