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Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy

Author

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  • Jean-Bernard Chatelain

    (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, PJSE - Paris Jourdan Sciences Economiques - 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

    (ESCE International Business School, INSEEC U. Research Center)

Abstract

This paper compares different implementations of monetary policy in a new-Keynesian setting. We can show that a shift from Ramsey optimal policy under short-term commitment (based on a negative feedback mechanism) to a Taylor rule (based on a positive feedback mechanism) corresponds to a Hopf bifurcation with opposite policy advice and a change of the dynamic properties. This bifurcation occurs because of the ad hoc assumption that interest rate is a forward-looking variable when policy targets (inflation and output gap) are forward-looking variables in the new-Keynesian theory.

Suggested Citation

  • Jean-Bernard Chatelain & Kirsten Ralf, 2021. "Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy," PSE-Ecole d'économie de Paris (Postprint) hal-01527872, HAL.
    • Handle: RePEc:hal:pseptp:hal-01527872
    DOI: 10.1017/S1365100519001032
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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2021. "Imperfect Credibility versus No Credibility of Optimal Monetary Policy," Revue économique, Presses de Sciences-Po, vol. 72(1), pages 43-63.
    3. Chatelain, Jean-Bernard & Ralf, Kirsten, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 39(4), pages 2429-2440.
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 40(2), pages 1797-1803.
    5. Chatelain, Jean-Bernard & Ralf, Kirsten, 2022. "Ramsey Optimal Policy In The New-Keynesian Model With Public Debt," Macroeconomic Dynamics, Cambridge University Press, vol. 26(6), pages 1588-1614, September.
    6. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Policy Maker’s Credibility with Predetermined Instruments for Forward-Looking Targets," Revue d'économie politique, Dalloz, vol. 130(5), pages 823-846.
    7. 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.
    8. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," Economics Bulletin, AccessEcon, vol. 39(4), pages 2429-2440.
    9. Jean-Bernard Chatelain & Kirsten Ralf, 2023. "Super-Inertial Interest Rate Rules are not Solutions of Ramsey Optimal Policy," Revue d'économie politique, Dalloz, vol. 133(1), pages 119-146.

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    More about this item

    Keywords

    Bifurcations; Commitment; Taylor Rule; Taylor Principle; New-Keynesian Model; Ramsey Optimal Policy;
    All these keywords.

    JEL classification:

    • 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
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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