Assignment reversals: Trade, skill allocation and wage inequality

Understanding the allocation of skilled labor across industries is necessary to explain inter-industry wage differences and the effect of trade on wages. This paper develops an assignment model with both labor and non-labor inputs in which the assignment of heterogeneous labor across sectors is driven by variation in non-labor input productivity. A scale of operations effect causes high skill agents to work in high input productivity sectors where they can best leverage their talent. Growth in input productivity raises wage inequality by increasing the scope for leverage. If the ranking of sectors by input productivity differs across countries, their ranking by workforce skill and average wage also differs – this is an assignment reversal. In a two sector, two country model the existence of an assignment reversal implies that each country has a comparative advantage in its high skill sector. Consequently, trade integration causes both the relative wage of high skill workers, and wage inequality within the high skill sector, to increase in both countries. Evidence from industry wage data supports the existence of assignment reversals and shows that exogenous differences in capital productivity induced by a country’s relative proximity to major capital exporters cause inter-industry wage variation consistent with the model’s predictions. ∗I am grateful to Pol Antràs, Arnaud Costinot, Elhanan Helpman, Marc Melitz and Nathan Nunn for helpful comments and suggestions and to Eli Berman and Gianluca Violante for sharing data with me. †E-mail: [email protected]