Identifying Multidiemsnional Adverse Selection Models

In this paper, I study the nonparametric identification of a multidimensional adverse selection model. In particular, I consider the screening model of Rochet and Chone (1998), where products have multiple characteristics and consumers have private information about their multidimensional taste for these characteristics, and determine the data features and additional condition(s) that identify model parameters. The parameters include the nonparametric joint density of consumer taste, the cost function, and the utility function, and the data includes individual-level data on choices and prices paid from one market. When the utility is nonlinear in product characteristics, however, data from one market is not enough, but with data from at least two markets, or over two periods, with different marginal prices is sufficient for identification as long as these price differences are due to exogenous (and binary) changes in cost and not because the two markets are inherently different. I also derive all testable conditions for a joint distribution of observed choices and prices to be rationalized by a model of multidimensional adverse selection.