IDEAS home Printed from https://ideas.repec.org/a/oup/restud/v89y2022i5p2600-2629..html
   My bibliography  Save this article

Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models

Author

Listed:
  • Alfred Galichon
  • Bernard Salanié

Abstract

We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006, Journal of Political Economy, 114, 175–201), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow’s empirical application to illustrate the potential of our more general approach.

Suggested Citation

  • Alfred Galichon & Bernard Salanié, 2022. "Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2600-2629.
    • Handle: RePEc:oup:restud:v:89:y:2022:i:5:p:2600-2629.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/restud/rdab090
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966-1005.
    2. Aloysius Siow, 2015. "Testing Becker's Theory of Positive Assortative Matching," Journal of Labor Economics, University of Chicago Press, vol. 33(2), pages 409-441.
    3. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    4. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 49-100.
    5. Maristella Botticini & Aloysius Siow, 2006. "Are There Increasing Returns in Marriage Markets?," Boston University - Department of Economics - Working Papers Series WP2006-050, Boston University - Department of Economics.
    6. Nicolas Jacquemet & Jean-Marc Robin, 2011. "Marriage with Labor Supply," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01073728, HAL.
    7. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 103-127, January.
    8. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," Working Papers hal-03588302, HAL.
    9. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
    10. de Palma, Andre & Kilani, Karim, 2007. "Invariance of conditional maximum utility," Journal of Economic Theory, Elsevier, vol. 132(1), pages 137-146, January.
    11. Gunter J. Hitsch & Ali Hortaçsu & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-163, March.
    12. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
    13. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09j00420pk7 is not listed on IDEAS
    14. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," Working Papers hal-03588302, HAL.
    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. "Who Marries Whom and Why," Journal of Political Economy, University of Chicago Press, vol. 114(1), pages 175-201, February.
    17. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09j00420pk7 is not listed on IDEAS
    18. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    19. repec:hal:spmain:info:hdl:2441/3sd5loegec9d3o795888da61tp is not listed on IDEAS
    20. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Goussé, Marion & Jacquemet, Nicolas & Robin, Jean-Marc, 2017. "Household labour supply and the marriage market in the UK, 1991-2008," Labour Economics, Elsevier, vol. 46(C), pages 131-149.
    2. repec:cte:werepe:23566 is not listed on IDEAS
    3. Cheremukhin, Anton & Restrepo-Echavarria, Paulina & Tutino, Antonella, 2020. "Targeted search in matching markets," Journal of Economic Theory, Elsevier, vol. 185(C).
    4. John K. Dagsvik & Zhiyang Jia, 2018. "Aggregate behavior in matching markets with flexible contracts and non-transferable representations of preferences," Discussion Papers 875, Statistics Norway, Research Department.
    5. Aloysius Siow, 2015. "Testing Becker's Theory of Positive Assortative Matching," Journal of Labor Economics, University of Chicago Press, vol. 33(2), pages 409-441.
    6. Yu Hao & Hiroyuki Kasahara, 2024. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models with 2-period Finite Dependence," Papers 2405.12467, arXiv.org.
    7. Pęski, Marcin, 2017. "Large roommate problem with non-transferable random utility," Journal of Economic Theory, Elsevier, vol. 168(C), pages 432-471.
    8. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," SciencePo Working papers hal-01070393, HAL.
    9. Pierre-Andr'e Chiappori & Robert McCann & Brendan Pass, 2016. "Multidimensional matching," Papers 1604.05771, arXiv.org.
    10. Jerez, Belén, 2017. "Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments," Journal of Economic Theory, Elsevier, vol. 172(C), pages 202-219.
    11. Veronica Rappoport & Catherine Thomas & Bernard Salanie & Maria Guadalupe, 2013. "The Perfect Match: Assortative Matching in International Acquisitions," 2013 Meeting Papers 1000, Society for Economic Dynamics.
    12. Taehoon Kim & Jacob Schwartz & Kyungchul Song & Yoon-Jae Whang, 2019. "Monte Carlo Inference on Two-Sided Matching Models," Econometrics, MDPI, vol. 7(1), pages 1-15, March.
    13. Seul-Ki Shin, 2014. "Preferences vs. Opportunities: Racial/Ethnic Intermarriage in the United States," PIER Working Paper Archive 14-040, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    14. Esben Scrivers Andersen, 2024. "Note on solving one-to-one matching models with linear transferable utility," Papers 2409.05518, arXiv.org, revised Dec 2024.
    15. Goussé, Marion & Jacquemet, Nicolas & Robin, Jean-Marc, 2017. "Household labour supply and the marriage market in the UK, 1991-2008," Labour Economics, Elsevier, vol. 46(C), pages 131-149.
    16. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," SciencePo Working papers Main hal-01070393, HAL.

