Abstract
Existence theory in economics is usually in real domains such as the findingsof chaotic trajectories in models of economic growth, tâtonnement, oroverlapping generations models. Computational examples, however, sometimesconverge rapidly to cyclic orbits when in theory they should be nonperiodicalmost surely. We explain this anomaly as the result of digital approximationand conclude that both theoretical and numerical behavior can still illuminateessential features of the real data.
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References
Aho, Alfred V. and Ullman, Jeffrey D. (1992). Foundations of Computer Science. Computer Science Press.
Day, Richard H. (1994). Complex Economic Dynamics, v.1. The MIT Press, Cambridge, MA.
Day, Richard H. (1975). Adaptive processes and economic theory. In Richard H. Day and Theodore Groves (eds.), Adaptive Economic Models. Academic Press.
Farebrother, Richard William (1991). The role of chaotic processes in econometric models. Manuscript.
Hommes, Cars H. (1998). On the consistency of backward-looking expectations: The case of the cobweb. Journal of Economic Behavior and Organization, 33, 333–362.
Kaplan, Daniel and Glass, Leon (1995). Understanding Nonlinear Dynamics. Springer-Verlag.
Li, T.Y. and Yorke, J. (1975). Period three implies chaos. American Mathematical Monthly, LXXXII, 985–992.
Martin-Löf, Per (1966). The definition of random sequences. Information and Control, 9, 602–619.
McCullough, B.D. and Vinod, H.D. (1999). The numerically reality of econometric software. Journal of Economic Literature, 37, 633–665.
Nishimura, Kazuo and Sorger, Gerhard (1996). Optimal cycles and chaos: A survey. Studies in Nonlinear Dynamics and Econometrics, 1 (1), 11–28.
Nishimura, Kazuo and Yano, Makoto (1995). Nonlinear dynamics and chaos in optimal growth: An example. Econometrica, 63 (4), 981–1001.
Nusse, Helena E. and Yorke, James A. (1994). Dynamics: Numerical Explorations. Springer-Verlag.
Sorger, Gerhard (1998). Imperfect foresight and chaos: An example of a self-fulfilling mistake. Journal of Economic Behavior and Organization, 33, 363–383.
Stein, P.R. and Ulam, S.M. (1964). Non-linear Transformation Studies on Electronic Computers. Rozprawy Matematycszne XXXIX, Warsaw.
Velupillai, K. Vela (2000). Computable Economics. Oxford University Press, Oxford.
Velupillai, K. Vela (forthcoming). Lectures on Algorithmic Economics: Computability, Complexity, Constructivity and Completeness in Economic Analysis. Oxford University Press, Oxford.
Vuilemin, Jean (1988). Exact real compute arithmetic with continued fractions. Association of Computing Machinery, 12 April, 7, 14–27.
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Day, R.H., Pavlov, O.V. Computing Economic Chaos. Computational Economics 23, 289–301 (2004). https://doi.org/10.1023/B:CSEM.0000026787.81469.1f
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DOI: https://doi.org/10.1023/B:CSEM.0000026787.81469.1f