On the Aggregation of Euler Equations for Consumption in Simple Overlapping-Generations Models

Abstract

If consumers have finite lives, the aggregate consumption growth equation is affected by entries and exits (births and deaths). We use two- and three-period overlapping-generations (OLG) models to show that entries and exits produce a relationship between aggregate con- sumption growth and the interest rate that is fundamentally different from the individual Euler equation for consumption. If aggregate data are used to estimate an 'aggregate' Euler equation, under plausible assumptions we show that the estimate of the elasticity of intertem- poral substitution is downward biased and that consumption growth exhibits excess sensitivity to labour income. Since Hall's (1978) paper, the life-cycle model of consumption has been exten- sively tested using aggregated consumption data. The assumption of an infin- itely lived representative agent has been exploited to justify using National Accounts data to estimate the structural parameters of the model. The moment restrictions implied by the first-order conditions of the representative agent intertemporal optimization problem have been used to such a purpose. When the over-identifying restrictions implied by the model are tested, they are typ- ically rejected. Furthermore, expected consumption changes are often found to be correlated with expected income changes (Campbell and Mankiw 1989). This indicates either a violation of the hypothesis of rational behaviour or, more likely, a violation of one of the many other assumptions used to make the model empirically operative. Surprisingly enough, aggregation issues have not received much attention as an explanation of the empirical failure of the model. Elsewhere (Attanasio and Weber 1993) we have shown how various aspects of aggregation, ranging from the issue of nonlinearities to the impossibility of controlling for individual variables that are likely to affect marginal utility, can explain the rejection of the model estimated on aggregate time-series data. In this paper we focus on another source of aggregation bias: finite lives and the lack of complete markets. If consumers are identical and infinitely lived, the Euler equation for con- sumption aggregates trivially. However, in the presence of finite lives and heterogeneous consumers, even though the Euler equation relating periods t and t + 1 holds for each set of similar consumers alive in those periods, when we consider aggregate consumption we do not necessarily have an aggregate Euler equation.