Testing the sender: When signaling is not enough

A worker, privately informed about his fit with a firm, chooses an action to signal this information. The firm might perform a test and decides whether to hire the worker. We define firm effectiveness as the difference between the optimal probabilities of hiring a good-fit and a bad-fit worker, and show that it has an inverted U-shape with respect to beliefs. When the worker's expected fit is low, firm effectiveness is increasing in beliefs, and information is revealed through both signaling and information acquisition. Since the high type is more likely to pass a more exacting test, he will exert costly effort to improve firm's beliefs. When, on the other hand, the worker's expected fit is high, firm effectiveness is decreasing in beliefs and any signaling effort made by the high type would be mimicked by the low type, who benefits more from relaxed standards, so that information is generated exclusively by the firm through tests.