Burdett-Mortensen model of on-the-job search with two sectors

The focus of this paper is on the steady state of a two-sector economy with undirected search where employed and unemployed workers can search for jobs, both within a sector and between the sectors. As in the one-sector model, on-the-job search generates wage dispersion among homogeneous workers. The analysis of the two-sector model uncovers a property called constant tension that is responsible for analytical tractability. We characterize the steady state in all cases with constant tension. When time discounting vanishes, constant tension yields the endogenous separation rate in each sector as a linear function of the present value for a worker. The one-sector economy automatically satisfies constant tension, in which case the linear separation rate implies that equilibrium offers of the worker value are uniformly distributed. Constant tension also has strong predictions for worker transitions and value/wage dispersion, both within a sector and between the two sectors. When constant tension does not hold, we compute the steady state numerically and illustrate its properties.