Identification and Estimation of Multidimensional Screening

Abstract

We study the identification and estimation of a multidimensional screening model in which a monopolist sells a product with multiple continuous attributes to consumers with private information about their multidimensional preferences. Optimal screening excludes ``low-type" consumers, bunches ``medium-type" consumers, and perfectly screens the ``high types." Assuming a quadratic, additively separable cost function, we identify sufficient conditions to recover the joint distribution of preferences and marginal costs from data on individual choices and payments in a single market. We propose estimators for these objects, establish their asymptotic properties, and assess their small-sample performance using Monte Carlo experiments. Finally, we illustrate our method using synthetic data on Chinese wireless service constructed using estimates from \cite{clx19}.