Chaotic sets and Euler equation branching
Abstract Some macroeconomic models may exhibit a type of 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 , where H is a set-valued function. In this paper, we introduce the concept of a chaotic set and explore its implications for Devaney chaos, Li-Yorke chaos and distributional chaos (adapted to dynamical systems generated by a differential inclusion). We show that a chaotic set will imply Devaney and Li-Yorke chaos and that a chaotic set with Euler equation branching will imply distributional chaos. We show that the existence of a steady state for a differential inclusion on the plane will generate a chaotic set and hence Devaney and Li-Yorke chaos. As an application, we show how these results can be applied to a one-sector growth model with a production externality - extending the results of Christiano and Harrison (1999). We show that chaotic (Devaney, Li-Yorke and distributional) and cyclic equilibria are possible and that this behavior is not dependent on the steady state being "locally" a saddle, sink or source.
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- Stockman, David R., 2009.
"Chaos and sector-specific externalities,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 33(12), pages 2030-2046, December.
- W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
- Stephanie Schmitt-Grohe & Martin Uribe, 1995.
"Balanced-budget rules, distortionary taxes, and aggregate instability,"
Finance and Economics Discussion Series
95-44, Board of Governors of the Federal Reserve System (U.S.).
- 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.
- Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
- Laura Gardini & Cars Hommes & Fabio Tramontana & Robin de Vilder, 2008.
"Forward and Backward Dynamics in Implicitly Defined Overlapping Generations Models,"
0806, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.
- Gardini, L. & Hommes, C.H. & Tramontana, F. & de Vilder, R., 2009. "Forward and Backward Dynamics in implicitly defined Overlapping Generations Models," CeNDEF Working Papers 09-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Benhabib, Jess & Farmer, Roger E.A., 1995.
"Indeterminacy and Sector-Specific Externalities,"
95-02, C.V. Starr Center for Applied Economics, New York University.
- Roger E.A. Farmer, 1994. "Indeterminacy and Sector-Specific Externalities," UCLA Economics Working Papers 722, UCLA Department of Economics.
- Benhabib, Jess & Farmer, Roger E A, 1996. "Indeterminacy and Sector-specific Externalities," CEPR Discussion Papers 1403, C.E.P.R. Discussion Papers.
- 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.
- Christiano, Lawrence J. & G. Harrison, Sharon, 1999.
"Chaos, sunspots and automatic stabilizers,"
Journal of Monetary Economics,
Elsevier, vol. 44(1), pages 3-31, August.
- Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, sunspots, and automatic stabilizers," Staff Report 214, Federal Reserve Bank of Minneapolis.
- Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, Sunspots, and Automatic Stabilizers," NBER Working Papers 5703, National Bureau of Economic Research, Inc.
- 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.
- Bastiaanssen, W. G. M. & van Dam, J. C. & Droogers, P., 2003. "Introduction," IWMI Books, Reports H043801, International Water Management Institute.
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