# INTERTEMPORAL CHOICE AND THE CROSS-SECTIONAL VARIANCE OF MARGINAL UTILITY: Introduction

One remarkable prediction of the permanent income hypothesis with certainty equivalence is that consumption inequality within a group of households with fixed membership should, on average and over long periods of time, increase with age. By this model, the change in individual consumption represents the annuity value of the revisions in labor income, which under rational expectations are unpredictable. Then, if income shocks are not perfectly correlated within the group, the cross-sectional variance of consumption will increase with age until retirement, i.e. until uncertainty is resolved. This prediction of the theory has recently been investigated by Deaton and Paxson (1994), who estimate the age-profile of the cross-sectional variance of consumption using average cohort data for the US, the UK and Taiwan and find that consumption inequality increases with age in all three countries. cash advance payday loans

If certainty equivalence is relaxed the permanent income hypothesis provides predictions about the marginal utility of consumption, not consumption itself. In particular, the model does not generate an explicit relation between age and consumption inequality or, for that matter, between consumption and income. We thus propose to focus directly on the Euler equation for consumption, and consider the time-series properties of the cross-sectional variance of an approximation of the marginal utility of consumption rather than consumption. Under the identifying assumptions discussed in Section 2, the theory implies that in a regression of the cross-sectional variance of the marginal utility of consumption on a constant and its own lag, the coefficient of the latter is unity. It is this hypothesis that we test in this paper. Our procedure allows us to specify quite flexible preferences without relying on certainty equivalence, does not impose assumptions about the relation between age, time and cohort effects in estimating the age-profile of the cross-sectional variance, and delivers a simple statistical test of a well-specified null hypothesis that allows us to apply standard inference tools.