Consumption of non-durables and durables

Economics Letters North-Holland

219

24 (1987) 219-222

CONSUMPTION OF NON-DURABLES An Empirical Note

AND

DURABLES

P. KUGLER

A. BOSSARD Uniuemty

Received

of Basel, CH-4051

Basel. Switzerland

26 May 1987

The empirical analysis of consumption in four European countries and the U.S.A. shows different autocorrelation patterns for non-durables and durables, which do not, however, correspond to the differences implied by the life cycle/permanent income model as formulated by Hall and Mankiw.

1. Introduction

Consumer expenditures on durables and non-durables are usually thought to evolve differently over the business cycle. This difference can be neatly characterized in the frame of the life cycle/permanent income model under rational expectations and some additional assumptions. As it was shown by Hall (1978), this theory predicts that non-durable consumption follows a first-order autoregressive [AR(l)] process describing a smooth adjustment of consumption to unexpected changes of income. By contrast, the extension of Hall’s model to durables by Mankiw (1982) results in a first-order autoregressive moving average [ARMA(l, l)] process for expenditures on durables, implying a sluggish adjustment pattern. The empirical tests of Hall and Mankiw, however, led to the surprising conclusion that the autocorrelation pattern of seasonally adjusted per capita U.S. consumption on non-durables and durables are very similar: both series can be reasonably well modelled as univariate AR(l) processes. The aim of this empirical note is to check whether this striking result obtained with U.S. data applies also for European countries, namely FRG, the U.K., France and Switzerland. For reasons of comparison this analysis is also carried out with U.S. data.

2. The model In the sequel the model is presented for consumption expenditures on durables. The case of non-durables is obtained in this framework by setting the depreciation rate equal to 1. It is assumed that the consumer maximizes the discounted utility provided by the services of the stock of durable goods subject to an intertemporal budget constraint. This proceeding results in the following 0165-1765/87/$3.50

0 1987, Elsevier Science Publishers

B.V. (North-Holland)

220

P. Kugler, A. Bossard / Consumptron

first-order

condition

linking

marginal

utility

of period

qf non-durahles and durahles

t + 1 and t:

EU’(K,,) = ++ U’(K,). U is the of period constant, If the following

strictly concave one-period utility function, E stands for expectations given the information t, S is the rate of time preference, i is the ex ante real rate of interest, assumed to be and K is the stock of durable goods. utility function is quadratic and expectations are rational in the sense of Muth (1961) the autoregressive equation is obtained for K,,,:

K 1+1 =q,+qKr+~,+1>

1+6 l+i’

a, = -

where u, + 1 is a non-autocorrelated random constant. Moreover, if 8 is the depreciation the following equation for K,,1: K (+I

=

error with expectation zero and a variance assumed to be rate of K and c is the expenditures on durables, we have

Cl- e>K,+ c,+I.

From (2) and (3) a first-order expenditures on durables:

c,+,=e(Yg+(Y,c,+u,+l-(l-B)u,.

(3) autoregressive

moving

average

process

is obtained

for

the

(4)

The case of non-durables is covered by restricting the depreciation rate (0) to 1. Then, c follows an AR(l)-process, which is a random walk when the ex ante real interest rate equals the time preference rate. The different implication of the model for durables can be emphasized by considering the benchmark assumption that (Y, is equal to 1 - 8. Under these circumstances the level of consumption expenditures on durables follows a white noise process [c,, , = (Ba,/(l - a,)) + u,, 1].

3. Estimation The consumption model outlined in the last section was estimated with quarterly seasonally adjusted data for per capita expenditures on consumer non-durables (including services) and durables, respectively. The sample period covers the years 196991983 (FRG, France), 1965-1983 (U.K., U.S.) and 1973-1983 (Switzerland). Details on the data series and their sources are available from the authors. Table 1 contains the estimated models for non-durables [AR(l)] and durables [ARMA(l, l)]. The LY,estimates for these models are very close to one. Indeed, calculation of the unit root ‘t’ tests do significance levels. ’ not reject the hypothesis (Y, = 1 at conventional The estimates of the ARMA(l, 1) model for durables exhibit for FRG, France and the U.S. a very small and statistically insignificant MA parameter. Thus, the data for FRG and France confirm the conclusion of Mankiw (obtained from U.S. data) that consumer expenditures on durables do not ’ This hypothesis can be tested by the usual t statistic, which, however, has to be compared to inflated critical values by Fuller (1976). Said and Dickey (1985) show that the tables of Fuller calculated for AR models are also appropriate for ARMA models.

P. Kugler, A. Bossard

Table 1 Estimation

of

/ Consumption

non-durables

221

and durables

results.

country FRG

Durables

Non-durables,

6’ = 1

a1

Q’22

R=

cTu

35.4

0.99

0.97

a1

t9

R=

4

15.7

1 .oo (0.020)

0.88 (0.11)

28.0

0.95

21 .o

(0.012) a

Q,,

h

U.K.

0.99 (0.012)

44.7

0.99

4.6

1.02 (0.061)

0.66 (0.12)

23.4

0.90

3.9

France

0.99 (0.007)

85.2

0.99

16.5

1 .Ol (0.017)

0.99 (0.12)

30.0

0.97

10.5

Switzerland

0.94 (0.061)

23.6

0.86

30.7

0.94 (0.063)

0.68 (0.11)

16.1

0.75

8.8

U.S.A.

