Why Does Economics Need Chaos Theory - Essay Example

Running Head: Chaos theory Implication of Chaos theory on financial forecasting of the of the What is chaos and chaos theory Chaos comes from the Greek word meaning "gaping void", which also sounds confusing and indefinite as the word itself. According to the Greek Mythology, Chaos represents the very previous moments of existence, when it is entirely filled with nothing a.k.a. the void. The ancient Roman writer Ovid described this state of Chaos as an unordered and formless primordial form of mass. Continuing with the mythology, Chaos gave life (or birth) to the Gaia, who is the creator of earth and grandmother of Zeus. Since Gaia and other gods who derived from her create all beings, we can reach the most exciting part of our little mythology trip, the word Chaos that means "gaping void" includes the meaning that existence is actually a projection of chaos. Nowadays modern science and daily life describes chaos similar to each other, both meaning something such as a state of unpredictable confusion and extreme disorder. According to the chaos theorists, chaos has two most important attributes which are both necessary for existence of a chaotic system but not sufficient; one, extreme sensitivity to its initial conditions (Ruelle, 2001:37-9), and two, complicated patterns of nonlinear relationships in it which are not truly random (James, 2003:123-6). The first attribute can be described in a way that as time progresses in a continuous chaotic system, the parameters are so distinctly determined that to reach (or to predict) a certain desired point, knowledge of the initial starting point of system gains extreme importance. A meteorologist named Edward Lorenz, who was trying to predict, first observed this factor weather conditions by using a computer simulation. He noticed that he made simple decimal mistakes that lead extreme distinct results as outcome (Lorenz, 1963:1-25). This was actually a hotspot in chaos theory history, which leaded scientists to think about fallacies made in the past by the use of word "negligible". The other attribute maintains the properties of relationships among the parameters in a system. Today we know that without complex no linearity, the system will usually be predictable and will not be oversensitive on initial conditions as it depends on non-linear scenarios. Some common misunderstanding among daily use of the word "chaos" mainly appears because of its literal meaning as lack of order. Contrary to this misnomer, in most cases systems that show a pattern of deterministic chaos are quite reared and even predictable on short time scales. Solution paths to chaotic systems are basically deterministic in their nature. Chaos theory generally assumes that, if complex interrelations among the particles of a system are known, then future movement of system is predictable. Regarding this property of chaotic systems, it is now possible or will be possible to find solutions to some problems in science that can't be solved before because of their complex nature. 2. Chaos Theory in Economics Throughout the development of economic theory, from Ancient Greek Philosophers to Today's sophisticated theorists; many different ideas shaped the evolution of economics. Although the assumptions, progress and results acquired are different, almost any theory has the same base point showing economics' as a unitary environment. The unitary term comes from the aspect of economy as being an entity that consists of sub-entities. These units are mainly the consumers and producers taking decisions to survive in the ecosystem of economics. It is an obvious fact that the decisions of particular objects in this system lead the way to the general movement of system. This nature of economics is the key feature that embraces Chaos Theory and economics, in the way that; Chaos Theory tries to explain, how does the behavior of small particles effects each other and the system as a whole and economics as being a social science that struggles with problems potentially exist because of its fragmented and uncertain nature. Why does Economics need Chaos Theory Most economic theories employ strictly assumption-based models to explain the economic phenomena. However by walking in the comfortable path of assumptions a Theorist can risk his theory's validity. A neat example would be the criticisms towards Neoclassical Theory: Neoclassical Theory is often criticized with one of its basic assumptions as being in a continuous equilibrium state if not disturbed by surprise shocks from external sources. Beyond discussion of whether this assumption or result is plausible or not we must first assess the base points of it. This result of being in continuous equilibrium is an achievement of many sub assumptions (Cassel, 1918:44-7). One of these assumptions is an individual unit acting rational which attracts our attention mostly because of its misinterpreted dynamics. Rational acting is an assumption that standardizes human acting as in fact it is not so (Bullen & Sacks, 2003:2-4). Human judgment and decision-making systems bases mainly on complex mechanisms of processing many different inputs simultaneously. Although this kind of flow usually does not affect the result -verifying Friedman's statements about rationality (Friedman, 1953:43-45) - it still does not changes the chaotic behavior of economic system; The disordered components that act in the decision-making process may generate disturbances that are not visible from certain point of view, but inevitably contain the unpredictability that leads to economic instability. Throughout previous arguments we can conclude that economics is a complex system because of its decision-making fragments' (consumers as individuals and producers as firms) complexity in their nature. Also Chaos Theory claims that as complexity increases in a system, its predictability decreases. So in order to find robust and significant explanations of economic phenomena that surrounds us we need to focus more on Complexity here describes the way of acting on an occasion, not the result obtained. Handling complexity of economic particles, rather than assuming them as their act is based on an identical behavior such as strict rationality. This outcome brings us to the fact that linear way of thinking may be a clear path to think but its progress is too straight to analyse systems that involve complexity. This handicap might cancel out the significant factors that affect the accuracy related to the prediction of destination point of the system. Chaos Theory applications in economics It has now been almost twenty years since economists first began searching for chaotic dynamics in economic time series and use Chaos Theory as a tool for analysis. This search has returned detailed understandings of the dynamics of many different series, and has led to the development of several useful tests for non-linear structure. However, the direct evidence for deterministic chaos in many economic series remains weak (LeBaron B., 1994:3-5). The enthusiasm of chaos in economic systems brought a massive amount of initial interest. The idea of