Incomplete Wage Posting

We consider a competitive search model where firms with vacancies choose between posting a wage ex ante and bargaining it with workers ex post. Workers apply for vacancies after observing firms' wage setting decisions, and differ in some observable but not verifiable qualifications that affect their productivity in the job. Thus posted wages prevent the hold-up problem associated with bargaining but are incomplete since they cannot be contingent on worker qualifications. In contrast, bargained wages are increasing in them and, thus, may serve to entice better workers into the vacancy. We find that when the hold-up problem is mild and workers' heterogeneity is large, firms opt for bargaining. Yet, equilibria with bargaining always fail to maximize aggregate net income and sometimes fail to be constrained Pareto optimal.