Macroelasticity vs. Individual Elasiticities: The Case of Consumption and Income

In this paper we assess the relationship between the aggregate income elasticity of aggregate demand and individual income elasticities of demand. We show that the aggregate elasticity is equal to the mean of individual elasticities plus a covariance term. Consequently, the sign of this covariance term determines whether the aggregate elasticity overestimates or underestimates the mean of individual elasticities. Predictions from economic theory with respect to the sign of this term depend crucially on the heterogeneity pattern of the population, which is unobservable. Therefore, in order to assess the sign and the magnitude of the covariance term we perform an empirical analysis based on the British Family Expenditure Survey (1974-1993). It turns out that the aggregate elasticity significantly overestimates the mean of individual elasticities for most commodity groups and for total expenditure.