Balanced-budget rules: Chaos and deterministic sunspots

• 成果类型: Article
• 署名作者: Stockman, David R.
• 署名单位: University of Delaware
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2009.10.014
• 发表日期: 2010
• 页码: 1060-1085
• 关键词: Balanced-budget rule; Euler equation branching; sunspots; indeterminacy; cycles; chaos; Multi-valued dynamical system; Differential inclusion; regime switching

摘要

Schmitt-Grohe 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 (x) over dot is an element of {f, g(x)}. 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 C(1) perturbations. This branching under a balanced-budget rule occurs independently of the local uniqueness of the equilibrium around the steady state(s). (C) 2009 Elsevier Inc. All rights reserved.