Markets (III): signaling in the labor market

In this section, we study a stylized model of signaling in the labor market that is based on the influential work of Spence (1973, 1974). Informally described, the setup is as follows. Two identical firms sell a certain homogeneous good whose price is fixed. The sole dimension in which firms compete concerns the wage they offer to the only worker available. The ability (or competence) of this worker in undertaking the required tasks is known only to herself. However, despite the fact that firms do not observe the worker's ability, they do observe her education level. The key assumption in this respect is that the cost incurred by the worker in attaining her particular level of education depends on her ability. Specifically, it is supposed that this cost is lower the higher is her ability. In this context, the following natural question is posed: Is it possible to have (as an equilibrium) a situation in which the worker, depending on her ability, chooses different education levels? If so, the ability and education level of the worker must be positively correlated, workers with different education levels also obtaining different equilibrium wages. The education level may then be seen as playing the role of a (credible) signal of the underlying ability, even if the education per se has no influence on productivity.

To study these issues formally, we formulate a game involving a single worker, two firms, and Nature that displays the following four stages:

1. Nature selects the worker's type, which is identified with her ability θ.