Informative tests in signaling environments

We study a receiver's learning problem of choosing an informative test in a signaling environment. Each test induces a signaling subgame. Thus, in addition to its direct effect on the receiver's information, a test has an indirect effect through the sender's signaling strategy. We show that the informativeness of signaling in the equilibrium that a test induces depends on the relative informativeness of the test's high and low grades. Consequently, we find that the receiver's preference relation over tests needs not comply with Blackwell's (1951) order. Our findings may shed light on phenomena such as grade inflation and information coarsening.