A consistent route to randomness

Fully rational agents are allowed to optimize over expectations formation technologies in an environment where it is costly to collect and process information. It is shown in a general equilibrium framework that optimization over expectations by rational and forward-oriented agents can lead to endogenous instability. Specifically, we illustrate that resulting equilibria can be both chaotic and self-consistent with the distribution of agents' expected forecasting errors coinciding with the actual errors implied by the endogenous dynamic process. Moreover, we show that the equilibrium dynamics, while being purely deterministic, need not be distinguishable from stochastic dynamics to an outside rational observer.