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Duality in dynamic discrete‐choice models

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  • Khai Xiang Chiong
  • Alfred Galichon
  • Matt Shum

Abstract

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 convex‐analytic 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.

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  • Khai Xiang Chiong & Alfred Galichon & Matt Shum, 2016. "Duality in dynamic discrete‐choice models," Quantitative Economics, Econometric Society, vol. 7(1), pages 83-115, March.
    • Handle: RePEc:wly:quante:v:7:y:2016:i:1:p:83-115
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    Cited by:

    1. Mogens Fosgerau & André De Palma, 2016. "Generalized entropy models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01291347, HAL.
    2. Fosgerau, Mogens & Melo, Emerson & Shum, Matt, 2017. "Discrete Choice and Rational Inattention: a General Equivalence Result�," MPRA Paper 76605, University Library of Munich, Germany.
    3. Mogens Fosgerau & Emerson Melo & André De Palma & Matthew Shum, 2017. "Discrete Choice and Rational Inattention: A General Equivalence Result," Working Papers hal-01501313, HAL.
    4. Mogens Fosgerau & André De Palma, 2016. "Generalized entropy models," Working Papers hal-01291347, HAL.

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