Substitutability,Separability,and the Distributional Implications of Public Goods

Abstract

This article demonstrates that the methodology developed by Aaron and McGuire (1970) and Maital (1973, 1975) for estimating the distributional implications of public goods, which has been extensively used in empirical studies, is critically dependent on a mathematically convenient but conceptually questionable assumption that has often resulted in implausible incidence conclusions. Specifically, the Aaron-McGuire-Maital approach assumes no substitutability between private income and public goods, which is technically translated into additively separate utility functions. This article reviews the distributional implications of public goods in the light of a generalized formulation of preference indicators. The most important conclusion is that if the assumption of separability is relaxed, the usual smooth neoclassical utility functions will at worst imply no redistribution—but never a progressive (that is, pro-rich) incidence outcome. Moreover, under the generalized formulation, the critical role in deriving the benefit incidence results is played by the elasticity of substitution between private and public goods and not by the elasticity of marginal utility of income, the importance of which is contingent on the particular functional form employed in the analysis.