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Chaotic dynamics and bifurcation in a macro model

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  • Michael J. Stutzer

Abstract

The qualitative dynamics of a discrete time version of a deterministic, continuous time, nonlinear macro model formulated by Haavelmo are fully characterized. Recently developed methods of symbolic dynamics and ergodic theory are shown to provide a simple, effective means of analyzing the behavior of the resulting one-parameter family of first-order, deterministic, nonlinear difference equations. A complex periodic and random “aperiodic” orbit structure dependent on a key structural parameter is present, which contrasts with the total absence of such complexity in Haavelmo’s continuous time version. Several implications for dynamic economic modelling are discussed.

Suggested Citation

  • Michael J. Stutzer, 1980. "Chaotic dynamics and bifurcation in a macro model," Staff Report 55, Federal Reserve Bank of Minneapolis.
  • Handle: RePEc:fip:fedmsr:55
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    References listed on IDEAS

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    1. Lars Peter Hansen & Thomas J. Sargent, 1980. "Rational expectations models and the aliasing phenomenon," Staff Report 60, Federal Reserve Bank of Minneapolis.
    2. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
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    5. Klein, Lawrence R & Preston, R S, 1969. "Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 37(1), pages 95-106, January.
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    Cited by:

    1. Frédéric Lordon, 1991. "Théorie de la croissance : quelques développements récents [Première partie : la croissance récente]," Revue de l'OFCE, Programme National Persée, vol. 36(1), pages 157-211.
    2. repec:eee:ecofin:v:42:y:2017:i:c:p:584-596 is not listed on IDEAS
    3. Michele Boldrin, 1988. "Persistent Oscillations and Chaos in Dynamic Economic Models: Notes for a Survey," UCLA Economics Working Papers 458A, UCLA Department of Economics.
    4. Max Stevenson, 1993. "An Economic Analysis of Genetic Improvement Within a Commercial Livestock Population," Working Paper Series 26, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Luis A. Aguirre & Antonio Aguirre, 1997. "A tutorial introduction to nonlinear dynamics in economics," Nova Economia, Economics Department, Universidade Federal de Minas Gerais (Brazil), pages 9-47.
    6. Nijkamp, P. & Reggiani, A., 1988. "Theory of chaos in a space-time perspective," Serie Research Memoranda 0029, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. Mahajan, Arvind & Wagner, Andrew J., 1999. "Nonlinear dynamics in foreign exchange rates," Global Finance Journal, Elsevier, vol. 10(1), pages 1-23.
    8. Nijkamp, P. & Reggiani, A., 1990. "Impacts of multiple period lags in dynamic logit models," Serie Research Memoranda 0083, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    9. Caballe, Jordi & Jarque, Xavier & Michetti, Elisabetta, 2006. "Chaotic dynamics in credit constrained emerging economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1261-1275, August.
    10. Wei-Bin Zhang, 2016. "Population Growth And Preference Change In A Generalized Solow Growth Model With Gender Time Distributions," Oradea Journal of Business and Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 7-30, September.
    11. Frédéric Lordon, 1995. "Cycles et chaos dans un modèle hétérodoxe de croissance endogène," Revue Économique, Programme National Persée, vol. 46(6), pages 1405-1432.
    12. Wei-Bin Zhang, 2016. "Endogenous Population Dynamics and Economic Growth with Free Trade between Countries," Social Sciences and Education Research Review, Department of Communication, Journalism and Education Sciences, University of Craiova, vol. 3(1), pages 3-30, May.
    13. Wei-Bin Zhang, 2017. "Economic Development and Environmental Change with Endogenous Birth and Mortality Rates," Asian Journal of Economic Modelling, Asian Economic and Social Society, vol. 5(1), pages 77-97, March.
    14. Grandmont, Jean-Michel, 1998. "Introduction to Market Psychology and Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 1-13, May.
    15. Luis A. Aguirre & Antonio Aguirre, 1997. "A tutorial introduction to nonlinear dynamics in economics," Nova Economia, Economics Department, Universidade Federal de Minas Gerais (Brazil), pages 9-47.
    16. Wei-Bin Zhang, 2014. "Endogenous population with human and physical capital accumulation," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 61(3), pages 231-252, September.
    17. Nijkamp, P. & Poot, J., 1991. "Lessons from non-linear dynamic economics," Serie Research Memoranda 0105, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    18. Nijkamp, P. & Reggiani, A., 1990. "Spatio-temporal processes in dynamic logit models," Serie Research Memoranda 0063, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    19. Zhang W.B., 2015. "Birth And Mortality Rates, Gender Division Of Labor, And Time Distribution In The Solow Growth Model," Revista Galega de Economía, University of Santiago de Compostela. Faculty of Economics and Business., pages 121-134.
    20. Kirkpatrick, Grant, 1984. "A continuous time cyclical growth model for the Federal Republic of Germany: Construction, estimation and analysis," Kiel Working Papers 219, Kiel Institute for the World Economy (IfW).
    21. Nijkamp, P. & Poot, J. & Rouwendal, J., 1988. "R & D policy in space and time : a nonlinear evolutionary growth model," Serie Research Memoranda 0030, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    22. Nijkamp, P. & Poot, J. & Rouwendal, J., 1988. "R & D policy in space and time : a nonlinear evolutionary growth model," Serie Research Memoranda 0030, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    23. Chatrath, Arjun & Adrangi, Bahram & Dhanda, Kanwalroop Kathy, 2002. "Are commodity prices chaotic?," Agricultural Economics of Agricultural Economists, International Association of Agricultural Economists, vol. 27(2), August.
    24. Peter Nijkamp & Jacques Poot & Jan Rouwendal, 1988. "R and D policy in space and time. A nonlinear evolutionary growth model," Working Papers hal-01541463, HAL.

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