Working Paper: NBER ID: w29290
Authors: Job Boerma; Aleh Tsyvinski; Alexander P. Zimin
Abstract: We fully solve an assignment problem with heterogeneous firms and multiple heterogeneous workers whose skills are imperfect substitutes, that is, when production is submodular. We show that sorting is neither positive nor negative and is characterized sufficiently by two regions. In the first region, mediocre firms sort with mediocre workers and coworkers such that output losses are equal across all these pairings (complete mixing). In the second region, high skill workers sort with a low skill coworker and a high productivity firm, while high productivity firms employ a low skill worker and a high skill coworker (pairwise countermonotonicity). The equilibrium assignment is also necessarily characterized by product countermonotonicity, meaning that sorting is negative for each dimension of heterogeneity with the product of heterogeneity in the other dimensions. The equilibrium assignment as well as wages and firm values are completely characterized in closed form. We illustrate our theory with an application to show that our model is consistent with the observed dispersion of earnings within and across U.S. firms. Our counterfactual analysis gives evidence that the change in the firm project distribution between 1981 and 2013 has a larger effect on the observed change in earnings dispersion than the change in the worker skill distribution.
Keywords: No keywords provided
JEL Codes: E0; J0
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| mediocre firms sort with mediocre workers (L29) | output losses are equal across these pairings (F11) |
| high-skill workers paired with low-skill coworkers at high-productivity firms (J24) | pairwise countermonotonicity (C72) |
| increased firm productivity (D21) | decreased product of worker skills (J24) |
| changes in firm project distribution (1981-2013) (D39) | changes in earnings dispersion (J31) |
| sorting mechanisms (C69) | observed variations in earnings (J31) |