We consider an equilibrium search model with on-the-job search where firms set wages. When an employee receives an outside job offer, it is optimal for the employer to try to retain the employee by matching the offer. This results in a wage increase for the worker. However, if workers are able to vary their search intensity, then this ‘offer-matching’ policy runs into a moral hazard problem. Knowing that outside offers lead to wage increases, workers tend to search more intensively, which is costly for the firms. Assuming that firms can commit never to match outside offers, we examine the set of firm types for which it is preferable to do so. In particular, we show that a plausible pattern is one where a ‘dual’ labor market emerges, with ‘bad’ jobs at low-productivity, nonmatching firms and ‘good’ jobs at high-productivity, matching firms.