A Theory of Firm Wage Dynamics

We develop a theory of firm wage dynamics that integrates the canonical wage-posting model à la Burdett and Mortensen (1998) with firm dynamics. Firms offer dynamic wage contracts under an equal-treatment constraint in the presence of search frictions. We provide an analytical characterization of equilibrium wage contracts and firm growth as functions only of the distribution of marginal surplus. Consistent with recent empirical evidence, the model implies that (i) firm wages are strongly linked to firm growth but not to firm size; (ii) firm wages decline over the firm life cycle; and (iii) the pass-through of permanent productivity shocks to wages is higher in the short run than in the long run. Firms at the top of the job ladder face excessive labor market competition, so the optimal policy subsidizes their hiring. At the macro level, the optimal policy elevates business dynamism in the steady state, and even more so along the transition.