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Solving generalized multivariate linear rational expectations models

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  • Tan, Fei
  • Walker, Todd B.

Abstract

We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This facilitates the use of a generic exogenous driving process that must only satisfy covariance stationarity. Multivariate cross-equation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the rational expectations model are obtained. We argue that this approach offers important insights into rational expectations models. We give two examples in the paper—an asset pricing model with incomplete information and a monetary model with observationally equivalent monetary-fiscal policy interactions. We relate our solution methodology to other popular approaches to solving multivariate linear rational expectations models, and provide user-friendly code that executes our approach.

Suggested Citation

  • Tan, Fei & Walker, Todd B., 2015. "Solving generalized multivariate linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 95-111.
    • Handle: RePEc:eee:dyncon:v:60:y:2015:i:c:p:95-111
    DOI: 10.1016/j.jedc.2015.07.007
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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. Meyer-Gohde, Alexander, 2024. "Solving and analyzing DSGE models in the frequency domain," IMFS Working Paper Series 207, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    3. Zhongjun Qu & Denis Tkachenko, 2023. "Using arbitrary precision arithmetic to sharpen identification analysis for DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 644-667, June.
    4. Nigel McClung, 2021. "The Power of Forward Guidance and the Fiscal Theory of the Price Level," International Journal of Central Banking, International Journal of Central Banking, vol. 17(71), pages 1-57, December.
    5. 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.
    6. John G. Thistle, 2018. "The Origin and the Resolution of Nonuniqueness in Linear Rational Expectations," Papers 1806.06657, arXiv.org, revised Apr 2019.
    7. Tan, Fei, 2017. "An analytical approach to new Keynesian models under the fiscal theory," Economics Letters, Elsevier, vol. 156(C), pages 133-137.
    8. Han, Zhao & Tan, Fei & Wu, Jieran, 2022. "Analytic policy function iteration," Journal of Economic Theory, Elsevier, vol. 200(C).
    9. Majid M. Al-Sadoon, 2020. "Regularized Solutions to Linear Rational Expectations Models," Papers 2009.05875, arXiv.org, revised Oct 2020.
    10. Majid M. Al-Sadoon, 2020. "The Spectral Approach to Linear Rational Expectations Models," Papers 2007.13804, arXiv.org, revised Aug 2024.
    11. Fei Tan, 2017. "Interpreting rational expectations econometrics via analytic function approach," Economics Bulletin, AccessEcon, vol. 37(2), pages 1182-1190.

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    More about this item

    Keywords

    Solution methods; Analytic functions; Rational expectations;
    All these keywords.

    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
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • E63 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Comparative or Joint Analysis of Fiscal and Monetary Policy; Stabilization; Treasury Policy

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