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A finite set of equilibria for the indeterminacy of linear rational expectations models

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  • Jean-Bernard Chatelain

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Kirsten Ralf

    (Ecole Supérieure du Commerce Extérieur - ESCE - International business school)

Abstract

This paper demonstates the existence of a finite set of equilibria in the case of the indeterminacy of linear rational expectations models. The number of equilibria corresponds to the number of ways to select n eigenvectors among a larger set of eigenvectors related to stable eigenvalues. A finite set of equilibria is a substitute to continuous (uncountable) sets of sunspots equilibria, when the number of independent eigenvectors for each stable eigenvalue is equal to one.

Suggested Citation

  • Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Working Papers halshs-01053484, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01053484
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01053484v2
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    References listed on IDEAS

    as
    1. Andrew P. Blake & Tatiana Kirsanova, 2012. "Discretionary Policy and Multiple Equilibria in LQ RE Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1309-1339.
    2. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    3. Le Van, Cuong, 1986. "Stationary uncertainty frontiers in macroeconometric models An approach for solving matrix Riccati equations," Journal of Economic Dynamics and Control, Elsevier, vol. 10(1-2), pages 225-229, June.
    4. Gourieroux, C & Laffont, J J & Monfort, Alain, 1982. "Rational Expectations in Dynamic Linear Models: Analysis of the Solutions," Econometrica, Econometric Society, vol. 50(2), pages 409-425, March.
    5. Andrew P. Blake, 2004. "Analytic Derivatives for Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 77-96, August.
    6. Boucekkine, Raouf & Le Van, Cuong, 1996. "Checking for Saddlepoint Stability: An Easy Test," Computational Economics, Springer;Society for Computational Economics, vol. 9(4), pages 317-330, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "The Indeterminacy of Determinacy with Fiscal, Macro-prudential or Taylor Rules," PSE Working Papers halshs-01877766, HAL.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," Working Papers halshs-01863367, HAL.
    3. Chatelain, Jean-Bernard & Ralf, Kirsten, 2021. "Hopf Bifurcation From New-Keynesian Taylor Rule To Ramsey Optimal Policy," Macroeconomic Dynamics, Cambridge University Press, vol. 25(8), pages 2204-2236, December.

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    More about this item

    Keywords

    Linear rational expectations models; indeterminacy; multiple equilibria; matrix Riccati equation; sunspots;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General

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