Matching in closed-form: equilibrium, identification, and comparative statics

Raicho Bojilov, Alfred Galichon

    Research output: Contribution to journalArticle

    Abstract

    This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are normal, and when the heterogeneity in tastes is of the continuous logit type, as in Choo and Siow (J Polit Econ 114:172–201, 2006), we show that the optimal matching distribution is also jointly normal and can be computed in closed form from the model primitives. Conversely, the quadratic surplus function can be identified from the optimal matching distribution, also in closed-form. The closed-form formulas make it computationally easy to solve problems with even a very large number of matches and allow for quantitative predictions about the evolution of the solution as the technology and the characteristics of the matching populations change.

    Original languageEnglish (US)
    Pages (from-to)587-609
    Number of pages23
    JournalEconomic Theory
    Volume61
    Issue number4
    DOIs
    StatePublished - Apr 1 2016

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    Comparative statics
    Optimal matching
    Surplus
    Two-sided matching
    Transferable utility
    Population change
    Matching problem
    Prediction
    Logit

    Keywords

    • Assignment
    • Marriage
    • Matching

    ASJC Scopus subject areas

    • Economics and Econometrics

    Cite this

    Matching in closed-form : equilibrium, identification, and comparative statics. / Bojilov, Raicho; Galichon, Alfred.

    In: Economic Theory, Vol. 61, No. 4, 01.04.2016, p. 587-609.

    Research output: Contribution to journalArticle

    Bojilov, Raicho ; Galichon, Alfred. / Matching in closed-form : equilibrium, identification, and comparative statics. In: Economic Theory. 2016 ; Vol. 61, No. 4. pp. 587-609.
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