We examine identification of differentiated products demand when one has “micro data” linking the characteristics and choices of individual consumers. Our model nests standard specifications featuring rich observed and unobserved consumer heterogeneity as well as product/market‐level unobservables that introduce the problem of econometric endogeneity. Previous work establishes identification of such models using market‐level data and instruments for all prices and quantities. Micro data provides a panel structure that facilitates richer demand specifications and reduces requirements on both the number and types of instrumental variables. We address identification of demand in the standard case in which nonprice product characteristics are assumed exogenous, but also cover identification of demand elasticities and other key features when these product characteristics are endogenous and not instrumented. We discuss implications of these results for applied work.

We present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a “residual index.†Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important results demonstrate identification when instruments have only limited variation. Even when instruments vary only over a small open ball, relatively mild conditions on the joint density suffice. We also show that the primary sufficient conditions for identification are verifiable and that the maintained hypotheses of the model are falsifiable.

We present new identification results for nonparametric models of differentiated products markets, using only market level observables. We specify a nonparametric random utility discrete choice model of demand allowing rich preference heterogeneity, product/market unobservables, and endogenous prices. Our supply model posits nonparametric 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 regression models. The second treats demand and supply in a system of nonparametric simultaneous 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 distinguishing 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 consider the invertibility (injectivity) of a nonparametric nonseparable demand system. Invertibility of demand is important in several contexts, including identification of demand, estimation of demand, testing of revealed preference, and economic theory exploiting existence of an inverse demand function or (in an exchange economy) uniqueness of Walrasian equilibrium prices. We introduce the notion of “connected substitutes” and show that this structure is sufficient for invertibility. The connected substitutes conditions require weak substitution between all goods and sufficient strict substitution to necessitate treating them in a single demand system. The connected substitutes conditions have transparent economic interpretation, are easily checked, and are satisfied in many standard models. They need only hold under some transformation of demand and can accommodate many models in which goods are complements. They allow one to show invertibility without strict gross substitutes, functional form restrictions, smoothness assumptions, or strong domain restrictions. When the restriction to weak substitutes is maintained, our sufficient conditions are also “nearly necessary” for even local invertibility.

We present new identification resiilts for models of first-price, second-price, ascending (English), and descending (Dutch) auctions.We analyze a general specification of bidders' preferences and the underlying information structure, nesting as special cases the pure private values and pure common values models, and allowing both ex ante symmetric and asymmetric bidders.We address identification of a series of such models and propose strategies for discriminating between them on the basis of observed data.In the simplest case, the symmetric independent pri- vate values model is nonparametrically identified even if only the transaction price from each auction is observed.For more complex models, we provide conditions for identification and testing when additional information of one of the following types is available: (i) one or more bids in addition to the transaction price; (ii) exogenous variation in the number of bidders; (iii) bidder-specific covariates that shift the distribution of valuations; (iv) the ex post reahzation of the value of the object sold.Our results include new tests that distinguish between private and common values models.

This paper presents new identification results for models of first–price, second–price, ascending (English), and descending (Dutch) auctions. We consider a general specification of the latent demand and information structure, nesting both private values and common values models, and allowing correlated types as well as ex ante asymmetry. We address identification of a series of nested models and derive testable restrictions enabling discrimination between models on the basis of observed data. The simplest model—symmetric independent private values—is nonparametrically identified even if only the transaction price from each auction is observed. For richer models, identification and testable restrictions may be obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders; (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidder–specific covariates. While many private values (PV) models are nonparametrically identified and testable with commonly available data, identification of common values (CV) models requires stringent assumptions. Nonetheless, the PV model can be tested against the CV alternative, even when neither model is identified.