Consistent expectations and misspecification in stochastic non-linear economies

This paper generalizes existence results on first-order Stochastic Consistent Expectations Equilibria (SCEE) obtained by Hommes et al. (Learning to Believe in Linearity in an Unknown Nonlinear Stochastic Economy, 2002). We present a stochastic non-linear self-referential model in which expectations are based on linear perceptions. In an SCEE the sample mean and correlation coefficients of the true and perceived processes coincide. We provide conditions on the non-linear maps governing the stochastic process that are sufficient to establish existence of SCEE. Our approach defines a map that takes linear perceptions to actual outcomes in such a way that fixed points of this map are SCEE; by establishing existence of fixed points, we are able to demonstrate existence of SCEE. Stability of SCEE under real-time learning is analyzed numerically.