# INTERTEMPORAL CHOICE AND THE CROSS-SECTIONAL VARIANCE OF MARGINAL UTILITY: Introduction 2

The benefits are not cost-free, however. The test we propose is based on assumptions about the properties of the residuals of the Euler equation. A rejection of the null hypothesis could therefore be due to the failure of these assumptions, and not necessarily of the permanent income model. Furthermore, since we relax certainty equivalence, we cannot exploit the relation between consumption, income innovations and age. For instance, we cannot check if the increase in consumption inequality slows down around retirement, as implied by the certainty equivalence case. Nor can we attribute the spreading of consumption inequality to permanent and transitory changes in uncertainty, as is proposed by Blundell and Preston (1997).

We use average cohort data to test our hypothesis. In the absence of long panel data on consumption, these data are particularly well-suited to the problem at hand. Although we cannot compute the cross-sectional variance of the same group of individuals over time, average cohort data allow us to track the variance of a representative sample of the same cohort. Another advantage of cohort data is that they allow us to apply an appropriate instrumental variables estimator. in detail

The empirical analysis, presented in Section 3, uses three approximations to the marginal utility of consumption. Initially, we measure marginal utility as the log of expenditure on non-durable goods. We then take into account the life-cycle of family size and define marginal utility as the log of-non-durable consumption expenditure per adult equivalent. Finally, we compute marginal utility by relying on available estimates of the parameters of a flexible utility function. These parameters have been estimated with the same data sets used in this paper. Having estimated the marginal utility for each household in the sample, we can then compute the cross-sectional variance of marginal utility of population groups defined by year of birth and test whether the coefficient of lagged on current variance is unity. The advantage of the third procedure is that marginal utility is allowed to depend on a full set of demographic and labor supply variables.

We use three sets of cohort data. The British Family Expenditure Survey (1974-1993) and the US Consumer Expenditure Survey (1980-1992) cover a sufficiently long time span and allow consistent estimation of an Euler equation for consumption. We also use data drawn from the Italian Survey of Household Income and Wealth ( 1987-1993); since this is too short a time span to provide reliable estimates of the Euler equation, in this case we do not attempt to measure marginal utility by using a flexible utility function. Section 4 summarizes the results and relates them to the debate over welfare comparisons.