IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp10449.html

Estimating Matching Affinity Matrix under Low-Rank Constraints

Author

Listed:
  • Dupuy, Arnaud

    (University of Luxembourg)

  • Galichon, Alfred

    (New York University)

  • Sun, Yifei

    (New York University)

Abstract

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory species the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix. The lowrank matrix estimated in this way reveals the main factors which are relevant for matching.

Suggested Citation

  • Dupuy, Arnaud & Galichon, Alfred & Sun, Yifei, 2016. "Estimating Matching Affinity Matrix under Low-Rank Constraints," IZA Discussion Papers 10449, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp10449
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp10449.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    2. 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.
    3. David Lam & Robert F. Schoeni, 1994. "Family Ties and Labor Markets in the United States and Brazil," Journal of Human Resources, University of Wisconsin Press, vol. 29(4), pages 1235-1258.
    4. repec:spo:wpmain:info:hdl:2441/361levbcs399s9oa154em6h9jl is not listed on IDEAS
    5. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    6. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    7. Gautier, Pieter A. & Svarer, Michael & Teulings, Coen N., 2010. "Marriage and the city: Search frictions and sorting of singles," Journal of Urban Economics, Elsevier, vol. 67(2), pages 206-218, March.
    8. Donkers, Bas & van Soest, Arthur, 1999. "Subjective measures of household preferences and financial decisions," Journal of Economic Psychology, Elsevier, vol. 20(6), pages 613-642, December.
    9. Lam, David & Schoeni, Robert F, 1993. "Effects of Family Background on Earnings and Returns to Schooling: Evidence from Brazil," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 710-740, August.
    10. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," Post-Print hal-03470458, HAL.
    11. Abhijit Banerjee & Esther Duflo & Maitreesh Ghatak & Jeanne Lafortune, 2013. "Marry for What? Caste and Mate Selection in Modern India," American Economic Journal: Microeconomics, American Economic Association, vol. 5(2), pages 33-72, May.
    12. Pierre-André Chiappori & Sonia Oreffice & Climent Quintana-Domeque, 2020. "Erratum: Fatter Attraction: Anthropometric and Socioeconomic Matching on the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 128(12), pages 4673-4675.
    13. Lisa Jepsen, 2005. "The Relationship Between Wife’s Education and Husband’s Earnings: Evidence from 1960 to 2000," Review of Economics of the Household, Springer, vol. 3(2), pages 197-214, June.
    14. 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..
    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. Arnaud Dupuy & Alfred Galichon, 2012. "Canonical Correlation and Assortative Matching: a remark," Working Papers 2012/40, Maastricht School of Management.
    2. 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.
    3. 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.
    4. Barban, Nicola & De Cao, Elisabetta & Oreffice, Sonia & Quintana-Domeque, Climent, 2021. "The effect of education on spousal education: A genetic approach," Labour Economics, Elsevier, vol. 71(C).
    5. repec:spo:wpmain:info:hdl:2441/45je9bvs5880japj06cptntfoa is not listed on IDEAS
    6. Sinha, Shruti, 2018. "Identification in One-to-One Matching Models with Nonparametric Unobservables," TSE Working Papers 18-897, Toulouse School of Economics (TSE).
    7. Alfred Galichon & Bernard Salani'e, 2021. "Structural Estimation of Matching Markets with Transferable Utility," Papers 2109.07932, arXiv.org.
    8. repec:spo:wpmain:info:hdl:2441/38n7438p68vmqd9om4bjj6l4c is not listed on IDEAS
    9. 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.
    10. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.
    11. Arnaud Dupuy & Alfred Galichon, 2012. "Canonical Correlation and Assortative Matching: A Remark," Sciences Po Economics Publications (main) hal-03568988, HAL.
    12. repec:spo:wpmain:info:hdl:2441/10gq8jbaid85sben727o7nd22a is not listed on IDEAS
    13. Arnaud Dupuy, 2021. "Migration in China: To work or to wed?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(4), pages 393-415, June.
    14. Arnaud Dupuy & Alfred Galichon, 2012. "Canonical Correlation and Assortative Matching: A Remark," Post-Print hal-03568988, HAL.
    15. Alfred Galichon & Bernard Salanié, 2023. "Structural Estimation of Matching Markets with Transferable Utility," Post-Print hal-03935865, HAL.
    16. Arnaud Dupuy & Alfred Galichon, 2012. "Canonical Correlation and Assortative Matching: A Remark," SciencePo Working papers hal-03568988, HAL.
    17. Carlier, Guillaume & Dupuy, Arnaud & Galichon, Alfred & Sun, Yifei, 2021. "SISTA: Learning Optimal Transport Costs under Sparsity Constraints," IZA Discussion Papers 14397, Institute of Labor Economics (IZA).
    18. Jérôme Adda & Paolo Pinotti & Giulia Tura, 2025. "There’s More to Marriage Than Love: The Effect of Legal Status and Cultural Distance on Intermarriages and Separations," Journal of Political Economy, University of Chicago Press, vol. 133(4), pages 1276-1333.
    19. Dan Anderberg & Jesper Bagger & V. Bhaskar & Tanya Wilson, 2019. "Marriage market equilibrium, qualifications, and ability," CESifo Working Paper Series 7570, CESifo.
    20. You, Jing & Yi, Xuejie & Chen, Meng, 2021. "Love, life, and “leftover ladies” in urban China: Staying modernly single in patriarchal traditions," China Economic Review, Elsevier, vol. 68(C).
    21. 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.
    22. Lippmann, Quentin & Surana, Khushboo, 2025. "The evolution of partner preferences: Evidence using matrimonial ads from Canada, France, India and the United States," Journal of Economic Behavior & Organization, Elsevier, vol. 233(C).
    23. Dupuy, Arnaud & Galichon, Alfred, 2017. "A Note on the Estimation of Job Amenities and Labor Productivity," IZA Discussion Papers 10900, Institute of Labor Economics (IZA).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • D3 - Microeconomics - - Distribution

    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:iza:izadps:dp10449. 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: Holger Hinte (email available below). General contact details of provider: https://edirc.repec.org/data/izaaade.html .

    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.