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THE SPECTRAL APPROACH TO LINEAR RATIONAL EXPECTATIONS MODELS

Published online by Cambridge University Press:  12 November 2024

Majid M. Al-Sadoon Open the ORCID record for Majid M. Al-Sadoon [Opens in a new window]
Majid M. Al-Sadoon*
Affiliation:
Durham University Business School
*
Address correspondence to Majid M. Al-Sadoon, Department of Economics, Durham University Business School, Durham, UK; e-mail: majid.al-sadoon@durham.ac.uk.
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Abstract

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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 nonuniqueness, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability properties.

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ARTICLES
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Econometric Theory , Volume 42 , Issue 1 , February 2026 , pp. 135 - 191
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

Thanks are due to Todd Walker, Bernd Funovits, Mauro Bambi, Piotr Zwiernik, Abderrahim Taamouti, Benedikt Pötscher, three anonymous referees, and seminar participants at Heriot-Watt University, Universitat Pompeu Fabra, University of Bologna, and Aarhus University.

References

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