Market Signaling with Grades

 We consider a market signaling game in which the market observes both the sender's costly signal as well as a stochastic grade that is correlated with the sender's type.  In equilibrium, the sender resolves the tradeoff between using the costly signal versus relying on the noisy grade to distinguish himsel. When the test is sufficiently informative, separating equilibria do not survive---the mere presence of an informative test necessitates pooling. Unlike gradeless models, the prediction depends on the prior---it involves full pooling when the prior puts sufficient weight on the high type and partial pooling otherwise. The equilibrium converges to the fully efficient outcome as the proportion of high types goes to one---resolving a long-standing paradox within the signaling literature.