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The Linear Systems Approach To Linear Rational Expectations Models

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  • Al-Sadoon, Majid M.

Abstract

This paper considers linear rational expectations models from the linear systems point of view. Using a generalization of the Wiener-Hopf factorization, the linear systems approach is able to furnish very simple conditions for existence and uniqueness of both particular and generic linear rational expectations models. To illustrate the applicability of this approach, the paper characterizes the structure of stationary and cointegrated solutions, including a generalization of Granger’s representation theorem.

Suggested Citation

  • Al-Sadoon, Majid M., 2018. "The Linear Systems Approach To Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 34(3), pages 628-658, June.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:03:p:628-658_00
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    Citations

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    Cited by:

    1. Tan, Fei, 2018. "A Frequency-Domain Approach to Dynamic Macroeconomic Models," MPRA Paper 90487, University Library of Munich, Germany.
    2. Zadrozny, Peter A., 2022. "Linear identification of linear rational-expectations models by exogenous variables reconciles Lucas and Sims," CFS Working Paper Series 682, Center for Financial Studies (CFS).
    3. Piotr Zwiernik & Majid M. Al-Sadoon, 2019. "The Identification Problem for Linear Rational Expectations Models," Working Papers 1114, Barcelona School of Economics.
    4. Alexander Meyer-Gohde, 2025. "Solving Linear DSGE Models with Bernoulli Iterations," Computational Economics, Springer;Society for Computational Economics, vol. 66(1), pages 593-643, July.
    5. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
    6. Marco M. Sorge, 2020. "Arbitrary initial conditions and the dimension of indeterminacy in linear rational expectations models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 363-372, June.
    7. Al-Sadoon, Majid M., 2019. "Testing subspace Granger causality," Econometrics and Statistics, Elsevier, vol. 9(C), pages 42-61.
    8. Han, Zhao & Tan, Fei & Wu, Jieran, 2022. "Analytic policy function iteration," Journal of Economic Theory, Elsevier, vol. 200(C).
    9. Bernd Funovits, 2020. "Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation," Papers 2002.04346, arXiv.org, revised Feb 2021.
    10. Majid M. Al-Sadoon, 2020. "Regularized Solutions to Linear Rational Expectations Models," Papers 2009.05875, arXiv.org, revised Oct 2020.
    11. Brendan K Beare & Massimo Franchi & Phil Howlett, 2024. "The general solution to an autoregressive law of motion," Working Papers 2024-01, University of Sydney, School of Economics.
    12. Meyer-Gohde, Alexander & Tzaawa-Krenzler, Mary, 2023. "Sticky information and the Taylor principle," IMFS Working Paper Series 189, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    13. Majid M. Al-Sadoon, 2020. "The Spectral Approach to Linear Rational Expectations Models," Papers 2007.13804, arXiv.org, revised Aug 2024.
    14. John G. Thistle, 2018. "The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations," Papers 1806.06657, arXiv.org, revised Apr 2019.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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