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

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 consumption 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 intertemporal substitution is downward biased and that consumption growth exhibits excess sensitivity to labor income.