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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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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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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. Lars Peter Hansen & Thomas J. Sargent, 1980. "Rational expectations models and the aliasing phenomenon," Staff Report 60, Federal Reserve Bank of Minneapolis. [Downloadable!]
  2. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-63, May. [Downloadable!] (restricted)
  3. Klein, Lawrence R & Preston, R S, 1969. "Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 37(1), pages 95-106, January. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  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. [Downloadable!]
  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. [Downloadable!]
  3. Jordi Caballe & Xavier Jarque & Elisabetta Michetti, 2004. "Chaotic Dynamics in Credit Constrained Emerging Economies," UFAE and IAE Working Papers 605.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC). [Downloadable!]
  4. Luis A. Aguirre & Antonio Aguirre, 1997. "A tutorial introduction to nonlinear dynamics in economics," Nova Economia, Economics Department, Universidade Federal de Minas Gerais (Brazil), vol. 7(2), pages 9-47. [Downloadable!]
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