Identifying a Model of Screening with Multidimensional Consumer Heterogeneity

In this paper, I study the nonparametric identification of a model of price discrimination with multidimensional consumer heterogeneity from disaggregated data on consumers' choices and characteristics. In particular, I consider the screening problem faced studied by Rochet and Chone (1998) where a seller of a product with multiple (and continuous) characteristics who only knows the joint density of consumer 'taste' and the production cost and chooses a product 'line' -- endogenous product characteristics. I determine the data features and additional conditions that are sufficient to identify the joint density of consumer heterogeneity, the cost function, and the utility functions that are common across consumers. If the product characteristics enter the utility function linearly, data from only one market is enough for identification, but if they enter nonlinearly we need data from at least two markets, or over two periods, with exogenous differences in costs. I also derive all testable restrictions imposed by the model on the data, i.e., the empirical content of the model, and also explore identification when prices are mismeasured and a product characteristic is missing.