The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations

Abstract

The nonuniqueness of rational expectations is explained: in the stochastic, discrete-time, linear, constant-coefficients case, the associated free parameters are coefficients that determine the public's most immediate reactions to shocks. The requirement of model-consistency may leave these parameters completely free, yet when their values are appropriately specified, a unique solution is determined. In a broad class of models, the requirement of least-square forecast errors determines the parameter values, and therefore defines a unique solution. This approach is independent of dynamical stability, and generally does not suppress model dynamics. Application to a standard New Keynesian example shows that the traditional solution suppresses precisely those dynamics that arise from rational expectations. The uncovering of those dynamics reveals their incompatibility with the new I-S equation and the expectational Phillips curve.