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Non-Robust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions

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

Abstract

Grandmont (1985) found that the parameter space of the most classical dynamic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with many forms of multiperiodic dynamics between. The econometric implications of Grandmont’s findings are particularly important, if bifurcation boundaries cross the confidence regions surrounding parameter estimates in policy-relevant models. Stratification of a confidence region into bifurcated subsets seriously damages robustness of dynamical inferences. Recently, interest in policy in some circles has moved to New Keynesian models. As a result, in this paper we explore bifurcation within the class of New Keynesian models. We develop the econometric theory needed to locate bifurcation boundaries in log-linearized New-Keynesian models with Taylor policy rules or inflation-targeting policy rules. Central results needed in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the cases that we consider.

Suggested Citation

  • Barnett, William A. & Duzhak, Evgeniya A., 2007. "Non-Robust Dynamic Inferences from Macroeconometric Models: Bifurcation Stratification of Confidence Regions," MPRA Paper 6005, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:6005
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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "Ramsey Optimal Policy in the New-Keynesian Model with Public Debt," PSE Working Papers halshs-02278781, HAL.
    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. 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.
    4. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    5. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    6. Mthuli Ncube & Mthokozisi M. Tshuma, 2010. "Working Paper 113 - Monetary Policy Conduct Based on Nonlinear Taylor Rule: Evidence from South Africa," Working Paper Series 250, African Development Bank.
    7. 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.
    8. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Hopf Bifurcation from New-Keynesian Taylor Rule to Ramsey Optimal Policy," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics.
    9. William A. Barnett & Jingxian Hu, 2021. "Capital Control, Exchange Rate Regime, and Monetary Policy: Indeterminacy and Bifurcation," Dynamic Modeling and Econometrics in Economics and Finance, in: Herbert Dawid & Jasmina Arifovic (ed.), Dynamic Analysis in Complex Economic Environments, pages 123-175, Springer.
    10. Barnett, William A. & Duzhak, Evgeniya A., 2019. "Structural Stability Of The Generalized Taylor Rule," Macroeconomic Dynamics, Cambridge University Press, vol. 23(4), pages 1664-1678, June.
    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. Mohd Naim Bin Mohd Johari & Adem Kilicman, 2017. "Hopf bifurcation in an open monetary economic system: Taylor vs. inflation targeting rules (Malaysian case)," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1327184-132, January.

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    More about this item

    Keywords

    Bifurcation; Hopf bifurcation; Euler equations; New Keynesian macroeconometrics; Bergstrom-Wymer model;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles

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