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Stability Analysis of Uzawa-Lucas Endogenous Growth Model

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  • William Barnett

    (Department of Economics, University of Kansas)

  • Taniya Ghosh

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

Abstract

This paper analyzes, within its feasible parameter space, the dynamics of the Uzawa-Lucas endogenous growth model. The model is solved from a centralized social planner perspective as well as in the modelís decentralized market economy form. We examine the stability properties of both versions of the model and locate Hopf and transcritical bifurcation boundaries. In an extended analysis, we investigate the existence of Andronov-Hopf bifurcation, branch point bifurcation, limit point cycle bifurcation, and period doubling bifurcations. While these all are local bifurcations, the presence of global bifurcation is confirmed as well. We find evidence that the model could produce chaotic dynamics, but our analysis cannot confirm that conjecture. 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 estimatesí confidence region, robustness of dynamical inferences from policy simulations are compromised, when conducted, in the usual manner, only at the parametersí point estimates.

Suggested Citation

  • 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.
  • Handle: RePEc:kan:wpaper:201304
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    bifurcation; endogenous growth; Lucas-Uzawa model; Hopf; inference robustness; dynamics; stability.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E0 - Macroeconomics and Monetary Economics - - General
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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