IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2106.02371.html
   My bibliography  Save this paper

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

Author

Listed:
  • Alfred Galichon
  • Bernard Salani'e

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), 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 Salani'e, 2021. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Papers 2106.02371, arXiv.org.
  • Handle: RePEc:arx:papers:2106.02371
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2106.02371
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 49-100.
    2. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    3. Arnaud Costinot & Jonathan Vogel, 2015. "Beyond Ricardo: Assignment Models in International Trade," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 31-62, August.
    4. 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.
    5. Edoardo Ciscato & Alfred Galichon & Marion Goussé, 2020. "Like Attract Like? A Structural Comparison of Homogamy across Same-Sex and Different-Sex Households," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 740-781.
    6. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
    7. 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.
    8. 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.
    9. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    10. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    11. Pierre-André Chiappori & Bernard Salanié & Yoram Weiss, 2017. "Partner Choice, Investment in Children, and the Marital College Premium," American Economic Review, American Economic Association, vol. 107(8), pages 2109-2167, August.
    12. Ismael Mourifié, 2019. "A marriage matching function with flexible spillover and substitution patterns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 421-461, March.
    13. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    14. 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.
    15. Nikhil Agarwal & Paulo J. Somaini, 2019. "Revealed Preference Analysis of School Choice Models," NBER Working Papers 26568, National Bureau of Economic Research, Inc.
    16. repec:dau:papers:123456789/6486 is not listed on IDEAS
    17. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    18. Jeremy T. Fox & Patrick Bajari, 2013. "Measuring the Efficiency of an FCC Spectrum Auction," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 100-146, February.
    19. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    20. Dagsvik, John K, 2000. "Aggregation in Matching Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 27-57, February.
    21. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    22. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    23. Anderson, Simon Peter & de Palma, Andre & Thisse, Jacques-Francois, 1988. "A Representative Consumer Theory of the Logit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 461-466, August.
    24. Ismael Mourifié & Aloysius Siow, 2021. "The Cobb-Douglas Marriage Matching Function: Marriage Matching with Peer and Scale Effects," Journal of Labor Economics, University of Chicago Press, vol. 39(S1), pages 239-274.
    25. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.
    26. 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.
    27. Jeremy T. Fox & Chenyu Yang & David H. Hsu, 2018. "Unobserved Heterogeneity in Matching Games," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1339-1373.
    28. Alfred Galichon & Bernard Salanié, 2017. "The Econometrics and Some Properties of Separable Matching Models," American Economic Review, American Economic Association, vol. 107(5), pages 251-255, May.
    29. Nikhil Agarwal & Paulo Somaini, 2020. "Revealed Preference Analysis of School Choice Models," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 471-501, August.
    30. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," Post-Print hal-03470458, HAL.
    31. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    32. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
    33. 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..
    34. 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.
    35. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    36. Steven Berry & Ariel Pakes, 2007. "The Pure Characteristics Demand Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1193-1225, November.
    37. 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. Augsburg, Britta & Baquero, Juan Pablo & Gautam, Sanghmitra & Rodriguez-Lesmes, Paul, 2021. "Sanitation and Marriage Markets in India: Evidence from the Total Sanitation Campaign," SocArXiv 58sdf, Center for Open Science.
    2. Akira Matsushita & Kei Ikegami & Kyohei Okumura & Yoji Tomita & Atsushi Iwasaki, 2022. "Regulating Matching Markets with Constraints: Data-driven Taxation," Papers 2205.14387, arXiv.org, revised Sep 2022.
    3. Chiappori, Pierre-Andre & Fioro, Carlo & Galichon, Alfred & Verzillo, Stefano, 2022. "Assortative Matching on Income," Working Papers 2022-07, Joint Research Centre, European Commission.
    4. Emerson Melo, 2021. "Learning in Random Utility Models Via Online Decision Problems," Papers 2112.10993, arXiv.org, revised Aug 2022.

    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. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    2. Nikhil Agarwal & Eric Budish, 2021. "Market Design," NBER Working Papers 29367, National Bureau of Economic Research, Inc.
    3. Sinha, Shruti, 2018. "Identification in One-to-One Matching Models with Nonparametric Unobservables," TSE Working Papers 18-897, Toulouse School of Economics (TSE).
    4. Alfred Galichon & Bernard Salani'e, 2021. "Structural Estimation of Matching Markets with Transferable Utility," Papers 2109.07932, arXiv.org.
    5. 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.
    6. Odran Bonnet & Alfred Galichon & Yu-Wei Hsieh & Keith O'Hara & Matt Shum, 2021. "Yogurts Choose Consumers? Estimation of Random-Utility Models via Two-Sided Matching," Papers 2111.13744, arXiv.org.
    7. Chiappori, Pierre-André & Salanié, Bernard, 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.
    8. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," SciencePo Working papers Main hal-03460155, HAL.
    9. Tamás Fleiner & Ravi Jagadeesan & Zsuzsanna Jankó & Alexander Teytelboym, 2019. "Trading Networks With Frictions," Econometrica, Econometric Society, vol. 87(5), pages 1633-1661, September.
    10. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    11. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.
    12. Bisin, Alberto & Tura, Giulia, 2019. "Marriage, Fertility, and Cultural Integration in Italy," CEPR Discussion Papers 14179, C.E.P.R. Discussion Papers.
    13. Gualdani, Cristina & Sinha, Shruti, 2019. "Partial identification in matching models for the marriage market," TSE Working Papers 19-993, Toulouse School of Economics (TSE), revised Aug 2022.
    14. Bernard Salanié & Alfred Galichon, 2012. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Working Papers hal-01053710, HAL.
    15. Alberto Bisin & Giulia Tura, 2019. "Marriage, Fertility, and Cultural Integration of Immigrants in Italy," Working Papers 2019-063, Human Capital and Economic Opportunity Working Group.
    16. Dupuy, Arnaud & Kennes, John & Lyng, Ran Sun, 2021. "The Market for CEOs: Building Legacy and Feeling Empowered Matter," IZA Discussion Papers 14803, Institute of Labor Economics (IZA).
    17. 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.
    18. Marion Goussé & Nicolas Jacquemet & Jean-Marc Robin, 2016. "Marriage, Labor Supply, and Home Production: A Longitudinal Microeconomic Analysis of Marriage, Intra-Household Bargaining and Time Use Using the BHPS, 1991-2008," Cahiers de recherche 1601, CIRPEE.
    19. 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.
    20. Marion Goussé & Nicolas Jacquemet & Jean‐Marc Robin, 2017. "Marriage, Labor Supply, and Home Production," Econometrica, Econometric Society, vol. 85(6), pages 1873-1919, November.

    More about this item

    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:arx:papers:2106.02371. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://arxiv.org/ .

    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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.