On rationally confident beliefs and rational overconfidence

The starting point for rational beliefs models is the existence of an empirical distribution for the stochastic process of observed exogenous and endogenous variables. Since the true, unknown stochastic process that generates this observed empirical distribution is only weakly asymptotic mean stationary (WAMS), i.e. not necessarily stationary, there are many possible processes that could have lead to this empirical distribution. The distribution of any process that is, in this sense, compatible with observations is called a rational belief. We provide a characterization of WAMS processes that among other things leads us to link rational beliefs and overconfidence: Rational beliefs exhibit rational confidence and, since different agents may hold different rational beliefs, the resulting diversity gives rise to rational overconfidence at the social level. In sum, the stylized facts of diversity of beliefs and overconfidence are replicated by rational belief models.