The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations

TL;DR

This paper investigates the nonuniqueness problem in linear rational expectations models, showing how appropriate parameter specification can ensure unique solutions and revealing overlooked dynamics in standard macroeconomic models.

Contribution

It clarifies the origin of nonuniqueness and proposes a method based on least-square forecast errors to select unique, dynamically consistent solutions.

Findings

Parameter choices determine solution uniqueness.

Least-square forecast errors lead to unique solutions.

Traditional solutions may suppress important dynamics.

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.