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A Geometric Description of a Macroeconomic Model with a Center Manifold

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  • Àlex Haro
  • Pere Gomis-Porqueras

Abstract

This paper presents a unified framework of different algorithms to numerically compute high order expansions of invariant manifolds associated to a steady state of a dynamical system. The framework is inspired in the parameterization method of Cabré, Fontich and de la Llave [7], and the semianalytical algorithms proposed by Simó [13], and those of Gomis-Porqueras and Haro [9]. Within this methodology, one can compute high order approximations of stable, unstable and center manifolds. In this last case the use of high order approximations (not just linear) are crucial in understanding the dynamic properties of the model near the steady state. To illustrate the algorithms we consider a model economy introduced by Azariadis, Bullard and Smith [6]. Besides its intrinsic importance, this four dimensional macroeconomic model is an ideal testing ground because it delivers steady states with stable and unstable manifolds (of dimensions 1 or 2), and each of them has also a one dimensional center manifold. Moreover, the numerical computations lead to a further theoretical study of the dynamical system completing some of the results in the original paper.

Suggested Citation

  • Àlex Haro & Pere Gomis-Porqueras, 2015. "A Geometric Description of a Macroeconomic Model with a Center Manifold," Working Papers 364, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:364
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    References listed on IDEAS

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    1. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 725-737.
    2. Gomis-Porqueras, Pere & Haro, Alex, 2003. "Global dynamics in macroeconomics: an overlapping generations example," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 1941-1959, September.
    3. Azariadis, Costas & Bullard, James & Smith, Bruce D., 2001. "Private and Public Circulating Liabilities," Journal of Economic Theory, Elsevier, vol. 99(1-2), pages 59-116, July.
    4. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-342, March.
    5. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    6. Gomis-Porqueras, Pere & Haro, Alex, 2007. "Global bifurcations, credit rationing and recurrent hyperinflations," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 473-491, February.
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    2. Tomi T. Kortela, 2011. "On the costs of disability insurance," 2011 Meeting Papers 445, Society for Economic Dynamics.
    3. James B. Bullard & Aarti Singh, 2016. "Incomplete Credit Markets and Monetary Policy with Heterogeneous Labor Supply : a presentation at Bank of Korea 2016 Conference, Employment and Growth, Seoul, Korea, May 30, 2016," Speech 270, Federal Reserve Bank of St. Louis.
    4. Azariadis, Costas & Bullard, James & Singh, Aarti & Suda, Jacek, 2019. "Incomplete credit markets and monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 103(C), pages 83-101.

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    Keywords

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    JEL classification:

    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles

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