Duality in Dynamic Discrete Choice Models
Discret choice model, Mass Transport Approach (MTA), Conjugate duality
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.