Learning Under Ambiguity

Abstract

This paper considers learning when the distinction between risk and ambiguity (Knightian uncertainty) matters. Working within the framework of recursive multiple-priors utility, the paper formulates a counterpart of the Bayesian model of learning about an uncertain parameter from conditionally i.i.d. signals. Ambiguous signals capture differences in information quality that cannot be captured by noisy signals. They may increase the volatility of conditional actions and they prevent ambiguity from vanishing in the limit.

Properties of the model are illustrated with two applications. First, in a dynamic portfolio choice model, stock market participation costs arise endogenously from preferences and depend on past market performance. Second, ambiguous news induce negative skewness of asset returns and may increase price volatility. Shocks that trigger a period of ambiguous news induce a price discount on impact and are likely to be followed by further negative price changes.

Keywords: ambiguity, learning, multiple-priors, portfolio choice, stock market participation, asset pricing

JEL Classification: D81, D83, G11, G12