Nonparametric Identification of Random Coefficients in Endogenous and Heterogeneous Aggregate Demand

This paper studies nonparametric identification in market level demand models for differentiated products with heterogeneous consumers. We consider a general class of models that allows for the individual specific coefficients to vary continuously across the population and give conditions under which the density of these coefficients, and hence also functionals such as welfare measures, is identified. Building on earlier work by Berry and Haile (2013), we show that key identifying restrictions are provided by (i) a set of moment conditions generated by instrumental variables together with an inversion of aggregate demand in unobserved product characteristics; and (ii) the variation of the product characteristics across markets that is exogenous to the individual heterogeneity. We further show that two leading models, the BLP-model (Berry, Levinsohn, and Pakes, 1995) and the pure characteristics model (Berry and Pakes, 2007), require considerably different conditions on the support of the product characteristics.