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1、Empirical and Theoretical Evidence of Economic ChaosSystem Dynamics Review Evidence of Economic Chaos Empirical and theoretical evidence of economic chaos Ping Chen* September 7, 71987 (revised October 29, 1987) System Dynamics Review Vol. 4, No.1-2, 1988 Ping Chen is a Research Fellow at the I. Pri
2、gogine Center for Studies in Statistical Mechanics and Research Associate at the IC2 Institute, University of Texas at Austin. He received a Ph.D. from that University through work on nonlinear dynamics and business cycle theory. Address : Ping Chen, I. Prigogine Center for Studies in Statistical Me
3、chanics, University of Texas, Austin, TX 78712. * The author is greatly indebted to Professor I. Prigogine for inspiring the research of economic chaos and to Professor W. A. Barnett for suggesting the test of monetary aggregates. The author is grateful to Professors. B. L. Hao, H. L. Swinney, G. Ni
4、colis, W. W. Rostow, and P. Allen, and to Drs. A. Arneodo, Y. Yamaguchi, A. Wolf, A. Brandstater, and W. M. Zheng for their valuable discussions. He also appreciates the stimulating comments from Professors J. D. Sterman, E. Mosekilde, P. A. Samuelson, and R. Solow. This research is supported by the
5、 IC2 Institute at Austin. Abstract Empirical and theoretical investigations of chaotic phenomena in macroeconomic systems are presented. Basic issues and techniques in testing economic aggregate movements are discussed. Evidence of low dimensional strange attractors is found in several empirical mon
6、etary aggregates. A continuous time deterministic model with delayed feedback is proposed to describe the monetary growth. Phase transition from periodic to chaotic motion occurs in the model. The model offers an explanation of the multiperiodicity and irregularity in business cycles and of the low-
7、dimensionality of chaotic monetary attractors. Implications in monetary control policy and a new approach to forecasting business cycles are suggested. 1 System Dynamics Review Evidence of Economic Chaos In recent years, there has been rapid progress in the studies of deterministic chaos, random beh
8、avior generated by deterministic systems with low dimensionality. This progress has been made not only in theoretical modelling, but also in experimental testing Abraham , Gollub, and Swinney 1984. Chaotic models have been applied to a variety of dynamic phenomena in the areas of fluid dynamics, opt
9、ics, chemistry, climate and neurobiology. Applications to economic theory have also been developed, especially in business cycle theory see review article: Grandmont and Malgrange 1986. Over the last century, the nature of business cycles has been one of the most important issues in economic theory
10、Zarnowitz 1985. Business cycles have several puzzling features. They have elements of a continuing wave-like movement; they are partially erratic and at the same time serially correlated. More than one periodicity has been identified in business cycles in addition to long growth trends. Most simplif
11、ied models in macroeconomics address one of these features Rau 1974 , while system dynamics models describe economic movements in terms of a large number of variables Forrester 1977. Two basic questions arise in studies of business cycles. Are endogenous mechanism or exogenous stochastics the main c
12、ause of economic fluctuations? And can complex phenomena be characterized by mathematical models as simple as, say, those for planetary motion and electricity? The early deterministic approach to business cycles with well-defined periodicity mainly discussed the endogenous mechanism of economic move
13、ments. A linear deterministic model was first proposed by Samuelson 1939, which generated damped or explosive cycles. Nonlinearities were introduced in terms of limit cycles to explain the self-sustained wavelike movement in economics Goodwin 1951. A stochastic approach seems to be convenient for de
14、scribing the fluctuating behavior in economic systems Osborne 1959; Lucas 1981. The problem with the stochastic models, however, lies in the fact that random noise with finite delay terms (usually less than ten lags, in practice) only explains the short term fluctuating behavior. Most aggregate econ
15、omic data are serially correlated not only in the short term but also over 2 System Dynamics Review Evidence of Economic Chaos long periods. Two methods dealing with long correlations are often used: longer lags in regression studies and multiple differencing time series in ARIMA models. Longer lags require estimating more ;free parameters;, while ARIMA models are essentially whitening processes that wipe out useful information about deterministic mechanism. Actually, fluctuations may be caused by both intrinsic mechanism
