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Bifurcation Analysis of an Endogenous Growth Model

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  • William Barnett

    (Department of Economics, The University of Kansas)

  • Taniya Ghosh

    (Indira Gandhi Institute of Development Research, Reserve Bank of India, Mumbai)

Abstract

This paper analyzes the dynamics of a variant of Jones (2002) semi-endogenous growth model within the feasible parameter space. We derive the long run growth rate of the economy and do a detailed bifurcation analysis of the equilibrium. We show the existence of codimension-1 bifurcations (Hopf, Branch Point, Limit Point of Cycles, and Period Doubling) and codimension-2 (Bogdanov-Takens and Generalized Hopf) bifurcations within the feasible parameter range of the model. It is important to recognize that bifurcation boundaries do not necessarily separate stable from unstable solution domains. Bifurcation boundaries can separate one kind of unstable dynamics domain from another kind of unstable dynamics domain, or one kind of stable dynamics domain from another kind (called soft bifurcation), such as bifurcation from monotonic stability to damped periodic stability or from damped periodic to damped multiperiodic stability. There are not only an infinite number of kinds of unstable dynamics, some very close to stability in appearance, but also an infinite number of kinds of stable dynamics. Hence subjective prior views on whether the economy is or is not stable provide little guidance without mathematical analysis of model dynamics. When a bifurcation boundary crosses the parameter estimates’ confidence region, robustness of dynamical inferences from policy simulations are compromised, when conducted, in the usual manner, only at the parameters’ point estimates.

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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 201306.

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Length: 22 pages
Date of creation: Oct 2013
Date of revision: Oct 2013
Handle: RePEc:kan:wpaper:201306

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Keywords: bifurcation; endogenous growth; Jones growth model; Hopf; inference robustness; dynamics; stability.;

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  1. Jones, C.I., 2000. "Sources of U.S. Economic Growth in a World of Ideas," Papers 99-29, United Nations World Employment Programme-.
  2. Mankiw, N Gregory & Romer, David & Weil, David N, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 407-37, May.
  3. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
  4. Bucci, Alberto, 2008. "Population growth in a model of economic growth with human capital accumulation and horizontal R&D," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1124-1147, September.
  5. Mondal, Debasis, 2008. "Stability analysis of the Grossman-Helpman model of endogenous product cycles," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1302-1322, September.
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