Incorporating Flexible Demand Systems in Empirical Models of Market Power

TLDR: In this article, the authors determine whether using more flexible demand systems can yield a set of first-order profit maximization conditions that are mathematically tractable and amendable to estimation.

Abstract: Measuring the degree of price coordination between firms in a differentiated products industry is particularly challenging because it is necessary to utilize a demand system that is sufficiently flexible, allows the imposition of theoretical restrictions, and allow for the derivation of the functional form of the corresponding price reaction functions. Previous research has relied on restrictive demand systems in order to maintain the tractability of the price reaction functions. The purpose of this paper is determine whether using more flexible demand systems can yield a set of first-order profit maximization conditions that are mathematically tractable and amendable to estimation. The demand systems considered are the Almost Ideal Demand System (AIDS), the Linear Approximate Almost Ideal Demand System (LAIDS), and the Rotterdam demand system. This paper also expands prior work on estimating brand level demand elasticities by endogenizing category level expenditures in the context of a weakly separable demand system. This yields some new and interesting insights for the measurement of market power in differentiated product industries. We show that while it is not possible to derive explicit price reaction functions for any of these demand systems, given certain assumptions, the Rotterdam demand system does yield an explicit set of profit maximization first-order conditions that can be estimated.