Demand estimation under limited product availability

Abstract

Consumer purchases are determined, in part, by the assortment of products available at retailers. Despite this, commonly employed aggregate demand models fail to control for the fraction of stores that carry a given item. We detail the conditions under which aggregate demand is consistently estimated when heterogeneity in product assortment is ignored. The required assumptions are quite strict and likely violated in many empirical applications. Even when they hold, however, a problem of inference arises. One cannot tell whether a lack of interaction between two products is due to limited substitution in those stores where both are available or because many stores do not carry both products. This is a significant shortcoming since in many situations it is important to distinguish between these two possibilities.

Acknowledgements

Helpful comments from Chris Adams, Daniel Hosken, Shawn Ulrick, Michael Vita and John Yun are greatly appreciated. The views expressed in this article are those of the author, and do not necessarily represent the views of the Federal Trade Commission or any individual Commissioner.

Notes

¹‘Federal Trade Commission v. H. J. Heinz, Company, et al .,’ United States District Court for the District of Columbia, Civil Action No. 00-1688. 18 October 2000.

² Demand studies based on ACNielsen or IRI scanner data could (partially) test this assumption, since such data reports the univariate distribution of each product's availability. Assumption A2 is invalid when the percentage of stores that carries each product varies by market.

³ We abstract from the possible endogeneity of price (and the need for instruments), since that is not the focus of this article.