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Empirical Assessment of Bifurcation Regions within New Keynesian Models

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  • William Barnett

    (Department of Economics, The University of Kansas)

  • Evgeniya Aleksandrovna Duzhak

    (Baruch College, City University of New York)

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 and their dependence upon policy-rule parameter settings.

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Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 200811.

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Length: 46 pages
Date of creation: Oct 2008
Date of revision: Oct 2008
Handle: RePEc:kan:wpaper:200811

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Keywords: Bifurcation; dynamic general equilibrium; Hopf bifurcation; flip bifurcation; period doubling bifurcation; robustness; New Keynesian macroeconometrics; Taylor rule; inflation targeting.;

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References

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  1. Clarida, R. & Gali, J. & Gertler, M., 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Working Papers 99-13, C.V. Starr Center for Applied Economics, New York University.
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Citations

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Cited by:
  1. Barnett, William A. & He, Susan, 2009. "Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right," MPRA Paper 12803, University Library of Munich, Germany.
  2. Sanjibani Banerjee & William Barnett & Evgeniya Duzhak & Ramu Gopalan, 2011. "Bifurcation Analysis of Zellner's Marshallian Macroeconomic Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201102, University of Kansas, Department of Economics, revised Apr 2011.
  3. 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.
  4. William Barnett & Unal Eryilmaz, 2012. "An Analytical and Numerical Search for Bifurcations in Open Economy New Keynesian Models," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201210, University of Kansas, Department of Economics, revised Aug 2012.
  5. William Barnett & Unal Eryilmaz, 2012. "Hopf Bifurcation in the Clarida, Gali, and Gertler Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201211, University of Kansas, Department of Economics, revised Sep 2012.
  6. Jacques Kibambe Ngoie & Arnold Zellner, 2012. "Evaluation of the Effects of Reduced Personal and Corporate Tax Rates on the Growth Rates of the U.S. Economy," Working Papers 201217, University of Pretoria, Department of Economics.
  7. William Barnett & Taniya Ghosh, 2013. "Stability Analysis of Uzawa-Lucas Endogenous Growth Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201304, University of Kansas, Department of Economics, revised May 2013.

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