Filling Out the Instrument Set in Mixed Logit Demand Systems for Aggregate Data

The random parameters logit model for aggregate data introduced by Berry, Levinsohn, and Pakes (1995) has been a driving force in empirical industrial organization for more than a decade. While these models are identified in theory, identification problems often occur in practice. In this paper we introduce the means of included demographics as a new set of readily available instruments that have the potential to substantially improve numerical performance in a variety of contexts. We use a set of endogenous price simulations to demonstrate that they are valid, and we use a real data illustration to demonstrate that they improve the numerical properties of the GMM objective function. In addition, we develop a metric that decomposes the explanatory power of the model into the proportion of market share variation that is explained by mean utility and that which is explained by the heterogeneity specification.