Signaling Through Tests

A firm, privately informed about product quality, chooses a public test. Tests vary in expertise, and return a binary result. A competitive market generates interim beliefs based on expertise and posteriors based on test results. We show that standard single-crossing does not hold. Higher expertise is less costly to the high type, who fails the test less often, while better interim beliefs may benefit either the high or the low type depending on the prior. When firm’s expected quality is low, an increase in beliefs makes the receiver more sensitive to test results, so that the high type has more incentives to choose a test with higher expertise and at least separation occurs. When firm’s expected quality is high, a further increase in beliefs makes the receiver less sensitive to test results, and the unique equilibrium is pooling with both types choosing a test with intermediate level of expertise