Balanced-budget rules: Chaos and deterministic sunspots |
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Authors: | David R Stockman |
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Institution: | Department of Economics, University of Delaware, Newark, DE 19716, United States |
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Abstract: | Schmitt-Grohé and Uribe 11] 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 C1 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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Keywords: | E13 E32 E62 |
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