Duality in Dynamic Discrete Choice Models

42 Pages Posted: 9 Dec 2015  

Khai Xiang Chiong

USC Dornsife Institute for New Economic Thinking

Alfred Galichon

NYU, Department of Economics and Courant Institute

Matthew Shum

California Institute of Technology

Date Written: May 2015

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.

Suggested Citation

Chiong, Khai Xiang and Galichon, Alfred and Shum, Matthew, Duality in Dynamic Discrete Choice Models (May 2015). Available at SSRN: https://ssrn.com/abstract=2700773 or http://dx.doi.org/10.2139/ssrn.2700773

Khai Xiang Chiong

USC Dornsife Institute for New Economic Thinking ( email )

United States

Alfred Galichon

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Matthew Shum (Contact Author)

California Institute of Technology ( email )

Pasadena, CA 91125
United States

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