Boundaries of Differentiated Product Markets and Retailer Pricing

Abstract

This paper studies the effects of misspecified boundaries of competition on optimal retail pricing using store-level supermarket scanner data. We focus on two types of misspecification: (i) misspecification of the demand estimation problem arising from overly restrictive functional forms or the omission of relevant goods; (ii) misspecification of the retailer's decision problem, in which prices are set separately rather than jointly across related categories. Quantifying the costs associated with either form of misspecification is challenging because it requires a flexible yet valid demand system. We take a nonparametric approach to estimating demand that imposes minimal restrictions on cross-price effects, satisfies properties required by economic theory, and nests standard parametric models. In our empirical analysis, we provide descriptive evidence across nine product groups that cross-category effects are large and often nuanced in their sign and magnitude. We then zoom in on refrigerated juices and estimate multi-category demand systems with varying degrees of flexibility. We document and explain differences in elasticity estimates across specifications, and solve for optimal prices under each model to quantify losses in profits due to misspecification.

Keywords: multi-category demand, nonparametric demand estimation, Bernstein polynomials, model misspecification, omitted variable bias

JEL Classification: C10, C14, D12, D40, L11, M31