Examining Demand Elasticities in Hanemann's Framework: A Theoretical and Empirical Analysis

Abstract

This paper examines demand elasticities using an integrated framework proposed by Hanemann [Hanemann, M. W. 1984. Discrete/continuous models of consumer demand. Econometrica 52(3) 541–561], which models the incidence, brand choice, and quantity decisions of a consumer as an outcome of her utility maximization subject to budget constraints. Although the Hanemann framework has been the mainstay of earlier efforts to examine these decisions jointly, empirical researchers who have used the it to study purchase behavior have often found that the quantity elasticities are around −1, regardless of the brand or category. We attempt to uncover the underlying reasons for this finding and propose approaches to get as close to the “true” quantity elasticities as possible. We do this by (i) analytically demonstrating how assumptions on the distribution of the brand-specific econometrician's errors imply certain restrictions that in turn force quantity elasticities to −1, (ii) discussing how these restrictions can be alleviated by considering a suitable specification of unobserved parameter heterogeneity, and (iii) using scanner data to empirically illustrate the impact of the restrictions on quantity elasticities and the relative efficacy of multiple specifications of unobserved heterogeneity in easing those restrictions. We find that the specification of unobserved heterogeneity crucially influences estimates of quantity elasticities and that the mixture normal specification outperforms the alternatives.