Bayesian learning with catastrophe risk : information externalities in a large economy
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Based on a previous study by Amador and Weill (2009), I study the diffusion of dispersed private information in a large economy subject to a ”catastrophe risk” state. I assume that agents learn from the actions of oth- ers through two channels: a public channel, that represents learning from prices, and a bi-dimensional private channel that represents learning from lo- cal interactions via information concerning the good state and the catastrophe probability. I show an equilibrium solution based on conditional Bayes rule, which weakens the usual condition of ”slow learning” as presented in Amador and Weill and first introduced by Vives (1993). I study asymptotic conver- gence ”to the truth” deriving that ”catastrophe risk” can lead to ”non-linear” adjustments that could in principle explain fluctuations of price aggregates. I finally discuss robustness issues and potential applications of this work to models of ”reaching consensus”, ”investments under uncertainty”, ”market efficiency” and ”prediction markets”.