Demand estimation under limited product availability

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.