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Balanced-budget rules: Chaos and deterministic sunspots

  • Stockman, David R.

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 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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 3 (May)
Pages: 1060-1085

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:3:p:1060-1085
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  1. 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.
  2. 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.
  3. 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.
  4. Guo, Jang-Ting & Harrison, Sharon G., 2004. "Balanced-budget rules and macroeconomic (in)stability," Journal of Economic Theory, Elsevier, vol. 119(2), pages 357-363, December.
  5. GRANDMONT, Jean-Michel & PINTUS, Patrick & de VILDER, Robin, 1997. "Capital-labor substitution and competitive nonlinear endogenous business cycles," CORE Discussion Papers 1997087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1633-1671, May.
  7. Seierstad, Atle & Sydsaeter, Knut, 1977. "Sufficient Conditions in Optimal Control Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 367-91, June.
  8. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  9. Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
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