Duality in dynamic discrete-choice models

TL;DR

This paper introduces a novel approach to identifying and estimating dynamic discrete-choice models using convex analysis and mass transport theory, establishing a connection with two-sided matching models and proposing a new two-step estimator.

Contribution

It presents the Mass Transport Approach (MTA) for dynamic discrete-choice models, linking conjugate duality with mass transport problems and introducing a linear programming estimator.

Findings

Identification problem is a mass transport problem.

First step involves solving a linear program identical to a classic matching game.

Application of convex analysis to dynamic discrete choice models is new.

Abstract

Using results from convex analysis, we investigate a novel approach to identification and estimation of discrete choice models which we call the Mass Transport Approach (MTA). 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 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.