Duality in dynamic discrete-choice models

Using results from Convex Analysis, we investigate a novel approach to identification and estimation of discrete-choice models that we call the mass transport approach . We show that the conditional choice probabilities and the choice-specific payoffs in these models are related in the sense of conjugate duality , and that the identification problem is a mass transport problem. 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 that is identical to the classic assignment (two-sided matching) game of Shapley and Shubik (1971). The application of convexanalytic tools to dynamic discrete-choice models and the connection with two-sided matching models is new in the literature. Monte Carlo results demonstrate the good performance of this estimator, and we provide an empirical application based on Rust’s ( 1987) bus engine replacement model.