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Chaotic Dynamics and Bifurcation in a Macro Model

Working Paper 140 | Published January 1, 1980

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Michael J. Stutzer Professor of Finance, University of Iowa

Chaotic Dynamics and Bifurcation in a Macro Model


The qualitative dynamics of a discrete time version of a deterministic, continuous time, nonlinear macro model formulated by Haavelmo are fully characterized. The 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.