Learning and informational stability of dynamic REE with incomplete information

In the context of dynamic models of incomplete information, we show that slight perturbations to the agents' information sets can lead to vastly different Rational Expectations Equilibria (REE). The difference is due to a hidden instability (i.e., an exact cancellation of an explosive autoregressive root) that is a property of the full-information equilibrium but not present in the partial-information equilibrium. Due to the multitude of potential equilibria, we use least-squares learnability as a refinement mechanism. We find that models with complete information revelation are not least-squares learnable, while information structures that do not fully reveal the underlying shocks are learnable. We show that learnability relates to the informational stability properties of an equilibrium, whereby an equilibrium is said to be informationally unstable if it vanishes when information is slightly perturbed. We present application to a model with productivity shocks and nominal rigidities. In both cases we show that equilibria with complete information are informationally unstable, and thus not learnable; while equilibria that preserve incomplete information are informationally stable and learnable.