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Structural Stability of the Generalized Taylor Rule

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  • Barnett, William A.
  • Duzhak, Evgeniya A.

Abstract

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the existence of a period doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We demonstrate that while the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations, a hybrid rule exhibits the same pattern of period doubling bifurcations as the basic setup.

Suggested Citation

  • Barnett, William A. & Duzhak, Evgeniya A., 2014. "Structural Stability of the Generalized Taylor Rule," MPRA Paper 58737, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:58737
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    References listed on IDEAS

    as
    1. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    2. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    3. John B. Taylor, 1999. "Introduction to "Monetary Policy Rules"," NBER Chapters,in: Monetary Policy Rules, pages 1-14 National Bureau of Economic Research, Inc.
    4. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    5. Carl E. Walsh, 2003. "Monetary Theory and Policy, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232316, January.
    6. John B. Taylor, 1999. "A Historical Analysis of Monetary Policy Rules," NBER Chapters,in: Monetary Policy Rules, pages 319-348 National Bureau of Economic Research, Inc.
    7. Galí, Jordi & Gertler, Mark, 1999. "Inflation Dynamics: A Structural Economic Analysis," CEPR Discussion Papers 2246, C.E.P.R. Discussion Papers.
    8. Roger E.A. Farmer & Daniel F. Waggoner & Tao Zha, 2007. "Understanding the New-Keynesian Model when Monetary Policy Switches Regimes," NBER Working Papers 12965, National Bureau of Economic Research, Inc.
    9. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    11. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
    12. George Evans, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, Oxford University Press, vol. 100(4), pages 1217-1233.
    13. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    14. Barnett, William A. & He, Yijun, 2002. "Stabilization Policy As Bifurcation Selection: Would Stabilization Policy Work If The Economy Really Were Unstable?," Macroeconomic Dynamics, Cambridge University Press, vol. 6(05), pages 713-747, November.
    15. Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
    16. Groen, Jan J J & Mumtaz, Haroon, 2008. "Investigating the structural stability of the Phillips curve relationship," Bank of England working papers 350, Bank of England.
    17. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    18. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
    19. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, June.
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    More about this item

    Keywords

    New Keynesian; Taylor Rule; regime switching; bifurcation analysis; structural stability.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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