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

TLDR

Demand system specifications are often derived from utility functions belonging to a class defined by the polar form, which permits aggregation across consumers and includes homothetic, affine homothetic, and minus‑infinity homothetic preferences. The study seeks to characterize the class of direct preference orderings dual to the Gorman polar form. The authors specify and estimate a member of this class that generalizes previously estimated Gorman polar form specifications. Using a likelihood ratio test, the authors reject the S‑branch utility tree and its special cases, as well as affine homotheticity, as descriptions of preferences.

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 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 tha. 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 specications 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.