Asymptotic Learning with Ambiguous Information

We study asymptotic learning when the decision-maker faces ambiguity in the precision of her information sources. She aims to estimate a state and evaluates outcomes according to the worst-case scenario. Under prior-by-prior updating, we characterize the set of asymptotic posteriors the decision-maker entertains, which consists of a continuum of degenerate distributions over an interval. Moreover, her asymptotic estimate of the state is generically incorrect. We show that even a small amount of ambiguity may lead to large estimation errors and illustrate how an econometrician who learns from observing others' actions may over- or underreact to information. (JEL D82, D83)