There are two contrasting viewpoints concerning the explanation of observed fluctuations in economic and financial markets. According to the first {Newclassical) view the main source of fluctuations is to be found in exogenous, random shocks to fundamentals. In the absence of shocks, prices and other variables would converge to a steady state (growth) path, completely determined by fundamentals. According to the second [Keynesian) view a significant part of observed fluctuations is caused by nonlinear economic laws. Even in the absence of any external shocks, nonlinear market laws can generate endogenous business fluctuations. The newclassical view is intimately related to the concept of rational expectations, whereas animal spirits or market psychology have been an important Keynesian theme.
In finance the two different viewpoints lead to opposite views concerning the efficiency of financial markets. In the efficient market hypothesis (EMH) the current price already contains all information and past prices can not help in predicting future prices. Parametric stochastic processes have been used in the empirical literature that are consistent with the EMH. Examples include random walk processes, GARCH-processes and the like. In contrast, Keynes already argued that stock prices are not only determined by fundamentals, but in addition market psychology and investors animal spirits influence financial markets significantly. In the Keynesian view, simple technical trading rules, such as extrapolation of a trend, may help predict future price changes. In fact, recently Brock, Lakonishok and LeBaron (1992) have indeed shown that simple technical trading rules, such as moving average and trading range break, when used in predicting the Dow Jones Index, consistently outperform several popular stochastic finance models, such as the random walk and the GARCH-model.
The discovery of chaotic, seemingly random looking dynamical behaviour in simple deterministic models sheds important new light on this debate. A simple deterministic financial market model with a strange attractor may generate erratic, seemingly unpredictable stock price fluctuations very similar to a random walk. Prices moving on a strange attractor may be very difficult to predict and chaos may thus be consistent with a weak form of the EMH. Intermittent chaotic time series, characterized by irregular switching between a stable phase of low volatility and an unstable phase of high volatility, may explain the well known GARCH effects frequently observed in financial data.
At this point, let us briefly review the "state of the art" concerning chaos in economics and finance. It has been shown that simple nonlinear general equilibrium models, satisfying the currently dominating assumptions in economic theory (i.e. utility or profit maximizing agents, rational, self fulfilling expectations and market clearing), can generate chaotic equilibrium dynamics. For the popular overlapping generations (OLG) model this has been shown by Benhabib and Day (1982) and Grandmont (1985) and in optimal growth models by Boldrin and Montrucchio (1986), as e.g. surveyed in Boldrin and Woodford (1990) and Nishimura and Sorger (1996). In all these examples the dynamics can be reduced to a one-dimensional nonlinear difference equation. Only very recently there have been some two-dimensional generalisations, e.g. an OLG-economy with production (Medio and Negroni (1993) and de Vilder (1995). In higher dimensional models, chaos may arise with much less nonlinearity than in the one dimensional case. For example in the one dimensional OLG-model a strong income effect is needed to generate chaotic equilibrium cycles, whereas in the two dimensional OLG model with production, chaos may arise even when the two goods, current leisure and future consumption, are gross substitutes.
The (chaotic) time series generated by these models all seem to be clearly different from actual (macro) economic data however. Apparantly, the models are still "too simple to be true". In fact, there is little empirical evidence for low dimensional chaos in (macro) economic data. But as Brock and Sayers (1988, p.78) emphasize, "..the methods we utilized may be too weak to detect chaos if it exists". The main reason is that macro economic time series are too short and probably too noisy to detect chaos, even if it were present. For surveys on testing for chaos in economics and finance, see e.g. Brock (1986) and Brock, Hsieh and LeBaron (1991).
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