Market signaling with grades

We consider a signaling model in which receivers observe 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 trade-off between using the costly signal versus relying on the noisy grade to distinguish himself. We derive a necessary and sufficient condition-loosely, that the grade is sufficiently informative relative to the dispersion of (marginal) signaling costs across types-under which the presence of grades substantively alters the equilibrium predictions. Specifically, separating equilibria do not survive stability-based refinements. Instead, the prediction depends on the prior distribution over the sender's type. For example, with two types it involves full pooling when the distribution places sufficient weight on the high type and partial pooling otherwise. Finally, the equilibrium converges to the complete-information outcome as the distribution tends to a degenerate one-resolving a long-standing paradox within the signaling literature.