close predictability and complex dynamical properties has very Powerful and appealing for economics. Beginning with forecasting movements in foreign exchange and stock markets, to the understanding international business cycles, Chaos Theory in economics had a wide range of potential application space. This opening led to a significant amount of empirical work searching for possible chaotic behavior in all types of economic and financial time series. However increasing amount of investigation Resulted fruitless. As a matter of fact these studies have found little or no evidence for chaos in any economic time series (LeBaron B., 1994:10-2), but this outcome did not lead to a grief, since this massive amount of work brought up a surprising quantity of It was a congress at 1984 which began first scientific attraction in economics to the Chaos Theory. The congress has participants from physics, mathematicians and economists. This congress has also led to a book titled as The Economy as an Evolving Complex System (1988) by the collective work of P.W. Anderson, K. J Arrow and D. Pines, unexplained non-linear structure in many economic time series. Macroeconomic Applications Researchers that focus on macroeconomic and financial series face certain constraints, which make the likelihood of directly seeing chaotic effects infinitesimal. In Macroeconomics, the problem of short and noisy time series, taking place from a system whose dynamics and measurement analysis may be changing over time, totally handicaps the ability to precisely estimate non-linear processes. Ultimately there were two different paths of research in this area. The first tests for chaotic dynamics in macro economic series used several different diagnostic tests. Many of them began the research with an application of the Grassberger- Procacia dimension estimation algorithm (P. Grassberger & I. Procaccia , 1982:346-349) and most came to the same conclusion: "The series were probably not deterministic chaos, but many showed evidence for interesting non-linear structure". (LeBaron B., 1994:2-3). Initially, the diagnostics estimated were traditional invariants such as information. The second research branch leaded to directly fit non-linear specifications to Macroeconomic data. This approach has generally been more successful at finding strong evidence for nonlinearities in these series. However it generally supports the conjecture Those business cycles behave differently during expansions and recessions, and that there are different leads from the impact on future growth from positive and negative shocks Today. Two other papers directly use a non-linear forecasting framework to evaluate nonlinearities in macro economic time series. Granger (Granger C. W. J. & Terasvirta, T. and Anderson H. M, 1993:311-8) and Jaditz and Sayers (Jaditz T. & Sayers C., 1993:1-5) both find that a non-linear forecasting framework does not add much in terms of out of Some researches that target this branch; Beaudry and Koop with, Hamilton (1989), McQueen and Thorley(1993), Neftci(1984), Potter(1990) , and Terasvirta and Anderson(1992) sample forecast performance. This may suggest some problems in terms of stability of the Previously documented results. In macroeconomic series the greatest achievements have come from fitting non-linear models, which address certain well-known features, which are not part of a linear framework. As a result second approach often has detected interesting nonlinearities, which were missed using diagnostic tests alone. Financial Applications Chaos Theory and its implications for forecasting have been even more enthusiastically debated in financial markets. Even external authors from different areas of science, for example, Mandelbrot have been widely interested in the subject. Financial series are known to provide potentially longer and cleaner series on which to do estimation and out of sample testing. These tests are alike to those used for Macroeconomic time series. On the discussion of Chaos Theory the results often find strong evidence for non-linear dependence, but no convincing evidence for chaotic dynamics here as well. The issue of whether a financial series is indeed chaotic may not be of great importance to a financial forecaster who is only interested in adjusting Dynamic trading strategies according to apparent predictability in time series. There is interesting evidence of potential predictability in many of these series (Mandelbrot B., 1999:70-1), and these claims attracts too many opportunists for high gains, but before Concluding as that there is lots of positive gain to be made forecasting financial series, several precautions should be made. First, the actual implementation of a forecasting rule for trading may involve unforeseen costs, and prices taken from recorded data sets may not actually be tradable. Second, taking on some of these dynamic strategies may involve exposure to extensive risks. The large expected returns might be included with a high Probability of the strategy losing a considerable amount of money. To this point, this non-linear predictability has still ignored the original question about Chaos Theory existing in financial series. Given the support for some kind of non-linear structure the question of chaos still appears very interesting. It is possible that identifying Chaos for actual returns series may run up against another barrier. The problem this time is not the absence of data (it is gatherable because of high load of financial data is already available). The problem this time may be related to how much predictability can be left around in a financial time series. Forecasts of high precision (quality) may be Unreasonable for financial time series at all if we regard high costs. As a result for financial series there may be an extremely wide gap between successful non-linear forecasting, and actual identification of chaotic dynamics in a financial market. References Bullen G. & Sacks L, 2003, "Towards new Modes of Decision Making-Complexity and Human factors", University College London, 2003, 1(a), 2-4 Cassel G., 1918, "Theory of Social Economy", Quart. Journal of Economics, 1918, 17, 1-32 Friedman M., 1953, "The methodology of positive economics", University of Chicago Press, 1970, 10(1), 43-65 Granger C. W. J. & Terasvirta T. & Anderson H. M, 1993, "Modeling nonlinearity over the business Cycle", in: J.H. Stock and M.W. Watson (eds.) Business Cycles, Indicator and Forecasting, Chicago: University of Chicago Press for NBER, 1993, 311-325. Jaditz T. & Sayers C., 1993, "Using out of sample forecasting performance to evaluate model specification.", Bureau of Labor Statistics, 1993, 1(1), 1-12 James F., "Comment on 'Exact solutions to chaotic and stochastic systems'", Chaos: An Interdisciplinary Journal of Nonlinear Science, March 2003, 13(1), 123 LeBaron B., 1994, "Chaos and Nonlinear Forecastability in Economics and Finance", University of Wisconsin, 1994, 2, 1-10 Lorenz E., 1963, "Deterministic non-periodic flow", Journal of Atmospheric Sciences, 1963, 20, 130-141 Mandelbrot B., 1999, "A Multifractal Walk down Wall Street", Scientific American, 1999, 1, 70-74 Read More