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 a multi-sector assignment model with both heterogeneous labor and a non-labor input in which high skill agents match with high input productivity sectors where they can best leverage their talent. When the ranking of sectors by input productivity differs across countries, their ranking by workforce skill 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. Using exogenous differences in capital productivity induced by a country's proximity to major capital exporters the paper shows that international variation in the industry wage structure supports the existence of assignment reversals and is consistent with the model's sorting predictions.