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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).

Suggested Citation

  • Stockman, David R., 2010. "Balanced-budget rules: Chaos and deterministic sunspots," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1060-1085, May.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:3:p:1060-1085
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    References listed on IDEAS

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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. 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.
    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 367-391, June.
    4. Christiano, Lawrence J. & G. Harrison, Sharon, 1999. "Chaos, sunspots and automatic stabilizers," Journal of Monetary Economics, Elsevier, vol. 44(1), pages 3-31, August.
    5. 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.
    6. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
    7. 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.
    8. 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.
    9. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    10. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
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    Citations

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    Cited by:

    1. Matteo F. Ghilardi & Raffaele Rossi, 2014. "Aggregate Stability and Balanced‐Budget Rules," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 46(8), pages 1787-1809, December.
    2. Richard Barnett & Joydeep Bhattacharya & Helle Bunzel, 2013. "Deviant generations, Ricardian equivalence, and growth cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 367-396, January.
    3. repec:eee:mateco:v:74:y:2018:i:c:p:46-55 is not listed on IDEAS
    4. 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.
    5. Zhang, Yan & Chen, Yan, 2012. "Tariff And Equilibrium Indeterminacy: A Global Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S3), pages 394-410, November.
    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.
    7. Huang, Kevin X.D. & Meng, Qinglai & Xue, Jianpo, 2017. "Balanced-budget income taxes and aggregate stability in a small open economy," Journal of International Economics, Elsevier, vol. 105(C), pages 90-101.
    8. 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) ITALY -NOW- Research Institute on Sustainable Economic Growth - Moncalieri (TO) ITALY.
    9. Kevin x.d. Huang & Qinglai Meng & Jianpo Xue, 2017. "Balanced-budget rules and aggregate instability: The role of endogenous capital utilization," Vanderbilt University Department of Economics Working Papers 17-00005, Vanderbilt University Department of Economics.
    10. 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.

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