Estimating Discrete Choice Models of Demand with Market Level Variation

In this paper we develop and apply a new empirical approach to estimating a widely used class of models of demand for differentiated products. Our approach is applicable to the often encountered situation where the researcher has data on a sample of markets (i.e., the “many markets” setting). Our focus on the “many markets” setting stands in contrast to the “many products” setting that was famously studied by Berry, Levinsohn, and Pakes (1995). We first show that the key identification restriction underlying the Berry, Levinsohn, and Pakes (1995) approach to estimation does not have any identifying power in the many markets setting without further restrictions – the essential problem being the presence of sampling variability in market shares. Furthermore, their inference methods do not apply because of the presence of strategic dependence among products within a market. We show that if choice probabilities are bounded away from zero, the standard consumer model implies enough demand restrictions that we can use to form a system of moment inequalities which hold at the market level. We also construct a profiling approach for parameter inference with moment inequalities, which allows us to study models with a large number of parameters (as typically required in demand applications) by focusing attention on a generalized profile of the parameters, such as the price coefficient. We use our approach to study UPC level demand on scanner data from the Dominick’s Fine Foods database, and find that even for the baseline logit model, demand elasticities nearly double when the “many markets” structure of the data is taken into account.