Duality in dynamic discrete-choice models

Khai Xiang Chiong, Alfred Galichon, Matt Shum

    Research output: Contribution to journalArticlepeer-review

    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.

    Original languageEnglish (US)
    Pages (from-to)83-115
    Number of pages33
    JournalQuantitative Economics
    Volume7
    Issue number1
    DOIs
    StatePublished - Mar 1 2016

    Keywords

    • Conditional choice probability inversion
    • Estimation of discrete choice models
    • Mass transportation approach

    ASJC Scopus subject areas

    • Economics and Econometrics

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