To Match or Not To Match? Optimal Wage Policy with Variable Worker Search Intensity

We consider an equilibrium search model with on-the-job search where firms set wages. If employers are perfectly aware of all workers' job opportunities, then when an employee receives an outside job offer, it is optimal for his employer to try to retain him by matching the offer, so long as the resulting wage doesn't exceed the worker's productivity. A Bertrand competition is thus triggered between the incumbent employer and the "poacher", which 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 are induced 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. We derive sufficient conditions for the equilibrium to be of the sort "all firms match" or "no firm matches". Finally, computed examples show that, even though virtually any situation can be observed in equilibrium when the sufficient conditions are not met, 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.