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

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  • Jean-Bernard Chatelain

    () (PSE - Paris School of Economics)

  • Kirsten Ralf

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

Abstract

This paper shows that a shift from Ramsey optimal policy under short term commitment (based on a negative-feedback mechanism) to a Taylor rule (based on positive-feedback mechanism) in the new-Keynesian model is in fact a Hopf bifurcation, with opposite policy advice. The number of stable eigenvalues corresponds to the number of predetermined variables including the interest rate and its lag as policy instruments for Ramsey optimal policy. With a new-Keynesian Taylor rule, however, these policy instruments are arbitrarily assumed to be forward-looking variables when policy targets (inflation and output gap) are forward-looking variables. For new-Keynesian Taylor rule, this Hopf bifurcation implies a lack of robustness and multiple equilibria if public debt is not set to zero for all observation.

Suggested Citation

  • Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy," Working Papers hal-01527872, HAL.
  • Handle: RePEc:hal:wpaper:hal-01527872
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01527872
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    References listed on IDEAS

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    Cited by:

    1. Chatelain, Jean-Bernard & Ralf, Kirsten, 2017. "Can we Identify the Fed's Preferences?," EconStor Preprints 149993, ZBW - German National Library of Economics.
    2. Chatelain, Jean-Bernard & Ralf, Kirsten, 2017. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," EconStor Preprints 168031, ZBW - German National Library of Economics.
    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.

    More about this item

    Keywords

    Bifurcations; Taylor rule; Taylor principle; new-Keynesian model; Ramsey optimal policy; Finite horizon commitment;

    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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