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Estimation of Demand Systems Generated by the Gorman Polar Form; A Generalization of the S-Branch Utility Tree

Charles Blackorby
Richard Boyce
R. Robert Russell

Abstract

Many demand system specifications employed in empirical studies are generated by utility functions which belong to the class that is characterized in the dual by what we call the "Gorman polar form." This class has the attractive property that membership is equivalent to the satisfaction of necessary and sufficient conditions for aggregation across consumers. We characterize the class of (direct) preference orderings that is dual to the Gorman polar form; this class includes, as special cases, homotheticity, affine homotheticity, and homotheticity to minus infinity. We also specify and estimate a member of this class which generalizes previously estimated specifications of Gorman polar forms.Finally, employing a likelihood ratio test, we reject the hypothesis that preferences are described by the S-branch utility tree (or, of course, any of its special cases) and concomitantly reject the hypothesis of affine homotheticity of preferences.