Incomplete Wage Posting

We consider a directed search model in which workers differ in productivity. Productivity becomes observable to firms after assessing their workers on the job, but it is not verifiable. Firms with vacancies choose between posting a noncontingent wage and leaving wages subject to bargaining with the worker. Under wage bargaining, firms cannot optimize the trade‐off between paying higher wages and having a larger probability of filling vacancies. But wage bargaining makes wages increasing in worker productivity and so may allow firms to attract better workers into the vacancy. When workers’ heterogeneity is large and bargaining powers come close to satisfying Hosios’s rule, firms opt for bargaining. Yet, equilibria with bargaining fail to maximize aggregate net income and sometimes are not constrained Pareto optimal.