A Brownian Motion Foundation for Informational Diversity and Proximity, with Application to Rational Expectations Equilibrium.

Abstract

We propose a tractable new informational framework for large economies with informationally heterogeneous individuals, and then apply it to analyze rational expectations equilibria. Our framework subsumes both public and conditionally independent private signals as special cases, but most importantly captures informational geography and social network effects. Our approach is to identify agents in a formally static world with moments in time: Agent t's signal is then a time-t realization of a Gaussian stochastic process with a known covariance function and uncertain mean. Individuals differ by their social weighting function used in this stochastic process. As an application, we explore rational expectations equilibria with conditionally correlated information. We find that the behaviour of prices and investors substantially differs from the world with conditionally independent signals. For instance, an agent's price impact is no longer solely determined by her signal's precision. Furthermore, investors may trade against their information and, in particular, rationally trade on different sides of the market at a public announcement. In a focal example of a circular world, we explore how correlation affects market efficiency and expected prices. We find, for instance, that for a fixed precision of individual signals, prices convey less information as the quality of aggregate information improves, provided the signal correlation is high enough.