An alternative to signaling: directed search and substitution

This paper analyzes a labor market, where (i) workers can acquire an observable skill at no cost, (ii) firms differ in unobserved productivity, (iii) workers' skill and firms' productivity are substitutes and (iv) firms' search is directed. The main result is that, if the entry cost of firms is small, no worker acquires the skill in the unique equilibrium. For intermediate entry costs, a positive measure of workers obtain the skill, and the number of skilled workers goes to one as entry costs become large. Welfare is highest when the entry cost is high.