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Optimal Cycles and Chaos: A Survey

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Author Info
Kazuo Nishimura (Kyoto University)
Gerhard Sorger (University of Vienna)

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Abstract

This paper surveys the literature on cyclical and chaotic equilibrium paths in deterministic optimal growth models with infinitely lived agents. We focus on discrete time models but also briefly mention results for continuous time models. We start by reviewing those results that have been proved for optimal growth models in reduced form. Then we discuss results for two-sector optimal growth models in primitive form. Finally, we summarize a few results that have been obtained for other variants of the model, including models with recursive preferences and models with heterogeneous agents.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 1 (1996)
Issue (Month): 1 ()
Pages: 11-28
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Handle: RePEc:bep:sndecm:1:1996:1:11-28

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. George W. Stadler, 1994. "Real Business Cycles," Journal of Economic Literature, American Economic Association, vol. 32(4), pages 1750-1783, December. [Downloadable!] (restricted)
  2. Sorger, Gerhard, 1992. "On the minimum rate of impatience for complicated optimal growth paths," Journal of Economic Theory, Elsevier, vol. 56(1), pages 160-179, February. [Downloadable!] (restricted)
  3. William A. Brock, 1993. "Pathways to randomness in the economy: Emergent nonlinearity and chaos in economics and finance," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(1), pages 3-55.
    Other versions:
  4. Benhabib, Jess & Majumdar, M. & Nishimura, Kazuo, 1987. "Global Equilibrium Dynamics with Stationary Recursive Preferences," Working Papers 87-05, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
    Other versions:
  5. Benhabib, Jess & Jafarey, Saqib & Nishimura, Kazuo, 1988. "The dynamics of efficient intertemporal allocations with many agents, recursive preferences, and production," Journal of Economic Theory, Elsevier, vol. 44(2), pages 301-320, April. [Downloadable!] (restricted)
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  6. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December. [Downloadable!] (restricted)
  7. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66, pages 467. [Downloadable!] (restricted)
  8. Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February. [Downloadable!] (restricted)
  9. Nishimura, Kazuo & Yano, Makoto, 1995. "Durable capital and chaos in competitive business cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 165-181, July. [Downloadable!] (restricted)
  10. Montrucchio, Luigi & Sorger, Gerhard, 1996. "Topological entropy of policy functions in concave dynamic optimization models," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 181-194. [Downloadable!] (restricted)
  11. Deneckere, Raymond & Pelikan, Steve, 1986. "Competitive chaos," Journal of Economic Theory, Elsevier, vol. 40(1), pages 13-25, October. [Downloadable!] (restricted)
  12. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February. [Downloadable!] (restricted)
  13. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October. [Downloadable!] (restricted)
  14. Sorger, Gerhard, 1994. "Policy functions of strictly concave optimal growth models," Ricerche Economiche, Elsevier, vol. 48(3), pages 195-212, September. [Downloadable!] (restricted)
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  15. Neumann, Dean & O'Brien, Thomas & Hoag, John & Kim, Kyoo, 1988. "Policy functions for capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 46(1), pages 205-214, October. [Downloadable!] (restricted)
  16. Boldrin, Michele & Deneckere, Raymond J., 1990. "Sources of complex dynamics in two-sector growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 627-653, October. [Downloadable!] (restricted)
  17. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March. [Downloadable!] (restricted)
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  18. McKenzie, Lionel W., 1983. "Turnpike theory, discounted utility, and the von Neumann facet," Journal of Economic Theory, Elsevier, vol. 30(2), pages 330-352, August. [Downloadable!] (restricted)
  19. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September. [Downloadable!] (restricted)
