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Euler Equation Branching

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Author Info
David R. Stockman () (Department of Economics,University of Delaware, Department of Mathematics,Baylor University)

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Abstract

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.

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File URL: http://www.lerner.udel.edu/economics/WorkingPapers/2008/UDWP2008-26.pdf
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Publisher Info
Paper provided by University of Delaware, Department of Economics in its series Working Papers with number 08-26.

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Length: 23 pages
Date of creation: 2008
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Handle: RePEc:dlw:wpaper:08-26.

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Web page: http://www.lerner.udel.edu/departments/economics/
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Related research
Keywords: global indeterminacy; Euler equation branching; multiple equilibria; cycles; chaos; increasing returns to scale; externality; regime switching;

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Find related papers by 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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Jang-Ting Guo & Kevin Lansing, 1999. "Fiscal policy, increasing returns, and endogenous fluctuations," Working Papers in Applied Economic Theory 99-08, Federal Reserve Bank of San Francisco. [Downloadable!]
    Other versions:
  2. Benhabib, Jess & Farmer, Roger E.A., 1996. "Indeterminacy and Sector-Specific Externalities," Working Papers 96-12, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
    Other versions:
  3. Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, sunspots, and automatic stabilizers," Working Paper Series, Macroeconomic Issues WP-96-16, Federal Reserve Bank of Chicago.
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
    Other versions:
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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Cited by:
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  1. David R. Stockman, 2007. "Chaos and Sector-specific Externalities," Working Papers 07-17, University of Delaware, Department of Economics. [Downloadable!]
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