Consistency of linear forecasts in a nonlinear stochastic economy

The notion of consistent expectations equilibrium is extended to economies that are described by a nonlinear stochastic system. Agents in the model do not know the nonlinear law of motion and use a simple linear forecasting rule to form their expectations. Along a stochastic consistent expectations equilibrium (SCEE), these expectations are correct in a linear statistical sense, i.e., the unconditional mean and autocovariances of the actual (but unknown) nonlinear stochastic process coincide with those of the linear stochastic process on which the agents base their beliefs. In general, the linear forecasts do not coincide with the true conditional expectation, but an SCEE is an ‘approximate rational expectations equilibrium’ in the sense that forecasting errors are unbiased and uncorrelated. Adaptive learning of SCEE is studied in an overlapping generations framework.