Identification in differentiated products markets using market level data. Working paper

We present new identification results for nonparametric models of differentiated prod-ucts markets, using only market level observables. We specify a nonparametric random utility discrete choice model of demand allowing rich preference heterogeneity, prod-uct/market unobservables, and endogenous prices. Our supply model posits nonpara-metric cost functions, allows latent cost shocks, and nests a range of standard oligopoly models. We consider identification of demand, identification of changes in aggregate consumer welfare, identification of marginal costs, identification of firms ’ marginal cost functions, and discrimination between alternative models of firm conduct. We explore two complementary approaches. The first demonstrates identification under the same nonparametric instrumental variables conditions required for identification of regres-sion models. The second treats demand and supply in a system of nonparametric si-multaneous equations, leading to constructive proofs exploiting exogenous variation in demand shifters and cost shifters. We also derive testable restrictions that provide the first general formalization of Bresnahan’s (1982) intuition for empirically distinguish-ing between alternative models of oligopoly competition. From a practical perspective, our results clarify the types of instrumental variables needed with market level data, including tradeoffs between functional form and exclusion restrictions. ∗We had helpful early conversations on this topic with Rosa Matzkin and Yuichi Kitamura, as well as valuable feedback from Liran Einav, Jon Levin, Tim Bresnahan, and participants in many seminars and conferences. We have also benefitted from the constructive comments of the co-editor and referees. Adam Kapor provided capable research assistance. Financial support from the National Science Foundation is gratefully acknowledged.