Duality in dynamic discrete-choice models

Khai Xiang Chiong, Alfred Galichon and Matt Shum

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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.

Date: 2021-02, Revised 2021-02
New Economics Papers: this item is included in nep-dcm
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Published in Quantitative Economics 7 (2016) pp. 83-115

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