    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. Bernard Salanié & Alfred Galichon, 2012. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Working Papers hal-01053710, HAL.
    2. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    3. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    4. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    5. Arnaud Dupuy & Alfred Galichon, 2014. "Personality Traits and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1271-1319.
    6. 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.
    7. Sinha, Shruti, 2018. "Identification in One-to-One Matching Models with Nonparametric Unobservables," TSE Working Papers 18-897, Toulouse School of Economics (TSE).
    8. repec:spo:wpmain:info:hdl:2441/7o52iohb7k6srk09mj4j5amb8 is not listed on IDEAS
    9. repec:hal:wpspec:info:hdl:2441/7o52iohb7k6srk09mj4j5amb8 is not listed on IDEAS
    10. Jeremy T. Fox & David H. Hsu & Chenyu Yang, 2012. "Unobserved Heterogeneity in Matching Games with an Application to Venture Capital," NBER Working Papers 18168, National Bureau of Economic Research, Inc.
    11. Veli Safak, 2020. "Matching Multidimensional Types: Theory and Application," Papers 2006.14243, arXiv.org.
    12. repec:hal:spmain:info:hdl:2441/7o52iohb7k6srk09mj4j5amb8 is not listed on IDEAS
    13. repec:spo:wpecon:info:hdl:2441/7o52iohb7k6srk09mj4j5amb8 is not listed on IDEAS
    14. Pierre-André Chiappori & Bernard Salanié, 2016. "The Econometrics of Matching Models," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 832-861, September.
    15. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," Working Papers hal-03588302, HAL.
    16. McCann, Robert J. & Shi, Xianwen & Siow, Aloysius & Wolthoff, Ronald P., 2012. "Becker Meets Ricardo: Multisector Matching with Social and Cognitive Skills," IZA Discussion Papers 6533, Institute of Labor Economics (IZA).
    17. Decker, Colin & Lieb, Elliott H. & McCann, Robert J. & Stephens, Benjamin K., 2013. "Unique equilibria and substitution effects in a stochastic model of the marriage market," Journal of Economic Theory, Elsevier, vol. 148(2), pages 778-792.
    18. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," SciencePo Working papers hal-01070393, HAL.
    19. Salanié, Bernard & Chiappori, Pierre-André, 2021. "Mating Markets," CEPR Discussion Papers 16041, C.E.P.R. Discussion Papers.
      • Pierre-André Chiappori & Bernard Salanié, 2021. "Mating Markets," Working Papers 2021-016, Human Capital and Economic Opportunity Working Group.
    20. Arnaud Dupuy & Alfred Galichon, 2012. "Personality traits and the marriage market," SciencePo Working papers Main hal-01070393, HAL.
    21. Aloysius Siow, 2015. "Testing Becker's Theory of Positive Assortative Matching," Journal of Labor Economics, University of Chicago Press, vol. 33(2), pages 409-441.
    22. repec:hal:spmain:info:hdl:2441/1293p84sf58s482v2dpn0gsd67 is not listed on IDEAS
    23. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-Offs," Working Papers hal-03596979, HAL.
    24. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org, revised Oct 2024.
    25. repec:hal:spmain:info:hdl:2441/3sd5loegec9d3o795888da61tp is not listed on IDEAS
    26. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-Offs," Working Papers hal-03596979, HAL.
    27. repec:spo:wpmain:info:hdl:2441/1293p84sf58s482v2dpn0gsd67 is not listed on IDEAS
    28. Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2012. "The Roommate Problem is More Stable than You Think," Working Papers hal-03588302, HAL.
    29. repec:spo:wpmain:info:hdl:2441/38n7438p68vmqd9om4bjj6l4c is not listed on IDEAS
    30. Han, Seungjin & Yamaguchi, Shintaro, 2015. "Compensating wage differentials in stable job matching equilibrium," Journal of Economic Behavior & Organization, Elsevier, vol. 114(C), pages 36-45.
    31. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.

    More about this item

    Keywords

    Matching; Marriage; Assignment; Hedonic prices;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:oup:restud:v:89:y:2022:i:5:p:2600-2629.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/restud .

    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.