Dynamic Multivariate Learning with Generalized Information

Abstract

Agents are generally uncertain about multiple, and possibly time-varying, structural parameters that drive consumption and financial payoffs but learn through noisy correlated signals, such as aggregate or macroeconomic news. We find that dynamic learning of multivariate time-varying parameters with correlated signals generates endogenous long-run risks resulting in large and never-decaying equity risk premium. In general, the risk premium is driven by intertemporal co-uncertainty, that is, the dynamic covariance of posterior means, rather than uncertainty (i.e., variance of beliefs) that is highlighted in the literature. Signal correlation structure plays a crucial role in the dynamics of beliefs and asset prices and hence the determination of the equity premium. Apart from its quantitative implications, signal correlation generates non-monotone effects of information quality on the equity premium. We also present empirical evidence of the prevalence of highly correlated signals. Our general learning framework highlights the economic effects of correlated signals on Bayesian learning.