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Balanced-budget rules: Chaos and deterministic sunspots

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  • Stockman, David R.

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 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 Info

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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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Balanced-budget rule Euler equation branching Sunspots Indeterminacy Cycles Chaos Multi-valued dynamical system Differential inclusion Regime switching;

References

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  1. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.
  2. 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.
  3. 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.
  4. 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).
  5. Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, sunspots, and automatic stabilizers," Staff Report 214, Federal Reserve Bank of Minneapolis.
  6. 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.
  7. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  8. 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.
  9. Stephanie Schmitt-Grohe & Martin Uribe, 1995. "Balanced-budget rules, distortionary taxes, and aggregate instability," Finance and Economics Discussion Series 95-44, Board of Governors of the Federal Reserve System (U.S.).
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Citations

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Cited by:
  1. Zhang, Yan & Chen, Yan, 2012. "Tariff And Equilibrium Indeterminacy: A Global Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S3), pages 394-410, November.
  2. Nicolas Abad & Thomas Seegmuller & Alain Venditti, 2012. "Aggregate Instability under Labor Income Taxation and Balanced-Budget Rules: Preferences Matter," AMSE Working Papers 1217, Aix-Marseille School of Economics, Marseille, France, revised Apr 2012.
  3. Raines, Brian E. & Stockman, David R., 2010. "Chaotic sets and Euler equation branching," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1173-1193, November.
  4. Mario Coccia, 2012. "What are the effects of public debt on innovation and employment growth?," CERIS Working Paper 201206, Institute for Economic Research on Firms and Growth - Moncalieri (TO).
  5. Richard Barnett & Joydeep Bhattacharya & Helle Bunzel, 2013. "Deviant generations, Ricardian equivalence, and growth cycles," Economic Theory, Springer, vol. 52(1), pages 367-396, January.
  6. Stockman, David R., 2011. "Chaos and capacity utilization under increasing returns to scale," Journal of Economic Behavior & Organization, Elsevier, vol. 77(2), pages 147-162, February.

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