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.

In this paper, we exploit new sources of cross-sectional data to estimate a detailed product-level demand system for new passenger vehicles. We use four data sources: on the characteristics of products, on the attributes of the U.S. population of households, on the match between the first and second vehicle choices of the household, and on the match between households attributes and first choice vehicles. We show that these data solve some, but not all, of the traditional problems in estimating differentiated products demand systems and indicate which data sources are important for which problem. The data is rich enough to reveal a rather complex substitution pattern, requiring a quite general modeling framework. Together the data and model make a detailed analysis of industry demand possible. 1 Introduction In Berry, Levinsohn, and Pakes (1995) (BLP) we provide an algorithm for obtaining estimates of demand parameters for a class of differentiated product models. Demand-side models ...