IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-01053484.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-01053484v2/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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.
    4. 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.
    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "The Indeterminacy of Determinacy with Fiscal, Macro-prudential or Taylor Rules," Working Papers halshs-01877766, HAL.
    3. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," PSE Working Papers halshs-01863367, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Working Papers halshs-01044432, HAL.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Post-Print halshs-01053484, HAL.
    3. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Papers 1407.6222, arXiv.org.
    4. Patrick Minford & Naveen Srinivasan, 2015. "Can the Learnability Criterion Ensure Determinacy in New Keynesian Models?," South Asian Journal of Macroeconomics and Public Finance, , vol. 4(1), pages 43-61, June.
    5. Broze, Laurence & Gourieroux Christian & Szafarz A, 1986. "Reduction and identification of simultaneous equations models with rational expectations," CEPREMAP Working Papers (Couverture Orange) 8601, CEPREMAP.
    6. Atıcı, Ferhan M. & Ekiz, Funda & Lebedinsky, Alex, 2014. "Cagan type rational expectation model on complex discrete time domains," European Journal of Operational Research, Elsevier, vol. 237(1), pages 148-151.
    7. Evans, George W. & McGough, Bruce, 2005. "Stable sunspot solutions in models with predetermined variables," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 601-625, April.
    8. Himmels, Christoph & Kirsanova, Tatiana, 2013. "Escaping expectation traps: How much commitment is required?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 649-665.
    9. Christoph Himmels & Tatiana Kirsanova, 2011. "Expectations Traps and Monetary Policy with Limited Commitment," Discussion Papers 1102, University of Exeter, Department of Economics.
    10. Loumrhari, Ghizlan, 2016. "Vieillissement démographique et réforme paramétrique des retraites. Les enseignements d’un modèle EGC-GI pour le Maroc [Ageing and pension reform. A computational olg model for Morocco]," MPRA Paper 74077, University Library of Munich, Germany.
    11. Stradi-Granados, Benito A. & Haven, Emmanuel, 2010. "The use of interval arithmetic in solving a non-linear rational expectation based multiperiod output-inflation process model: The case of the IN/GB method," European Journal of Operational Research, Elsevier, vol. 203(1), pages 222-229, May.
    12. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "Stability and Identification with Optimal Macroprudential Policy Rules," Documents de travail du Centre d'Economie de la Sorbonne 14034, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    13. Matheny, K. J., 1998. "Equilibrium beliefs in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 393-413, November.
    14. Boyd Iii, J.H. & Dotsey, M., 1990. "Interest Rate Rules And Nominal Determinacy," RCER Working Papers 222, University of Rochester - Center for Economic Research (RCER).
    15. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    16. Debortoli, Davide & Maih, Junior & Nunes, Ricardo, 2014. "Loose Commitment In Medium-Scale Macroeconomic Models: Theory And Applications," Macroeconomic Dynamics, Cambridge University Press, vol. 18(1), pages 175-198, January.
    17. Bernd Funovits, 2014. "Implications of Stochastic Singularity in Linear Multivariate Rational Expectations Models," Vienna Economics Papers vie1405, University of Vienna, Department of Economics.
    18. Volker Hahn, 2021. "Discretionary policy and multiple equilibria in a new Keynesian model," Oxford Economic Papers, Oxford University Press, vol. 73(1), pages 423-445.
    19. 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.
    20. Gauthier, Stephane, 2004. "Determinacy in linear rational expectations models," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 815-830, November.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-01053484. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.