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A geometric description of a macroeconomic model with a center manifold


  • Gomis-Porqueras, Pere
  • Haro, Àlex


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 et al. [2003. The parameterization method for invariant manifolds. I. Manifolds associated to non-resonant subspaces. Indiana University Mathematics Journal 52(2), 283-328], and the semianalytical algorithms proposed by Simó [1990. On the analytical and numerical approximation of invariant manifolds. In: Benest, D., Froeschlé, C. (Eds.), Les Méthodes Modernes de la Mecánique Céleste (Course given at Goutelas, France, 1989), Editions Frontières, Paris, pp. 285-329], and those of Gomis-Porqueras and Haro [2003. Global dynamics in macroeconomics: an overlapping generations example. Journal of Economic Dynamics and Control 27, 1941-1959]. 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 et al. [2001. Public and private circulating liabilities. Journal of Economic Theory 99, 59-116]. 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

  • Gomis-Porqueras, Pere & Haro, Àlex, 2009. "A geometric description of a macroeconomic model with a center manifold," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1217-1235, June.
  • Handle: RePEc:eee:dyncon:v:33:y:2009:i:6:p:1217-1235

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    References listed on IDEAS

    1. 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.
    2. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-342, March.
    3. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    4. 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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    Cited by:

    1. Azariadis, Costas & Bullard, James & Singh, Aarti & Suda, Jacek, 2015. "Incomplete Credit Markets and Monetary Policy," Working Papers 2015-12, University of Sydney, School of Economics, revised Feb 2017.
    2. Bullard, James B. & Singh, Aarti, 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.
    3. Azariadis, Costas & Bullard, James B. & Singh, Aarti & Suda, Jacek, 2015. "Optimal Monetary Policy at the Zero Lower Bound," Working Papers 2015-10, Federal Reserve Bank of St. Louis.
    4. Tomi T. Kortela, 2011. "On the costs of disability insurance," 2011 Meeting Papers 445, Society for Economic Dynamics.

    More about this item


    Invariant manifold Center manifold Global dynamics;

    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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