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Hopf bifurcation in the Clarida, Gali, and Gertler model

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  • Barnett, William A.
  • Eryilmaz, Unal

Abstract

We explore bifurcation phenomena in the open-economy New Keynesian CGG Model based on Clarida et al. (2001, 2002). We find that the open economy framework can bring about more complex dynamics, along with a wider variety of qualitative behaviors and policy responses. Introducing parameters related to the open economy structure affects the values of bifurcation parameters and changes the location of bifurcation boundaries. As a result, the stratification of the confidence region, as previously seen in closed-economy New Keynesian models, remains an important research and policy risk to be considered in the context of the open-economy New Keynesian functional structures. In fact, econometrics and optimal policy design become more complex within an open economy. Dynamical inferences need to be qualified by the risk of bifurcation boundaries crossing the confidence regions. Without adequate prior econometric research, policy design needs to take into consideration that a change in monetary policy can produce an unanticipated bifurcation.

Suggested Citation

  • Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
  • Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:401-404
    DOI: 10.1016/j.econmod.2012.11.051
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    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. 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.
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    13. 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(2), pages 482-503, March.
    14. Eric M. Leeper & Christopher A. Sims, 1994. "Toward a Modern Macroeconomic Model Usable for Policy Analysis," NBER Chapters, in: NBER Macroeconomics Annual 1994, Volume 9, pages 81-140, National Bureau of Economic Research, Inc.
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    Cited by:

    1. 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.
    2. 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.
    3. Alexeeva, Tatyana A. & Barnett, William A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2020. "Dynamics of the Shapovalov mid-size firm model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. 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.
    5. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
    6. William A. Barnett & Unal Eryilmaz, 2023. "Monetary Policy and Determinacy: An Inquiry into Open Economy New Keynesian Macrodynamics," Open Economies Review, Springer, vol. 34(2), pages 217-253, April.
    7. Moosavi Mohseni, Reza & Kilicman, Adem, 2014. "Hopf bifurcation in an open monetary economic system: Taylor versus inflation targeting rules," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 8-12.
    8. 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

    Stability; Bifurcation; Open economy; New Keynesian; Macroeconomics; Dynamic systems;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • 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
    • 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
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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