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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    5. 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.
    6. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    7. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    8. 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.
    9. Pierre-André Chiappori & Sonia Oreffice & Climent Quintana-Domeque, 2012. "Fatter Attraction: Anthropometric and Socioeconomic Matching on the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 120(4), pages 659-695.
    10. 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.
    11. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," Post-Print hal-03470458, HAL.
    12. 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.
    13. 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..
    14. repec:hal:spmain:info:hdl:2441/361levbcs399s9oa154em6h9jl is not listed on IDEAS
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    More about this item

    Keywords

    inverse optimal transport; rank-constrained estimation; bipartite matching; marriage market;
    All these keywords.

    JEL classification:

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

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