Estimating Matching Affinity Matrix Under Low-Rank Constraints

31 Pages Posted: 10 Jan 2017

See all articles by Arnaud Dupuy

Arnaud Dupuy

Centre de Recherche en Économie Appliquée (CREA)

Alfred Galichon

NYU, Department of Economics and Courant Institute

Yifei Sun

New York University (NYU) - Courant Institute of Mathematical Sciences

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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.

Keywords: inverse optimal transport, rank-constrained estimation, bipartite matching, marriage market

JEL Classification: C5, D3

Suggested Citation

Dupuy, Arnaud and Galichon, Alfred and Sun, Yifei, Estimating Matching Affinity Matrix Under Low-Rank Constraints. IZA Discussion Paper No. 10449, Available at SSRN: https://ssrn.com/abstract=2895297 or http://dx.doi.org/10.2139/ssrn.2895297

Arnaud Dupuy (Contact Author)

Centre de Recherche en Économie Appliquée (CREA) ( email )

Campus Limpertsberg
162A, avenue de la Faïencerie
Luxembourg, 1511
Luxembourg

Alfred Galichon

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Yifei Sun

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

251 Mercer Street
New York, NY - 10012
United States

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