Information and Volatility

Abstract

In an economy of interacting agents with both idiosyncratic and aggregate shocks, we examine how the structure of private information in‡fluences aggregate volatility. The maximal aggregate volatility is attained in a noise free information structure in which the agents confound idiosyncratic and aggregate shocks, and display excess response to the aggregate shocks, as in Lucas. For any given variance of aggregate shocks, the upper bound on aggregate volatility is linearly increasing in the variance of the idiosyncratic shocks. Our results hold in a setting of symmetric agents with linear best responses and normal uncertainty. We establish our results by providing a characterization of the set of all joint distributions over actions and states that can arise in equilibrium under any information structure. This tractable characterization, extending results in Bergemann and Morris, can be used to address a wide variety of questions linking information with the statistical moments of the economy.

Keywords: Incomplete Information, Bayes Correlated Equilibrium, Volatility, Moments Restrictions, Linear Best Responses, Quadratic Payoffs

JEL Classification: C72, C73, D43, D83