Cointegration of consumption and disposable income: evidence from twelve OECD countries.

• Author: Jin, Fuchun
• Position: Organization for Economic Cooperation and Development

1. Introduction

   One of the implications of the rational expectation-permanent income hypothesis is that consumption and disposable income are cointegrated. Campbell [3], using tests that are developed in Engle and Granger [7], concludes that this implication holds on the quarterly aggregate data of the U.S. He finds that although a Philips-Perron test could not reject the nonstationarity of the disposable income and consumption processes, an augmented Dickey-Fuller test rejects the existence of a unit root in the residuals obtained from the least square regression of disposable income on consumption. Campbell and Clarida [4] confirm those conclusions with the quarterly aggregate time series data of Canada.

   These tests, however, may yield different conclusions if they are applied to data from other countries. This is because the unit root tests in the literature have rather weak power when they are applied to individual time series of moderate length, particularly when the alternative is close to the null. Indeed, Attfield, Demery and Duck [1], using quarterly aggregate time series data of the U.K.,(1) find that Philips-Perron test strongly rejects (at the 1% level) the nonstationarity of the disposable income process. They also find no evidence (at even the 10% level) against a unit root in the residuals of the regression between disposable income and consumption with augmented Dickey-Fuller tests of 1 or 4 lags. Campbell and Clarida [4) indicate that, for the United Kingdom, the unit root hypothesis for the disposable income is rejected at the 5% level, and the hypothesis of no cointegration between consumption and disposable income can only be rejected at the 10% level.(2)

   The conflicting results documented in this literature reveal that empirical findings of nonstationarity of both consumption and disposable income, as well as cointegration between them, may simply be due to the weak power of the unit root tests that they are based upon. In this paper I use the national accounts data from twelve OECD countries to test the nonstationarity of consumption and disposable income as well as the cointegration of them that is implied by the RE-PIH. The econometric method used in this paper is based on the theory of testing unit roots with panel data developed by Levin and Lin [9]. The advantage of using panel data is that a substantial gain in the power of the test can be obtained, even with a moderate number of cross sections and time series observations.

   The findings of this paper confirm that consumption and disposable income are cointegrated. They also provide comparisons between the conclusions obtained using only individual time series data and those obtained using pooled data of time series and cross sections. Specifically, I find that residual based cointegration tests cannot reject the hypothesis that consumption and income are not cointegrated when performed on individual time series data of each country. Nevertheless, when the data are pooled as a panel with time series and cross sections, the evidence strongly rejects the hypothesis of no cointegration between consumption and disposable income.

   The rest of the paper is organized as follows. In section II, I briefly review the cointegration of consumption and disposable income as an implication of the RE-PIH. I also show that this cointegration relationship should hold regardless of whether some consumers are liquidity constrained. In section III, I briefly review the econometric methods of testing unit roots and cointegration with panel data. Data used in the paper are described in section IV. Empirical results are presented in section V. Section VI contains the results of Monte Carlo simulations for the finite sample distributions of the test statistics used in statistical inferences. The conclusion of the paper follows in section VII.

2. RE-PIH: Its Cointegration Implications

   The starting point of this paper is the consumption function under the rational expectation-permanent income hypothesis; i.e.,

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   where [C.sub.t], [W.sub.t], and [A.sub.t], are respectively, consumption, labor income and asset holding in period t. The real interest rate r is assumed to be a constant and equal to the consumer's subjective time discount rate. [E.sub.t], is the mathematical expectation conditional on all information available to the consumer in period t. [Beta] is the marginal propensity to consume for a unitary increase in the consumer's permanent income.

   Following Campbell [3], if the tth period consumption [C.sub.t] can be described by equation (1), it should be cointegrated with the tth period disposable income [Y.sub.t], which is equal to [W.sub.t] + [rA.sub.t-1]. This can be seen from the following,

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   If [Delta][W.sub.t+i] for i = 1, 2, ... are covariance stationary, then the right hand side of equation (2) should also be stationary since the coefficients [[1/(1 + r)].sup.] sum to 1/r. This implies that disposable income and consumption are cointegrated with cointegrating vector (1, - [Beta][(1 + r)/r]).

   In the special case when [Beta] = r/(1 + r), equation (2) has a straightforward economic interpretation. Under the RE-PIH, consumption equals the annuity value of permanent income. Saving forecasts declines in future labor income, because only when current income is high relative to permanent income will a rational consumer save.

   A similar result can be obtained if [Beta] = r/(i + r), and a fraction [lambda] of total disposable labor income in the economy accrues to liquidity constrained...