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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.

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  • 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. L. G. Telser & R. L. Graves, 1968. "Continuous and Discrete Time Approaches to a Maximization Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(3), pages 307-325.
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    4. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
    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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