Sorting by search intensity

In this paper, I analyze a general equilibrium on-the-job search model with endogenous search intensity and heterogenous workers and firms. Wages are set through bargaining as in Cahuc, Postel-Vinay, and Robin (2006). I provide proof of existence and uniqueness of steady state equilibrium. Given equally efficient search on and off the job, I provide proof that the equilibrium firm productivity distribution is stochastically increasing (decreasing) in worker skill if the match production function is supermodular (submodular). By implication, if the production function is supermodular (submodular) high skill workers on average match with more (less) productive firms. I also show that this strong notion of sorting does not obtain everywhere for the reverse conditioning.