Gorman revisited: nonparametric conditions for exact linear aggregation

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.