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Empirical assessment of bifurcation regions within New Keynesian models

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  • William Barnett

    ()

  • Evgeniya Duzhak

    ()

Abstract

As is well known in systems theory, the parameter space of most dynamic models is stratified into subsets, each of which supports a different kind of dynamic solution. Since we do not know the parameters with certainty, knowledge of the location of the bifurcation boundaries is of fundamental importance. Without knowledge of the location of such boundaries, there is no way to know whether the confidence region about the parameters’ point estimates might be crossed by one or more such boundaries. If there are intersections between bifurcation boundaries and a confidence region, the resulting stratification of the confidence region damages inference robustness about dynamics, when such dynamical inferences are produced by the usual simulations at the point estimates only. Recently, interest in policy in some circles has moved to New Keynesian models, which have become common in monetary policy formulations. As a result, we explore bifurcations within the class of New Keynesian models. We study different specifications of monetary policy rules within the New Keynesian functional structure. In initial research in this area, Barnett and Duzhak (2008) found a New Keynesian Hopf bifurcation boundary, with the setting of the policy parameters influencing the existence and location of the bifurcation boundary. Hopf bifurcation is the most commonly encountered type of bifurcation boundary found among economic models, since the existence of a Hopf bifurcation boundary is accompanied by regular oscillations within a neighborhood of the bifurcation boundary. Now, following a more extensive and systematic search of the parameter space, we also find the existence of Period Doubling (flip) bifurcation boundaries in the class of models. Central results in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the considered cases. We also solve numerically for the location and properties of the Period Doubling bifurcation boundaries an
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:45:y:2010:i:1:p:99-128
    DOI: 10.1007/s00199-008-0430-0
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    Cited by:

    1. Arnold Zellner & Jacques Kibambe Ngoie, 2015. "Evaluation of the Effects of Reduced Personal and Corporate Tax Rates on the Growth Rates of the U.S. Economy," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 56-81, February.
    2. Banerjee, Sanjibani & A. Barnett, William & A. Duzhak, Evgeniya & Gopalan, Ramu, 2011. "Bifurcation analysis of Zellner's Marshallian Macroeconomic Model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1577-1585, September.
    3. Chatelain, Jean-Bernard & Ralf, Kirsten, 2017. "Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy," EconStor Preprints 158001, ZBW - German National Library of Economics.
    4. Barnett, William A. & Eryilmaz, Unal, 2016. "An Analytical And Numerical Search For Bifurcations In Open Economy New Keynesian Models," Macroeconomic Dynamics, Cambridge University Press, vol. 20(02), pages 482-503, March.
    5. repec:eee:joecas:v:10:y:2013:i:1:p:53-64 is not listed on IDEAS
    6. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    7. William A. Barnett & Taniya Ghosh, 2014. "Stability analysis of Uzawa–Lucas endogenous growth model," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 33-44, April.
    8. Cornaro, Alessandra & Agliari, Anna, 2011. "Global and local determinacy in a one-step forward looking New Keynesian model," Economic Modelling, Elsevier, vol. 28(3), pages 1354-1362, May.
    9. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," PSE Working Papers halshs-01549929, HAL.
    10. William Barnett & Evgeniya A. Duzhak, "undated". "Structural Stability of the Generalized Taylor Rule," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201404, University of Kansas, Department of Economics.
    11. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, vol. 27(6), pages 1345-1354, November.
    12. Barnett, William A. & Ghosh, Taniya, 2013. "Bifurcation analysis of an endogenous growth model," The Journal of Economic Asymmetries, Elsevier, vol. 10(1), pages 53-64.
    13. Fabrizio Orrego, 2014. "Habit formation and indeterminacy in overlapping generations models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 225-241, January.

    More about this item

    Keywords

    Bifurcation; Dynamic general equilibrium; Hopf bifurcation; Flip bifurcation; Period doubling bifurcation; Robustness; New Keynesian macroeconometrics; Taylor rule; Inflation targeting; C10; C30; C52; E32; E37; E60;

    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
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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