Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T18:36:30.240Z Has data issue: false hasContentIssue false
  • English
  • Français

APERIODIC DYNAMICS IN THE BERGSTROM/WYMER MODEL OF THE UNITED KINGDOM

Published online by Cambridge University Press:  01 August 2009

Clifford R. Wymer
Get access Rights & Permissions [Opens in a new window]

Abstract

Lyapunov exponents may be used to provide information on attractors of nonlinear models and, if strange, their aperiodic dynamics, in much the same way as eigenvalues of a linear model. An advantage of calculating these from an estimated model, rather than calculating the largest ones from a time series, is that economic theory is used to help distinguish between deterministic and stochastic behavior. Estimates of the Bergstrom/Wymer model of the United Kingdom, and of some other models of a similar form, were unstable in a classical sense, to some extent being caused by policy parameters. The Lyapunov exponents show that this model, and variants of it, have strange attractors in the neighborhood of the estimated parameter values and hence are stable but with aperiodic oscillations.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 4: Bergstrom Memorial Dedication Issue , August 2009 , pp. 1099 - 1111
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bergstrom, A.R. (1984) Monetary, fiscal and exchange rate policy in a continuous time model of the United Kingdom. In Malgrange, P. & Muet, P. (eds.), Contemporary Macroeconomic Modelling, pp. 183–206. Blackwell.Google Scholar
Bergstrom, A.R. & Nowman, K.B. (2007) A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends. (First presented as “Gaussian estimation of a continous time macroeconometric model of the United Kingdom with unobservable stochastic trends,”Cowles Foundation Conference on Recent Developments in Times Series Econometrics, Yale, 23–24 October 1999.)CrossRefGoogle Scholar
Bergstrom, A.R., Nowman, K.B., & Wymer, C.R. (1992) Gaussian estimation of a second order continuous time macroeconometric model of the United Kingdom. Economic Modelling 9, 313–51.CrossRefGoogle Scholar
Bergstrom, A.R. & Wymer, C.R. (1976) A model of disequilibrium neoclassical growth and its application to the United Kingdom. In Bergstrom, A.R. (ed.), Statistical Inference in Continuous-Time Economic Models, pp. 267–328. North-Holland.Google Scholar
Barnett, W.A., Gallant, A.R., Hinich, M.J., Jungeilges, J.A., Kaplan, D.T., & Jensen, M.J. (1997) A single blind controlled competition among tests for non-linearity and chaos. Journal of Econometrics 82, 157–192.CrossRefGoogle Scholar
Barnett, W.A. & He, Yijun (1999) Stability analysis of continuous time macroeconomic systems. Studies in Non-Linear Dynamics and Control 3, 169–188.Google Scholar
Barnett, W.A. & He, Yijun (2002) Stabilization policy as bifurcation selection: Would stabilization policy work if the economy really were unstable? Macroeconomic Dynamics 6, 713–747.CrossRefGoogle Scholar
Brock, W. & Dechert, W.D. (1988) Theorems on distinguishing deterministic and random systems. In Barnett, W.A., Berndt, E.R., & White, H. (eds.), Dynamic Econometric Modelling. Cambridge University Press.Google Scholar
Donaghy, K.P. (1993) A continuous time model of the United States economy. In Gandolfo, G. (ed.), Continuous Time Econometrics: Theory and Applications, pp. 151–193. Chapman-Hall.CrossRefGoogle Scholar
Eckmann, J-P. & Ruelle, D. (1985) Ergodic theory of chaos and strange attractors. Reviews of Modern Physics 57, 617–656.CrossRefGoogle Scholar
Gandolfo, G. & Padoan, P.C. (1990) The Italian continuous time model: Theory and empirical results. Economic Modelling 7, 91–132.CrossRefGoogle Scholar
Goodwin, R.M. (1990) Chaotic Economic Dynamics. Clarendon Press.CrossRefGoogle Scholar
Grassberger, P. & Procaccia, I. (1983) Estimation of Kolmogorov entropy from a chaotic signal. Physical Review A 28, 2591–2593.CrossRefGoogle Scholar
Jonson, P.D., Moses, E.R., & Wymer, C.R. (1977) A minimal model of the Australian economy. In Norton, W.E. (ed.), Conference in Applied Economic Research. Reserve Bank of Australia.Google Scholar
Knight, M.D. & Wymer, C.R. (1978) A Macroeconomic Model of the United Kingdom. IMF Staff Papers 25, 742–778.CrossRefGoogle Scholar
Lorenz, H-W. (1989) Non-Linear Dynamical Economics and Chaotic Motion. Springer-Verlag.CrossRefGoogle Scholar
Wymer, C.R. (1996) The role of continuous time disequilibrium models in macro-economics. In Barnett, W.A., Gandolfo, G., & Hillinger, C. (eds.), Dynamic Disequilibrium Modelling. Cambridge University Press.Google Scholar