Wage bargaining and turnover costs with heterogenous labor and perfect history screening

We study effects of mobility costs in a model of (Nash) wage bargaining between workers and firms, with instantaneous matching, heterogeneous workers, identical firms and free firm entry, and where firms can screen workers perfectly according to their previous work history but not their actual productivity. We derive the employment level and the minimum worker quality standard, in the market solution, and in the efficient solution established by a social planner. When workers have positive bargaining power, there is always some inefficient unemployment among desired workers in the market solution. The lowest hiring standard chosen by firms is higher than the planner's standard when firing costs are high relative to hiring costs, but may be lower in the opposite case. We show that any higher established hiring standard corresponds to a market equilibrium. The model explains a tendency for a high initial unemployment rate to remain high, particularly for low-skilled workers.