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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.

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File URL: http://graduate.lerner.udel.edu/sites/default/files/ECON/PDFs/RePEc/dlw/WorkingPapers/2008/UDWP2008-26.pdf
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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
Date of revision:
Handle: RePEc:dlw:wpaper:08-26.
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Web page: http://www.lerner.udel.edu/departments/economics/department-economics/

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  1. Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, sunspots, and automatic stabilizers," Staff Report 214, Federal Reserve Bank of Minneapolis.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
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