The Spectral Approach to Linear Rational Expectations Models

Abstract

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to be a finite dimensional affine space in the frequency domain. It is demonstrated that solutions can be discontinuous with respect to the parameters of the models in the context of non-uniqueness, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability properties.

This is the final version of the paper accepted for publication at Econometric Theory. Please do not cite earlier versions as they contain errors that were corrected in the review process. I am grateful to Benedikt Pötscher and to three anonymous referees for the substantial improvements to the paper since it first appeared. Any remaining errors are my own responsibility

References in corpus (5)

• On the Factorization of Rational Discrete-Time Spectral Densities
• Quantitative results on continuity of the spectral factorization mapping
• Regularized Solutions to Linear Rational Expectations Models
• The Identification Problem for Linear Rational Expectations Models
• The Dimension of the Set of Causal Solutions of Linear Multivariate Rational Expectations Models

Cited by in corpus (1)

• Regularized Solutions to Linear Rational Expectations Models