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Semi-nonparametric models of multidimensional matching: an optimal transport approach

Dongwoo Kim, Young Jun Lee

arXiv 28 May 2024 · Econometrics · publishedJournal of Econometrics (2026)

arXiv:2405.18089 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper proposes empirically tractable multidimensional matching models, focusing on worker-job matching. We generalize the parametric model proposed by Lindenlaub (2017), which relies on the assumption of joint normality of observed characteristics of workers and jobs. In our paper, we allow unrestricted distributions of characteristics and show identification of the production technology, and equilibrium wage and matching functions using tools from optimal transport theory. Given identification, we propose efficient, consistent, asymptotically normal sieve estimators. We revisit Lindenlaub's empirical application and show that, between 1990 and 2010, the U.S. economy experienced much larger technological progress favoring cognitive abilities than the original findings suggest. Furthermore, our flexible model specifications provide a significantly better fit for patterns in the evolution of wage inequality.

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55
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Lindenlaub, Ilse (2017) Sorting Multidimensional Types: Theory and Application0.96035889%
2Ai, Chunrong and Xiaohong Chen (2003) Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions0.9416383%
3Villani, Cédric (2008) Optimal Transport: Old and New0.81142100%
4Chen, Xiaohong (2007) Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models, Elsevier, vol. 6 of0.77615447%
5Becker, Gary S (1973) A Theory of Marriage: Part I0.64422100%
6Caffarelli, Luis A (1992) a): Boundary regularity of maps with convex potentials0.64422100%
7Caffarelli, Luis A (1992) b): The regularity of mappings with a convex potential0.64422100%
8Caffarelli, Luis A (1996) Boundary regularity of maps with convex potentials–II0.64422100%
9Chiappori, Pierre-André, Robert J McCann, and Lars P Nesheim (2010) Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness0.64422100%
10Cordero-Erausquin, Dario and Alessio Figalli (2019) Regularity of monotone transport maps between unbounded domains0.64422100%

Showing the top 10 of 55 scored citations.