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Imperfect Signaling and the Local Credibility Test

In this paper we study equilibrium refinement in signaling models. We propose a Local Credibility Test (LCT) that is somewhat stronger than the Cho and Kreps Intuitive Criterion but weaker than the refinement concept proposed by Grossman and Perry. Allowing deviations by a pool of “nearby” types, the LCT gives consistent solutions for any positive, though not necessarily perfect correlation between the signal sender’s true types (e.g., signaling cost) and the value to the signal receiver (e.g., marginal product). Furthermore, it avoids selecting separating equilibria when they do not make sense. We identify conditions for an equilibrium to satisfy the LCT in both the finite and continuous type cases, and demonstrate that the conditions are identical as we take the limit in the finite type case. Intuitively, the conditions for an equilibrium to survive our LCT test require that a measure of signaling “effectiveness” is sufficiently high for every type and that the type distribution is not tilted upwards too much. We then apply the characterization results to several signaling applications.