Post-Match Investment and Dynamic Sorting between Capital and Labor

53 Pages Posted: 11 Sep 2018 Last revised: 29 Feb 2020

See all articles by Shouyong Shi

Shouyong Shi

Pennsylvania State University

Date Written: August 29, 2018


By integrating frictional sorting into the neoclassical framework with post-match investment by firms, this paper analyzes the social optimum and the equilibrium. A main theoretical result is that post-match investment restores positive assortative matching (PAM) to the social optimum in the long run, but increases the likelihood of negative assortative matching (NAM) at the beginning of a match. The stronger is the complementarity between capital and the skill in production, the more likely is NAM to occur at the beginning of a match. I calibrate the model to show that sorting is NAM initially but becomes PAM on average over time. Workers with a higher skill have higher labor productivity and wages throughout the match. They also have steeper time profiles of these variables. There is sizable within-skill inequality in labor productivity and wages. Moreover, an increase in the matching efficiency reduces the labor share and increases the skill premium.

Keywords: Dynamic sorting, Investment, Inequality

JEL Classification: E22, J60, C78

Suggested Citation

Shi, Shouyong, Post-Match Investment and Dynamic Sorting between Capital and Labor (August 29, 2018). Available at SSRN: or

Shouyong Shi (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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