Identi cation in di erentiated products markets using market level data

We consider nonparametric identi\u85cation in models of di¤erentiated products mar-kets, using only market level observables. On the demand side we consider a non-parametric random utility model nesting random coe ¢ cients discrete choice models widely used in applied work. We allow for product/market-speci\u85c unobservables, en-dogenous product characteristics (e.g., prices), and high-dimensional taste shocks with arbitrary correlation and heteroskedasticity. On the supply side we specify marginal costs nonparametrically, allow for unobserved \u85rm heterogeneity, and nest a variety of equilibrium oligopoly models. We pursue two approaches to identi\u85cation. One relies on instrumental variables conditions used previously to demonstrate identi\u85cation in a nonparametric regression framework. With this approach we can show identi\u85cation of the demand side without reference to a particular supply model. Adding the supply side allows identi\u85cation of \u85rmsmarginal costs as well. Our second approach, more closely linked to classical identi\u85cation arguments for supply and demand models, em-ploys a change of variables approach. This leads to constructive identi\u85cation results relying on exclusion and support conditions. Our results lead to a testable restric-tion that provides the \u85rst general formalization of Bresnahans (1982) intuition for empirically discriminating between alternative models of oligopoly competition. Earlier drafts were circulated under the title Identi\u85cation of Discrete Choice Demand From Market Level Data. We had helpful early conversations on this topic with Rosa Matzkin and Yuichi Kitamura