This paper identifies a data-consistent, equilibrium model of unemployment, wage dispersion, quit turnover and firm growth dynamics. In a separating equilibrium, more productive firms signal their type by paying strictly higher wages in every state of the market. Workers optimally quit to firms paying a higher wage and so move effciently from less to more productive firms. Start-up firms are initially small and grow endogenously over time. Consistent with Gibrat's law, individual firm growth rates depend on firm productivity but not on firm size. Aggregate unemployment evolves endogenously. Restrictions are identified so that the model is consistent with empirical wage distributions.