Sorting in a General Equilibrium On-the-Job Search Model

In this paper, I analyze a general equilibrium on-the-job search model with endogenous search intensity and heterogenous workers and firms. I provide proof of existence and uniqueness of steady state equilibrium. In equilibrium equally efficient search on and off the job and supermodularity of the production function imply that higher skilled workers are matched with more productive firms in the sense that the steady state firm productivity distribution is stochastically increasing in worker skill. By implication, higher skilled workers on average match with more productive firms (that is, E[p|h] is increasing in h, where h is worker skill and p is firm productivity). In this sense, the positive assortative matching result in Becker (1973) is shown to generalize to this paper's search friction setting. However, the positive assortative matching result does not generalize given the reverse conditioning; it need not be that E[h|p] is everywhere increasing in p