Duality in Dynamic Discrete Choice Models

Abstract

Using results from convex analysis, we characterize the identification and estimation of dynamic discrete-choice models based on the random utility framework. We show that the conditional choice probabilities and the choice-specific payoffs in these models are related in the sense of conjugate duality. Based on this, we propose a new two-step estimator for these models; interestingly, the first step of our estimator involves solving a linear program which is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971). The application of convex-analytic tools to dynamic discrete choice models, and the connection with two-sided matching models, is new in the literature.