Competitive on-the-job search

The paper proposes a model of on-the-job search and industry dynamics in which search is directed. Firms permanently differ in productivity levels, their production function features constant returns to scale, and search costs are convex in search intensity. Wages are determined in a competitive manner, as firms advertise wage contracts (expected discounted incomes) so as to balance wage costs and search costs (queue length). Firms are assumed to sort out their coordination problems with their employees in such a way that the on-the-job search behavior of workers maximizes the match surplus. Our model has several novel features. First, it is close in spirit to the competitive model, with a tractable and unique equilibrium, and is therefore useful for empirical testing. Second, on-the-job search is an efficient response to firm heterogeneities and convex search costs. Third, the equilibrium leans towards a job ladder, where unemployed workers apply to low-productivity firms offering low wages, and then gradually move on to more productive, higher-paying firms. With a continuum of firm types, the job ladder is strict, in the sense that there is a one-to-one correspondence between the productivity of the current employer and that of the firms she searches for. The paper also contributes methodologically, as the existence proof requires a version of Schauder's fixed point theorem that is not commonly used by economists. Finally, our model offers different implications for the dynamics of job-to-job transitions than existing models of random search.