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Duality in dynamic discrete-choice models

Chiong, Khai Xiang and Galichon, Alfred and Shum, Matt (2016) Duality in dynamic discrete-choice models. Quantitative Economics, 7 (1). pp. 83-115. ISSN 1759-7323. doi:10.3982/QE436.

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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.

Item Type:Article
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URLURL TypeDescription ItemWorking Paper
Chiong, Khai Xiang0000-0002-6713-8907
Shum, Matt0000-0002-6262-915X
Additional Information:© 2016 Khai Xiang Chiong, Alfred Galichon, and Matt Shum. Licensed under the Creative Commons Attribution-NonCommercial License 3.0. Submitted February, 2014. Final version accepted June, 2015. Article first published online: 4 Apr 2016. The authors thank the editor and three anonymous referees, as well as Benjamin Connault, Thierry Magnac, Emerson Melo, Bob Miller, Sergio Montero, John Rust, Sorawoot (Tang) Srisuma, and Haiqing Xu for useful comments. We are especially grateful to Guillaume Carlier for providing decisive help with the proof of Theorem 5. We also thank audiences at Michigan, Northwestern, NYU, Pittsburgh, UCSD, the CEMMAP Conference on Inference in Game-Theoretic Models (June 2013), UCLA Econometrics Mini-Conference (June 2013), the Boston College Econometrics of Demand Conference (December 2013), and the Toulouse Conference on Recent Advances in Set Identification (December 2013) for helpful comments. Galichon’s research has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant 313699.
Funding AgencyGrant Number
European Research Council (ERC)313699
Subject Keywords:Conditional choice probability inversion, estimation of discrete choice models, mass transportation approach
Issue or Number:1
Classification Code:JEL: C35, C61, D90
Record Number:CaltechAUTHORS:20160429-103911310
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Official Citation:Chiong, K. X., Galichon, A. and Shum, M. (2016), Duality in dynamic discrete-choice models. Quantitative Economics, 7: 83–115. doi: 10.3982/QE436
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66549
Deposited By: Tony Diaz
Deposited On:29 Apr 2016 19:27
Last Modified:10 Nov 2021 23:59

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