Identifying a Model of Screening with Multidimensional Consumer Heterogeneity

In this paper we study the identification of a screening model with multidimensional unobserved consumer heterogeneity, using transaction level data and consumers' socio-economic characteristics. In multidimensional screening a seller of a multi-attribute product “screens” by offering a menu of product attributes and prices to consumers who have private information about their multidimensional taste for each attribute. This menu maximizes expected profit subject to the incentive compatibility and the participation constraints. We show that, if utility is linear in product attributes, the demand and supply optimality conditions can be “inverted” to identify the joint density of “high-types” –those with high willingness to pay– and the cost function. To identify the joint density of the “medium-types” –those who are bunched– we can use independent variation in consumer characteristics. If, however, the utility function is nonlinear in product attributes, we show that data from only one market is insufficient for identification. But if we have data from two different markets (or the same market over two periods) that are separated by a binary cost shifter that does not affect the preferences, then we can also identify the vector of non-linear utility functions