The more we know, the less we agree: Public announcements, higher-order expectations and rational inattention

Why do announcements of public information set o¤ a frenzy of trading? Usually, public information brings beliefs closer to each other. With less disagreement, there should be less reason to trade. I highlight two novel properties of certain Gaussian information structures and show that they explain hectic and informative trading around announcements. First, announcements can lead to contrarian higher-order expectations. That is, the more optimistic an agent is regarding the fundamental value, the more pessimistic she is regarding the expectations of others. Second, the announcements can polarize higher-order expectations. That is, the announcement can increase the dispersion of expectations regarding the expectations of others. An information structure with both properties is the equilibrium outcome in a Grossman-Stiglitz type asset pricing model, where agents are subject to rational inattention.