Resumen

We consider a signaling model in which firms not only observe the worker's costly signal, but may also acquire information. The worker's productivity depends on his type (innate skills) as well as his quality (the match between the worker and the firm). A good-type worker is more likely to be a better fit for a firm, but it will not be necessarily so. While the worker's quality is initially unknown to both the worker and the firm, the type is private information, and can be communicated through the choice of a costly action, e.g. the education level. The firm might complement this information by performing a test to learn the match between the worker and the firm. We model the firm's information acquisition problem using the rational inattention approach. That is, we allow the firm to choose any information structure with no restriction on a particular signal distribution, and with a cost proportional to the entropy between prior and posterior beliefs. In equilibrium, the firm will prefer more informative signals when beliefs are intermediate. More importantly, beliefs are determined by the costly action chosen by the worker through signaling. We characterize the set of Perfect Bayesian Equillibria that satisfy the divinity criterion (D1). We show that workers fully disclose their type up to intermediate beliefs about quality. In particular, the LCSE is the only equilibrium when the expected match between the firm and the worker is low, even for the good-type. In that case, most of the information acquisition is left to the firm. Tests will be more sofisticated when beliefs about the worker-firm match are pessimistic. Thus bad-type workers will be dissuaded from mimicking good-type education level in order to avoid a more precise test. The opposite happens when the expected fit is high even for the bad type. When beliefs are sufficiently optimistic, firms relax their standards. This is more beneficial for the bad-type worker who prefers to shroud information and pool with the good-type worker. Pooling is then the only equilibrium. Finally, when bad-type workers have low expected fit, and good-type ones have high expected fit, the equilibrium is semipooling. The good type partially signals its type, while the bad-type worker randomizing between no education and signaling.