Equilibrium Labor Turnover, Firm Growth and Unemployment

This paper considers a labor market employers differ in productivity, which is private information, and face hiring costs. Each employer sets its current wage but does not commit to future wages. Workers search on the job for better paid employment. A signalling equilibrium is show to exist and characterized in which more productive firms pay higher wages in every state of the market and workers transit from less to more productive employers. There is firm turnover: new small start-up firms are created while some existing firms die. Consistent with Gibrat's law, firm growth rates are size independent but increase with firm productivity (which evolves stochastically). With endogenous aggregate job creation rates and job-to-job transitions, the model provides a rich, coherent, non-steady state framework of equilibrium wage formation and worker flows. Existence of a steady state equilibrium for any finite number of firm productivity types is established. Steady state is unique when firm productivity is permanent and there are many firm types. A unique non-steady state equilibrium exists in the case of one type. In the general case, a unique equilibrium can be established when the elasticity of the hire rate with respect to productivity is sufficiently small.