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Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics

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  • Barnett, William
  • Bella, Giobanni
  • Ghosh, Taniya
  • Mattana, Paolo
  • Venturi, Beatrice

Abstract

The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent inflation rates, have declined to current low levels, such that the real rate of interest is below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Policy options to eliminate or control the chaotic dynamics are developed.

Suggested Citation

  • Barnett, William & Bella, Giobanni & Ghosh, Taniya & Mattana, Paolo & Venturi, Beatrice, 2020. "Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics," MPRA Paper 98417, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:98417
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    3. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "Ramsey Optimal Policy in the New-Keynesian Model with Public Debt," PSE Working Papers halshs-02278781, HAL.
    4. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Barnett, William A. & Bella, Giovanni & Ghosh, Taniya & Mattana, Paolo & Venturi, Beatrice, 2022. "Is policy causing chaos in the United Kingdom?," Economic Modelling, Elsevier, vol. 108(C).
    6. William Barnett & Unal Eryilmaz, 2022. "Monetary Policy and Determinacy: An Inquiry in Open Economy New Keynesian Framework," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202203, University of Kansas, Department of Economics.
    7. William A. Barnett & Taniya Ghosh & Masudul Hasan Adil, 2021. "Is money demand really unstable? Evidence from divisia monetary aggregates," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2021-005, Indira Gandhi Institute of Development Research, Mumbai, India.

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    More about this item

    Keywords

    Shilnikov chaos criterion; global indeterminacy; long-term un-predictability; liquidity trap;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • 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
    • E12 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Keynes; Keynesian; Post-Keynesian; Modern Monetary Theory
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E6 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook
    • 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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