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Euler Equation Branching


  • David R. Stockman and Brian E. Raines

    () (Department of Economics,University of Delaware
    Department of Mathematics,Baylor University)


Some macroeconomic models exhibit a type of global indeterminacy known as Euler equation branching (e.g., the one-sector growth model with a production externality). The dynamics in such models are governed by a differential inclusion. In this paper, we show that in models with Euler equation branching there are multiple equilibria and that the dynamics are chaotic. In particular, we provide sufficient conditions for a dynamical system on the plane with Euler equation branching to be chaotic and show analytically that in a neighborhood of a steady state, these sufficient conditions will typically be satisfied. We also extend the results of Christiano and Harrison (JME, 1999) for the one-sector growth model with a production externality. In a more general setting, we provide necessary and sufficient conditions for Euler equation branching in this model. We show that chaotic and cyclic equilibria are possible and that this behavior is not dependent on the steady state being "locally" determinate or indeterminate.

Suggested Citation

  • David R. Stockman and Brian E. Raines, 2008. "Euler Equation Branching," Working Papers 08-26, University of Delaware, Department of Economics.
  • Handle: RePEc:dlw:wpaper:08-26.

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    References listed on IDEAS

    1. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January.
    2. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
    3. Benhabib, Jess & Farmer, Roger E. A., 1996. "Indeterminacy and sector-specific externalities," Journal of Monetary Economics, Elsevier, vol. 37(3), pages 421-443, June.
    4. 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.
    5. Christiano, Lawrence J. & G. Harrison, Sharon, 1999. "Chaos, sunspots and automatic stabilizers," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 3-31, August.
    6. Boldrin, Michele & Nishimura, Kazuo & Shigoka, Tadashi & Yano, Makoto, 2001. "Chaotic Equilibrium Dynamics in Endogenous Growth Models," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 97-132, January.
    7. Schmitt-Grohe, Stephanie & Uribe, Martin, 1997. "Balanced-Budget Rules, Distortionary Taxes, and Aggregate Instability," Journal of Political Economy, University of Chicago Press, vol. 105(5), pages 976-1000, October.
    8. Guo, Jang-Ting & Lansing, Kevin J., 2002. "Fiscal Policy, Increasing Returns, And Endogenous Fluctuations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(05), pages 633-664, November.
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    Cited by:

    1. Stockman, David R., 2009. "Chaos and sector-specific externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 2030-2046, December.

    More about this item


    global indeterminacy; Euler equation branching; multiple equilibria; cycles; chaos; increasing returns to scale; externality; regime switching;

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy

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