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Estimating Matching Affinity Matrix under Low-Rank Constraints

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  • 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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    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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