Directed Search with Complementarity and Adverse Selection

I study a model in which firms invest in capital and post wages, and heterogeneous workers, who have private information about their skills, choose where to apply. Workers and firms match bilaterally. Each matched agent gets an exogenous payoff from the match before wages are paid. Each of these payoffs displays complementarity in capital and skill. I derive conditions under which the market exhibits PAM, positive assortative matching. Under these conditions, the firms over-invest in capital compared to the first best, because capital is used as a screening device.I show that the fact that firms need to screen workers in the presence of private information changes the predictions of the model compared to that in the presence of complete information. In particular, I show that the market economy exhibiting PAM is not necessary nor sufficient for the complete information allocation to exhibit PAM