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Chaotic dynamics and bifurcation in a macro model

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  • Michael J. Stutzer
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    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.

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    Bibliographic Info

    Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 55.

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    Date of creation: 1980
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    Handle: RePEc:fip:fedmsr:55

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    1. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May.
    2. Klein, Lawrence R & Preston, R S, 1969. "Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 37(1), pages 95-106, January.
    3. Lars Peter Hansen & Thomas J. Sargent, 1980. "Rational expectations models and the aliasing phenomenon," Staff Report 60, Federal Reserve Bank of Minneapolis.
    4. 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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    Cited by:
    1. 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.
    2. Michele Boldrin, 1988. "Persistent Oscillations and Chaos in Dynamic Economic Models: Notes for a Survey," UCLA Economics Working Papers 458A, UCLA Department of Economics.
    3. 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.
    4. 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.
    5. Luís A. Aguirre & Antônio Aguirre, 1995. "A tutorial introduction to nonlinear dynamics in economics," Textos para Discussão Cedeplar-UFMG td088, Cedeplar, Universidade Federal de Minas Gerais.
    6. 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.
    7. Mahajan, Arvind & Wagner, Andrew J., 1999. "Nonlinear dynamics in foreign exchange rates," Global Finance Journal, Elsevier, vol. 10(1), pages 1-23.

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