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Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation

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  • Liang Chen
  • Eugene Choo
  • Alfred Galichon
  • Simon Weber

Abstract

We argue that models coming from a variety of fields, such as matching models and discrete choice models among others, share a common structure that we call matching function equilibria with partial assignment. This structure includes an aggregate matching function and a system of nonlinear equations. We provide a proof of existence and uniqueness of an equilibrium and propose an efficient algorithm to compute it. For a subclass of matching models, we also develop a new parameter-free approach for constructing the counterfactual matching equilibrium. It has the advantage of not requiring parametric estimation when computing counterfactuals. We use our procedure to analyze the impact of the elimination of the Social Security Student Benefit Program in 1982 on the marriage market in the United States. We estimate several candidate models from our general class of matching functions and select the best fitting model using information based criterion.

Suggested Citation

  • Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2021. "Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation," Papers 2102.02071, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2102.02071
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    References listed on IDEAS

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    1. Alfred Galichon & Scott Duke Kominers & Simon Weber, 2019. "Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2875-2925.
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    9. Marion Goussé & Nicolas Jacquemet & Jean‐Marc Robin, 2017. "Marriage, Labor Supply, and Home Production," Econometrica, Econometric Society, vol. 85(6), pages 1873-1919, November.
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    15. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    16. Eugene Choo & Aloysius Siow, 2006. "Estimating a marriage matching model with spillover effects," Demography, Springer;Population Association of America (PAA), vol. 43(3), pages 463-490, August.
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    Cited by:

    1. Dupuy, Arnaud & Raux, Morgan & Signorelli, Sara, 2024. "Digitalization, Change in Skill Distance between Occupations and Worker Mobility: A Gravity Model Approach," IZA Discussion Papers 17535, Institute of Labor Economics (IZA).
    2. Bastian Schulz & Fabian Siuda, 2023. "Marriage and divorce: the role of unemployment insurance," Journal of Population Economics, Springer;European Society for Population Economics, vol. 36(4), pages 2277-2308, October.
    3. Arnaud Dupuy & Simon Weber, 2022. "Marriage Market Counterfactuals Using Matching Models," Economica, London School of Economics and Political Science, vol. 89(353), pages 29-43, January.
    4. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org, revised Oct 2024.

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