Bayesian Social Learning in a Dynamic Environment

Bayesian agents learn about a moving target, such as a commodity price, using private signals and their network neighbors' estimates. The weights agents place on these sources of information are endogenously determined by the precisions and correlations of the sources; the weights, in turn, determine future correlations. We study stationary equilibria\textemdash ones in which all of these quantities are constant over time. Equilibria in linear updating rules always exist, yielding a Bayesian learning model as tractable as the commonly-used DeGroot heuristic. Equilibria and the comparative statics of learning outcomes can be readily computed even in large networks. Substantively, we identify pervasive inefficiencies in Bayesian learning. In any stationary equilibrium where agents put positive weights on neighbors' actions, learning is Pareto inefficient in a generic network: agents rationally overuse social information and underuse their private signals.