Wage offers and on-the-job search

We study the wage-setting problem of an employer with private information about demand for its product when workers can engage in costly on-the-job search. Employers understand that low wage offers may convey bad news that induces workers to search. The unique perfect sequential equilibrium wage strategy is characterized by: (i) pooling by intermediate-revenue employers on a common wage that just deters search, (ii) discontinuously lower revealing offers by low-revenue employers for whom the benefit of deterring search fails to warrant the required high pooling wage and (iii) high revealing offers by high-revenue employers seeking to deter aggressive raiders.