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

TL;DR

This paper develops a flexible, empirically tractable multidimensional matching model using optimal transport theory, allowing for unrestricted characteristic distributions and improving understanding of wage inequality and technological progress.

Contribution

It generalizes previous parametric models by removing normality assumptions, providing identification and efficient estimation methods for complex matching models.

Findings

Revised estimates show greater technological progress favoring cognitive skills between 1990 and 2010.

Flexible models better fit observed patterns in wage inequality evolution.

Empirical application revises previous conclusions on technological change.

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.