Chaotic sets and Euler equation branching
AbstractAbstract 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 46 (2010)
Issue (Month): 6 (November)
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Web page: http://www.elsevier.com/locate/jmateco
Indeterminacy Euler equation branching Multiple equilibria Cycles Devaney chaos Li-Yorke chaos Distributional chaos Increasing returns to scale Externality Regime switching;
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