IDEAS home Printed from https://ideas.repec.org/p/hal/spmain/hal-03936296.html
   My bibliography  Save this paper

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," SciencePo Working papers Main hal-03936296, HAL.
    • Handle: RePEc:hal:spmain:hal-03936296
    Note: View the original document on HAL open archive server: https://hal-sciencespo.archives-ouvertes.fr/hal-03936296
    as

    Download full text from publisher

    File URL: https://hal-sciencespo.archives-ouvertes.fr/hal-03936296/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    5. 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.
    6. 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.
    7. 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.
    8. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2021. "Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation," Working Papers hal-03936296, HAL.
    2. 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.
    3. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org.
    4. Odran Bonnet & Alfred Galichon & Yu-Wei Hsieh & Keith O’Hara & Matt Shum, 2022. "Yogurts Choose Consumers? Estimation of Random-Utility Models via Two-Sided Matching [Unobserved Product Differentiation in Discrete-Choice Models: Estimating Price Elasticities and Welfare Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    5. Alfred Galichon & Bernard Salani'e, 2021. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Papers 2106.02371, arXiv.org, revised Jan 2023.
    6. Michael Cohen & Rui Huang, 2012. "Corporate Social Responsibility for Kids’ Sake: A Dynamic Model of Firm Participation," Working Papers 12, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    7. Xiong, Siqin & Yuan, Yi & Yao, Jia & Bai, Bo & Ma, Xiaoming, 2023. "Exploring consumer preferences for electric vehicles based on the random coefficient logit model," Energy, Elsevier, vol. 263(PA).
    8. Freyberger, Joachim, 2015. "Asymptotic theory for differentiated products demand models with many markets," Journal of Econometrics, Elsevier, vol. 185(1), pages 162-181.
    9. Greg Lewis & Bora Ozaltun & Georgios Zervas, 2021. "Maximum Likelihood Estimation of Differentiated Products Demand Systems," Papers 2111.12397, arXiv.org.
    10. Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2023. "Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models," Papers 2309.11416, arXiv.org.
    11. Dunker, Fabian & Hoderlein, Stefan & Kaido, Hiroaki, 2014. "Nonparametric Identification of Endogenous and Heterogeneous Aggregate Demand Models: Complements, Bundles and the Market Level," Economics Series 307, Institute for Advanced Studies.
    12. Alfred Galichon & Bernard Salanié, 2022. "Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models [An Empirical Model of the Medical Match]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2600-2629.
    13. Vergolini, Loris & Zanini, Nadir, 2015. "Away, but not too far from home. The effects of financial aid on university enrolment decisions," Economics of Education Review, Elsevier, vol. 49(C), pages 91-109.
    14. Benedikt Siegler, 2012. "The Effect of University Openings on Local Human Capital Formation: Difference-in-Differences Evidence from Germany," Working Papers 124, Bavarian Graduate Program in Economics (BGPE).
    15. Timothy B. Armstrong & Michal Kolesár, 2021. "Sensitivity analysis using approximate moment condition models," Quantitative Economics, Econometric Society, vol. 12(1), pages 77-108, January.
    16. Steven T. Berry & Philip A. Haile, 2021. "Foundations of Demand Estimation," Cowles Foundation Discussion Papers 2301, Cowles Foundation for Research in Economics, Yale University.
    17. Baiyu Dong & Yu-Wei Hsieh & Xing Zhang, 2022. "Implementing Maximum Likelihood Estimation of Empirical Matching Models," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 1-32, January.
    18. Stépahne Auray & Nicolas Lepage-Saucier & Purevdorj Tuvaandor, 2018. "Doubly Robust GMM Inference and Differentiated Products Demand Models," Working Papers 2018-13, Center for Research in Economics and Statistics.
    19. Friberg, Richard & Romahn, André, 2015. "Divestiture requirements as a tool for competition policy: A case from the Swedish beer market," International Journal of Industrial Organization, Elsevier, vol. 42(C), pages 1-18.
    20. Panle Jia Barwick & Shengmao Cao & Shanjun Li, 2021. "Local Protectionism, Market Structure, and Social Welfare: China's Automobile Market," American Economic Journal: Economic Policy, American Economic Association, vol. 13(4), pages 112-151, November.

    More about this item

    Keywords

    Matching function; Maximum likelihood estimation; Counterfactuals; Matching; Transferable utility; Imperfectly transferable utility;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:spmain:hal-03936296. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Contact - Sciences Po Departement of Economics (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.