0.99 (0.005)

28.2

0.99

14.7

1.02 (0.020)

0.97 (0.08)

49.0

0.96

20.4

a Estimated standard error. with m degrees h Ljung-Box (1978) statistic. Under the hypothesis of no autocorrelation Q,, is chi-square-distributed freedom. The critical value at the five percent significance level for m = 21 is 32.67 and for M = 22 is 33.92.

of

follow an ARMA(l,l) process. Our estimates suggest that per capita consumption of durables follows essentially a random walk, which is only appropriate, according to theory, for consumption of non-durables. The estimated MA coefficient is significantly different from zero in the British and Swiss case. However, the MA coefficient is rather small, implying an unreasonably high depreciation rate for durables. The two consumption series seem to differ only with respect to relative size of their innovation variance, which shows higher relative volatility for durables. To conclude from these results that per capita consumption of non-durables and durables have the same autocorrelation pattern is, however,

Table 2 Estimated

autocorrelation

functions

Country

for AC,

r2

‘3

r4

Q,x

f-5

Non-durahles

FRG U.K. France Switzerland U.S.A.

- 0.20 0.01 -0.36 ” -0.36 ’ 0.31 ‘I

0.33 rl 0.10 0.19 0.00 - 0.04

0.16 0.13 0.34 * - 0.01 0.16

0.04 ~ 0.06 PO.31 il 0.07 0.07

0.31 a1 0.07 0.31 ‘I 0.11 - 0.17

0.00 0.00 ~ 0.20 - 0.28 - 0.06

21.50 27.08 57.35 19.20 23.02

~ 0.22 0.30 il ~ 0.07 PO.39 il - 0.06

-0.07 - 0.07 0.14 0.12 0.22

0.29 a 0.22 -0.11 0.03 PO.11

-0.16 - 0.23 - 0.07 - 0.04 0.05

- 0.01 0.06 - 0.21 0.20 0.01

0.19 0.03 - 0.04 -0.14 - 0.01

17.12 20.81 12.33 14.62 15.96

Durahles

FRG U.K. France Switzerland U.S.A. ’ Significant

at the five percent

level.

‘I a * A

222

P. Kugler, A. Bossard / Consumption

of non-duruhles and durahles

premature. The Ljung-Box statistic indicates that some of the univariate time series models estimated so far are misspecified. In table 2 the estimated autocorrelation function of the first differences of the consumption series are presented. These estimates point to significant differences of the time series properties of consumption of non-durables and durables in all countries except Switzerland, where both series seem to follow the same MA(l) process. Some autocorrelation estimates as well as the Ljung-Boxstatistics for consumption of non-durables show significant autocorrelation of the first-differenced series. Thus, the life cycle/permanent income random-walk model has to be rejected for all countries considered. 2

4. Conclusion In this paper the time series properties of per capita consumption of non-durables and durables is analyzed using quarterly data covering five countries (FRG, the U.K., France, Switzerland and the U.S.A.). The direct estimation of the Hall AR(l) model for non-durables and the Mankiw ARMA(1, 1) model for durables leads to the conclusion that both time series follow an AR(l) process. However, this striking similarity of the two consumption aggregates is weakened when the estimated autocorrelation function of first-differenced series is considered. Our empirical results are in general at odds to the implications of the permanent income and rational expectation hypothesis. Of course, the rejection of the model can also be attributed to additional restrictions which were introduced in order to get a simple and testable hypothesis. These assumptions include (a) the constant ex ante real interest rate, (b) the additive separability of the utility function over time, non-durables, durables and leisure, (c) the quadratic approximation of the utility function, and (d) the absence of liquidity constraints. However, it should be noted that the relaxation of some of these assumptions were, with the expectation of Mankiw’s (1985) analysis of U.S. durables consumption, not very successful so far [Mankiw (1981), Bernanke (1985) Hall (1985). and Mankiw, Rotemberg and Summers (1985)].

References Bernanke, B.S.. 1985, AdJustment costs, durables and aggregate consumption. Journal of Monetary Economics 15, 41-68. Fuller. W.A., 1976, Introduction to statistical time series (Wiley. New York). Hall, R.E., 1978, Stochastic implications of the life cycle-permanent income hypothesis. theory and evidence, Journal of Political Economy 86, 971-987. Hall, R.E., 1985, Real interest rates and consumption, NBER working paper no. 1694. Kugler, P.. 1985, Autoregressive modelling of consumption, income. interest rate and inflation data: A multicountry study, Empirical Economics 10, 37-50. Ljung, G.M. and G.E.P. Box, 1978, On a measure of lack of fit in time series models, Biometrika 65. 297-303. Mankiw, N.G.. 1981. The permanent income hypothesis and real interest rates. Economics Letters 7. 3077311. Mankiw, N.G., 1982, Hall’s consumption hypothesis and durable goods, Journal of Monetary Economics 23, 2588274. Mankiw, N.G., 1985, Consumer durables and the real interest rate, Review of Economics and Statistics 67, 3533362. Mankiw, N.G., J.J. Rotemberg and L.H. Summers, 1985, Intemporal substitution in macroeconomics, Quarterly Journal of Economics 100, 223-251. Muellbauer, J., 1982, Surprises in the consumption function, Economic Journal. Conference Papers, 34-50. Muth, J.F., 1961. Rational expectations and the theory of price movements. Econometrica 29, 315-335. Said, ES. and D.A. Dickey, 1985, Hypothesis testing in ARIMA( p, 1, 9) models, Journal of the American Statistical Association 80. 369-374. * The same results were obtained

with multivariate

tests of the random

walk model with the same data [Kugler

(1985)]