Abstract
In the tradition of Afriat (Int Econ Rev 8:67–77, 1967), Diewert (Rev Econ Stud 40:419–425, 1973) and Varian (Econometrica 50:945–972, 1982), we provide a revealed preference characterisation of exact linear aggregation. This guarantees that aggregate demand can be written as a function of prices and aggregate income alone, while abstracting from income-distributional aspects. We also establish nonparametric conditions for individual consumption to be representable in terms of Gorman Polar Form preferences. Our results are simple and complement those of Gorman (1953, 1961). We illustrate the practical usefulness of our results by means of an empirical application to a Spanish balanced microdata panel. We find strong evidence against the existence of a limited set of representative agents, which in turn seems to empirically support the need for (macroeconomic) models using a continuum of heterogeneous agents.
Highlights
Many models in the theoretical and empirical literature on macroeconomics, international trade and industrial organisation assume, at least implicitly, that aggregate demand is invariant to changes in the income distribution over individual consumers and, that aggregate demand depends only on prices and aggregate income
Despite the fact that these households all satisfy the necessary condition (Gorman Polar Form preferences), and despite the very flexible nature of revealed preference tests, it seems that the additional restriction required for aggregation is too much: data cannot bear the weight of the theory required for exact linear aggregation
The conditions for the existence of such a distribution-independent aggregation have been argued to be demanding, it is fair to say that existing evidence is solely based on Gorman’s well-known exact linear aggregation results within a functionalderivative based framework
Summary
Many models in the theoretical and empirical literature on macroeconomics, international trade and industrial organisation assume, at least implicitly, that aggregate demand is invariant to changes in the income distribution over individual consumers and, that aggregate demand depends only on prices and aggregate income. Our second main result is that this rejection is primarily due to heterogeneity in the marginal utility of income To investigate this heterogeneity, we considered the possible partitioning of our sample of households into subsets for which exact linear aggregation holds. We use a slight adaptation of a method introduced by Crawford and Pendakur (2013) to define a partitioning that accounts for possibly unobserved household characteristics This method identifies the minimal number of subsets of households such that each individual subset is consistent with exact linear aggregation.
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