Wages as signals of worker mobility

We analyze a model in which workers direct their search on and off the job and employer-worker match productivities are private information. Employers can commit neither to post contracts such that wages are a function of tenure nor to disregard counteroffers. In this context, potential employers who do not observe workers' productivity in their current matches use wages as a signal of workers' willingness to switch jobs. In turn, this implies that the wage contracts that employers post in the market for entry jobs --- the jobs unemployed workers search for --- not only direct job search but also signal future worker mobility. When the costs of creating entry jobs are sufficiently small, the unique equilibrium supports the efficient allocation under full information. When the costs of creating entry jobs are sufficiently large, the efficient equilibrium may break down because match-specific risk gives rise to a holdup problem in the market for entry jobs. Then, the unique equilibrium may fail to reveal match productivities in the market for entry jobs. The non-revealing equilibrium features wage posting --- pooling wage contracts --- as well as counteroffers, which eliminates the holdup problem at the cost of distorting worker mobility.