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Duality in dynamic discrete choice models

Chiong, Khai X. and Galichon, Alfred and Shum, Matthew (2015) Duality in dynamic discrete choice models. Social Science Working Paper, 1403. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20160329-093057029

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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.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:20160429-103911310Related ItemLater version of this paper
ORCID:
AuthorORCID
Shum, Matthew0000-0002-6262-915X
Additional Information:Acknowledgements: First draft: April 2013. This version: February 2015. The authors thank the Editor, 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, Pitt, 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 agreement no. 313699 and from FiME, Laboratoire de Finance des Marches de l'Energie (www.fime-lab.org).
Group:Social Science Working Papers
Funders:
Funding AgencyGrant Number
European Community Seventh Framework ProgrammeFP7/2007-2013
European Research Council (ERC)313699
FiME, Laboratoire de Finance des Marches de l'EnergieUNSPECIFIED
Subject Keywords:Dynamic discrete choice models; Convex analysis; Mass Transport Approach (MTA)
Record Number:CaltechAUTHORS:20160329-093057029
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160329-093057029
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65730
Collection:CaltechAUTHORS
Deposited By: Susan Vite
Deposited On:14 Dec 2016 23:18
Last Modified:08 Sep 2017 20:14

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