Balanced-budget rules: Chaos and deterministic sunspots
AbstractSchmitt-Grohé and Uribe  illustrate that a balanced-budget rule can lead to aggregate instability. In particular, under such a rule it is possible for a steady state to be locally indeterminate, and therefore sunspot equilibria are possible. In this paper, I extend their analysis to investigate the possibility of chaotic equilibria under a balanced-budget rule. A global analysis reveals Euler equation branching which means that the dynamics going forward are generated by a differential inclusion of the form . Each branch alone will not imply interesting dynamics. However, by switching between the branches, I show that the existence of Euler equation branching in an arbitrarily small neighborhood of a steady state implies topological chaos in the sense of Devaney on a compact invariant set with non-empty interior (the chaos is "thick"). Moreover, the chaos is robust to small perturbations. This branching under a balanced-budget rule occurs independently of the local uniqueness of the equilibrium around the steady state(s).
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 145 (2010)
Issue (Month): 3 (May)
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Web page: http://www.elsevier.com/locate/inca/622869
Balanced-budget rule Euler equation branching Sunspots Indeterminacy Cycles Chaos Multi-valued dynamical system Differential inclusion Regime switching;
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