  20. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December. [Downloadable!] (restricted)
  21. Baumol, William J & Benhabib, Jess, 1989. "Chaos: Significance, Mechanism, and Economic Applications," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 77-105, Winter. [Downloadable!] (restricted)
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  22. Cartigny, Pierre & Venditti, Alain, 1994. "Turnpike theory : Some new results on the saddle point property of equilibria and on the existence of endogenous cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 957-974, September. [Downloadable!] (restricted)
  23. Amir, R., 1991. "Sensitivity analysis of multi-sector optimal economic dynamics," Papers 9106, Universite catholique de Louvain - Center for Operations Research and Economics (CORE).
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  24. Hernandez D, Alejandro, 1991. "The dynamics of competitive equilibrium allocations with borrowing constraints," Journal of Economic Theory, Elsevier, vol. 55(1), pages 180-191, October. [Downloadable!] (restricted)
  25. Scheinkman, Jose A, 1990. "Nonlinearities in Economic Dynamics," Economic Journal, Royal Economic Society, vol. 100(400), pages 33-48, Supplemen. [Downloadable!] (restricted)
  26. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation, Yale University. [Downloadable!]
  27. Frank, Murray Z & Stengos, Thanasis, 1988. " Chaotic Dynamics in Economic Time-Series," Journal of Economic Surveys, Blackwell Publishing, vol. 2(2), pages 103-33.
  28. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February. [Downloadable!] (restricted)
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  29. Becker, Robert A & Foias, Ciprian, 1994. "The Local Bifurcation of Ramsey Equilibrium," Economic Theory, Springer, vol. 4(5), pages 719-44, August.
  30. Nishimura, Kazuo & Yano, Makoto, 1994. "Optimal Chaos, Nonlinearity and Feasibility Conditions," Economic Theory, Springer, vol. 4(5), pages 689-704, August.
  31. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October. [Downloadable!] (restricted)
  32. Benhabib, Jess & Rustichini, Aldo, 1990. "Equilibrium cycling with small discounting," Journal of Economic Theory, Elsevier, vol. 52(2), pages 423-432, December. [Downloadable!] (restricted)
  33. Epstein, Larry G, 1987. "The Global Stability of Efficient Intertemporal Allocations," Econometrica, Econometric Society, vol. 55(2), pages 329-55, March. [Downloadable!] (restricted)
  34. Nishimura, Kazuo, 1985. "Competitive equilibrium cycles," Journal of Economic Theory, Elsevier, vol. 35(2), pages 284-306, August. [Downloadable!] (restricted)
  35. Nishimura, Kazuo & Sorger, Gerhard & Yano, Makoto, 1994. "Ergodic Chaos in Optimal Growth Models with Low Discount Rates," Economic Theory, Springer, vol. 4(5), pages 705-17, August.
  36. Medio, Alfredo, 1987. "Oscillations in optimal growth models," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 413-427, September. [Downloadable!] (restricted)
  37. Boldrin, Michele & Rustichini, Aldo, 1994. "Growth and Indeterminacy in Dynamic Models with Externalities," Econometrica, Econometric Society, vol. 62(2), pages 323-42, March. [Downloadable!] (restricted)
  38. Medio, Alfredo, 1987. "Oscillations in optimal growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 11(2), pages 201-206, June. [Downloadable!] (restricted)
  39. Nishimura, Kazuo & Yano, Makoto, 1993. "Interlinkage in the Endogenous Real Business Cycles of International Economies," Economic Theory, Springer, vol. 3(1), pages 151-68, January.
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jang-Ting Guo & Kevin Lansing, 1999. "Fiscal policy, increasing returns, and endogenous fluctuations," Working Papers in Applied Economic Theory 99-08, Federal Reserve Bank of San Francisco. [Downloadable!]
  2. Jess Benhabib, 1996. "On Cycles and Chaos in Economics," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 1(1), pages 1-2. [Downloadable!] (restricted)
  3. William A. Barnett & Alfredo Medio & Apostolos Serletis, 1997. "Nonlinear and Complex Dynamics in Economics," Econometrics 9709001, EconWPA. [Downloadable!]
  4. Pietro Reichlin, 1997. "Endogenous Cycles in Competitive Models: An Overview," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 1(4), pages 175-185. [Downloadable!] (restricted)
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