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

Author

Listed:
  • Liang Chen

    (Wuhan University [China])

  • Eugene Choo

    (Yale-NUS College)

  • Alfred Galichon

    (NYU - NYU System, CIMS - Courant Institute of Mathematical Sciences [New York] - NYU - New York University [New York] - NYU - NYU System, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Simon Weber

    (University of York [York, UK])

Abstract

In this paper, we argue that models coming from a variety of fields share a common structure that we call matching function equilibria with partial assignment. This structure revolves around an aggregate matching function and a system of nonlinear equations. This encompasses search and matching models, matching models with transferable, non-transferable and imperfectly transferable utility, and matching with peer effects. We provide a proof of existence and uniqueness of an equilibrium as well as an efficient algorithm to compute it. We show how to estimate parametric versions of these models by maximum likelihood. We also propose an approach to construct counterfactuals without estimating the matching functions for a subclass of models. We illustrate our estimation approach by analyzing the impact of the elimination of the Social Security Student Benefit Program in 1982 on the marriage market in the United States.

Suggested Citation

  • Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2021. "Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation," Working Papers hal-03936296, HAL.
    • Handle: RePEc:hal:wpaper:hal-03936296
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03936296v1
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    References listed on IDEAS

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    1. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    2. Aloysius Siow, 2008. "How does the marriage market clear? An empirical framework," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 41(4), pages 1121-1155, November.
    3. Head, Keith & Mayer, Thierry, 2014. "Gravity Equations: Workhorse,Toolkit, and Cookbook," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 131-195, Elsevier.
    4. Marion Goussé & Nicolas Jacquemet & Jean‐Marc Robin, 2017. "Marriage, Labor Supply, and Home Production," Econometrica, Econometric Society, vol. 85(6), pages 1873-1919, November.
    5. 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.
    6. Alfred Galichon & Scott Kominers & Simon Weber, 2015. "The Nonlinear Bernstein-Schrödinger Equation in Economics," SciencePo Working papers Main hal-03393000, HAL.
    7. Susan M. Dynarski, 2003. "Does Aid Matter? Measuring the Effect of Student Aid on College Attendance and Completion," American Economic Review, American Economic Association, vol. 93(1), pages 279-288, March.
    8. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
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    10. Kane, Thomas J, 1994. "College Entry by Blacks since 1970: The Role of College Costs, Family Background, and the Returns to Education," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 878-911, October.
    11. Ismael Mourifié & Aloysius Siow, 2017. "The Cobb Douglas marriage matching function: Marriage matching with peer and scale effects," Working Papers 2017-007, Human Capital and Economic Opportunity Working Group.
    12. Aloysius Siow, 2008. "How does the marriage market clear? An empirical framework," Canadian Journal of Economics, Canadian Economics Association, vol. 41(4), pages 1121-1155, November.
    13. Jong-Shi Pang & Che-Lin Su & Yu-Ching Lee, 2015. "A Constructive Approach to Estimating Pure Characteristics Demand Models with Pricing," Operations Research, INFORMS, vol. 63(3), pages 639-659, June.
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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..
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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. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org, revised Oct 2024.
    4. 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.

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