FRACTALS, CHAOS THEORY AND THE LIMITS OF ECONOMIC FORECASTING Foreword Economic forecasting is one of the mainstays of the economics profession. The importance of knowing where the economy is going, and at what speed, is considered essential by policy makers and of the greatest importance by businessmen and stock market professionals. Modern forecasting techniques grew out of wartime weather forecasting, where many of its techniques were developed, and business cycle analysis, where the movement of leading, concurrent, and lagging indicators has been studied for many years. When the Organization for Economic Cooperation and Development undertook its first exercise in group short-term forecasting in 1963, aware as it was of the shortcomings of any attempt to predict the future, it was convinced that through the exchange of forecasts and policy intentions on the part of the twenty-four most advanced economies in the Free World, "it would be difficult to provide more useful guidance as to how the economy was likely to develop than (these) official forecasting procedures would reveal." (Timmins & Timmins, The International Economic Policy Coordination Instrument: The OECD Experience , University Press, 1985, p.75). Since the recession of 1982-83, forecasting has fallen on hard times. This has been widely attributed to the rapidly changing parameters of the national and world economies, which, it is often asserted, have impaired the accuracy of its results. Nevertheless, its perceived importance is undiminished and the number of forecasts and forecasters has proliferated to the point where it has become a veritable industry--and where, at least in the United States, there are even forecasters who prepare forecasts consisting of the combined forecasts of other forecasters. Hubris: and Other Contemporary Problems Because of the nature of the material with which the discipline of economics works--money supply, expenditures, taxes, employment levels, and the inflation rate--all of which can be counted or estimated with reasonable accuracy, economic forecasting has developed tools and methods which have come to be widely adopted by the other social sciences. That economics should have striven to emulate the methods of the exact sciences should surprise no one. The 18th Century French mathematician Pierre Simon de Laplace once boasted that given the position and velocity of every particle in the universe, he could predict the future for the rest of time. And until recently, there was little reason to doubt that precise predictability could in principle be achieved. It was only necessary to refine our data gathering procedures and process adequate data with sufficient accuracy. Adjusting for the expectations of one's major trading partners and taking into account intended policy changes, it appeared not unreasonable that the OECD Secretariat could produce a short-term forecast with a plus or minus 2 or 3 percent degree of accuracy--adequate for member-country needs. Economic forecasting has always had to contend with an inherent problem. The "curves" with which it works do not always represent the reality it is trying to analyze. There is not only the problem of dealing with "straight line curves" to simplify the mathematics, there is the fact that even using the more difficult calculus to analyze a fitted curve, forecasters have been unable to deal with the irregularities inherent in the data, viz. abrupt shifts and occasional discontinuities in the data. Fractals & Chaos Theory Provide an Explanation This is a problem which confronted not only the social, but the natural sciences, until the recent development of "Fractal Geometry". And what is a "fractal"? It is an object or process -- a curve, for instance, or a set of points--that cannot be adequately represented by Euclidian geometry -- precisely the problem of economic analysis. The path of economic expansion and recession does not follow a regular wave-path. Nor does the growth of demand for a new product follow a smoothly ascending curve: though economists were compelled to treat them as such until the concept of fractals was introduced; which, as we gain familiarity with it, held the promise of enabling us to come to better terms with the complexities of economic reality. This hope has been radically disappointed in the exact sciences by a striking discovery: simple deterministic systems with only a few elements of freedom can generate random behavior which defeats all efforts at predictability. while fractals remain an exciting field of pure mathematics and an important new tool giving sharp new insights into the behavior and internal logic of nature and its processes, its promise of helping us to better understand the pace and direction of change seems to be limited. This limitation arises from a simultaneous new development in mathematics which has come to be called Chaos Theory -- which appears to be fully applicable in the realm of economic analysis and forecasting (See "Chaos", James P. Crutchfield, J. Doyne Farmer, Norman H. Packard, and Robert S. Shaw, Scientific American , December 1986). The traditional approach of economics, gathering more data, or processing it more elaborately, does not reduce this random unpredictability. Such "chaos" appears itself to be deterministic, being generated by fixed rules which do not themselves involve any elements of chance. In principle, therefore, while the future is completely determined by the past, in practice even small uncertainties are amplified, presenting fundamental limits to predicting more than the shortest of short-term events. For some time, at least since the serious forecasting problems of recent years arose, economists have been re-examining the reasons for their forecasting problems. Among the factors blamed have been the Heisenberg uncertainty principle of quantum mechanics, which states that there are fundamental limits to the accuracy with which phenomena can be measured, and Landau's theory of the complexity of independent oscillations. Landau's theory has, however, been disproved. It appears that chaotic systems are sensitive to exogenous forces not only at the beginning of an event, but at every point in their motion. It is the exponential amplification of errors due to this chaotic dynamic which provides the true undoing of Laplace's determinism. This dynamic was discovered by Professor Edward N. Lorenz of M.I.T., who in 1963 in the course of studying the unpredictability of weather, obtained a system with only three degrees of freedom, which nevertheless behaved in a totally random fashion which could not be explained by any then known physics. He found that even microscopic perturbations became quickly amplified to affect macroscopic behavior. This process is today known as the "Lorenz Attractor". Two orbits with essentially identical initial conditions, diverge exponentially fast and within half a dozen rotations become randomly (or chaotically) different. The basis for Lorenz' theory is, again, fractal mathematics, a relatively new branch of study which has attracted enormous attention in such diverse fields as biology, botany, and astrophysics. It appears to us to have applicability to economic theory as well. The stretching and folding operation of a chaotic attractor systematically removes the initial information and replaces it with new information. In their Scientific American article, Crutchfield, Farmer, Packard, and Shaw use the example of kneading bread with an internal spot of dye. The stretch makes small-scale uncertainties larger, the fold brings wide-separated trajectories together and erases large-scale information. Chaotic attractors act as a kind of pump bringing microscopic fluctuations up to macroscopic importance. It thus becomes clear that there can be no exact forecasts of the future. After a brief time interval the uncertainties in the initial measurements cover the entire attractor and all predictive power is lost. There is simply no causal connection between past and future. Even attempts to replace no longer functioning economic indicators following each episode of the business cycle can have no more than a minor effect in attempting to predict the next cycle. Chaos Theory also brings a new challenge to the econometric view that a system can be understood by breaking it down and studying each piece; i.e. by modeling the economy. The modeling approach has until now been prevalent in many scientific fields because there are so many systems for which the behavior of the whole is indeed the sum of its parts. Chaos demonstrates, however, that a system can have a complicated behavior that emerges as a consequence of the simple, nonlinear interaction of as few as three components, defeating elaborate attempts to fit together accurately measured sub-accounts of the economy for predictive purposes. And Widens Understanding While Opening New Perspectives This is not a counsel of despair for economists. It is rather a call for the recognition of the limits of accuracy and predictability in human inquiry -- not only for economics, but for a wide range of scientific disciplines. The ability to obtain detailed knowledge of a system's structure has undergone tremendous advances in recent years, but the ability to integrate this knowledge has been stymied by the lack of an adequate conceptual framework within which to describe qualitative behavior. The interaction of components on one scale can lead to complex global behavior on a larger scale that simply cannot be deduced from a knowledge of individual components. As Crutchfield, Farmer, Packard, and Shaw said in their own concluding paragraph, fractal chaos provides for the acceptance of free will in a universe governed by deterministic law. Can there be a more appropriately hopeful note for the practitioners of a profession in which prediction has seemingly reached its limits, and in which trademarks, advertising, and salesmanship to appeal to subtle differences in individual preference functions are our stock in trade?