Chaos and Complexity in Finance and Economics



Chaos and Complexity in Finance and Economics

Roger W. Clark

Austin Peay State University

P.O. Box 4415

Clarksville, TN 37044

United States of America

Phone: 931-221-7574

George C. Philippatos

432 Stokely Management Center

University of Tennessee

Knoxville, TN 37996-0540

United States of America

Voice: 865-974-1719

Fax: 865-974-1716

Abstract: This paper attempts to explain in general terms the differences between the Neo Classical view of economics that was based on the 19th Century economy of agriculture and industrialization and the technology based economies of the late 20th and early 21st centuries. This paper shows that technology based economies are not restrained by the decreasing returns of resource based industries in the Neo Classical sense. Without this restraint, increasing returns and multiple equilibriums are possible. Nonlinearities and externalities become driving forces in the economy, which is constantly on the edge of chaos; it rushes forward, structures coalescing, decaying, and changing. This can best be explained through the metaphor of “complex adaptive systems”. The greatest problem with complexity is that it is not susceptible to a mathematical solution. I appears the future of complexity lies in clinical studies and computer modeling.

Key words: Complexity, Deregulation, Strange attractors

1. Introduction

For over a century now economics and finance has been dominated by the principles of Alfred Marshall. This principles , known as the Neo Classical view of economics, was based on the 19th century view of industrialized capitalism. One of the cornerstones of this system was the concept of decreasing returns. A classic example would be adding labor to a production process. Adding a few workers to the process may give an increased return in the form of higher output per worker. Eventually the point is reached where adding labor gives no extra output per laborer. Adding more workers will then give decreasing returns per worker. Should a farmer double the amount of fertilizer he places on his land the amount of food produced will not double. In each of these examples equilibrium is reached at the point of decreasing returns. This view then lends itself to mathematical solutions. In general, this view lent rigor to the discipline of economics at the time and largely was an accurate reflection of an economy which was industrialized and traded in commodities.

The neo-classical view still holds in agricultural economies and economies dominated by trading in commodities and industrial goods. Technology, by contrast, is not constrained by diminishing returns. The rise of technology based economies has given birth to the concept of increasing returns. In addition, the neo-classical view assumed perfect rationality and complete knowledge among the agents in the economy. The concept of increasing returns holds that agents may sometimes act irrationally and do not always have perfect knowledge of the markets.

Increasing returns applies to technology and not necessarily an individual company. Microsoft could go out of business tomorrow and its basic operating system would continue to dominate the small computer industry (if the secret of the system were known to the rest of the industry). The concept states that as more agents adopt a technology, x, it in turn becomes more and more attractive for other agents to adopt. Soon these other agents are gearing their technologies and businesses toward this technology x, increasing further its attractiveness. As a recent example, in the 1970’s there were two technologies in the home video industry, VHS and Beta. VHS managed to gain an initial advantage in distributors. As competition heated up VHS managed to widen its lead. More and more tapes were made in VHS format while Beta shrank to virtually zero in sales. This was in spite of the fact that many engineers had stated that Beta was the better technology.

Work on positive feedbacks and increasing returns was initiated by Brian W. Arthur (1988) and the so-called Santa Fe group, and has continued unabated ever since under the overall rubric of “Evolutionary Economics.” The basic premise of this field of economics is that with the exception of resource-based industries and those engaged in bulk-commodity production, most modern information and technology-based production exhibits increasing returns, positive feedbacks, path dependence, and lock-in phenomena. Nonlinearities and externalities become driving forces in the economy, which is constantly on the edge of chaos; it rushes forward, structures coalescing, decaying, and changing. In the view of evolutionary economics, structure, pattern, self organization and lifecycle combine to make economics a high-complexity science. As such, this new strand of economics lends itself easily to inductive reasoning (clinical studies) as opposed to the deductive reasoning practiced by orthodox economics.

Example:

Assume for now that agent , i, adopts technology, x, and earns a return, ax, the total returns will consist of this return, plus the returns for other agents adopting the technology, inx. Hence the total return kx is given by equation (1) below:

Kx = ax + inx (1)

In cases of several competing technologies with increasing returns, Arthur shows that the technology adopted depends on initial conditions and random events during the period the technology is on the market. Extending these concepts to the overall economy, Arthur also shows that there are many parts of the economy in which stabilizing forces do not appear to operate. Here positive feedback will magnify the effects of every small economic shift. This differs from the traditional theory of diminishing returns[1] where a single-equilibrium solution is established. With increasing returns multiple equlibria are possible. Hence we employ a dynamic analysis of an economy that has already reached equilibrium and study the probability of occurrence of the factors that caused the final equilibrium.

2 The “Old” and “New” Economics

The following table outlines the differences between the “New” and the “Old” economics, according to Brian Arthur:

|Old Economics |New Economics |

|Decreasing Returns |Much use of increasing returns |

|Based on 19th century physics |Based on biology (structure, |

|(equilibrium, stability, |pattern, self-organization, life |

|deterministic dynamics) |cycle) |

|People identical |Focus on individual life; people |

| |separate and different. |

|If only there were no |Externalities and differences |

|externalities and all had equal |become driving force. No Nirvana.|

|abilities, we would reach Nirvana |System constantly unfolding. |

|Elements are quantities and prices|Elements are patterns and |

| |possibilities. |

|No real dynamics in the sense that|Economy is constantly on the edge |

|everything is at equilibrium |of time. It rushes forward, |

| |structures constantly coalescing, |

| |decaying, changing. |

|Sees subject as structurally |Sees subject as inherently |

|simple |complex. |

|Economics as soft physics |Economics as high-complexity |

| |science. |

Source: Complexity, pp. 37-38

2.1 Complexity, Phase Transitions, Emergence and Non-Linearities: An informal Systhesis

Now that we have reviewed some of the literature on complexity and its characteristics, we shall try to synthesize some of these concepts below, by way of some simple examples.

Complexity focuses on the self-consistent mutually supportive web of interactions in human societies. As such its scope encompasses social, political, and economic interactions. For example, an economy is viewed as a living, organic pattern that possesses emergent properties: an emergent property is defined here in terms of self- organization and patterns due to collective behavior of constituents. This emergent property is not directly anticipated by the properties of individual constituents of the system. Focusing, for the moment, on financial markets, it is relatively easy to visualize individual economic agents behaving rationally, estimating the expected net present values of future cash flows, riding up the yield curve, and bidding up prices. Under normal circumstances such collective behavior could lead to informational efficiency in the markets and eventually to improved allocation of resources. However, when the markets heat-up the same collective behavior leads to financial bubbles, where individual agents over (under) react and engage in such behavior as contrarian and momentum trading. In the same vein, when the financial bubble bursts, the individual agents switch from frenzied investment behavior to substitute consumption or plain inactivity. This is an example of emergence that materialized by the “phase transition” from “market boom” to “market bust” and can be conceptualized by reference to the “dot com” frenzy during the 1990’s in the U.S. financial markets.

In general, socio-economic and political behavior can be understood best within the metaphor of “Complex Adaptive Systems.” Such systems can be described by some simple attributes: (1) They are networks of many agents; (2) The control of such system is highly dispersed; any coherent behavior in the system has to arise from cooperation and competition among the agents themselves; (3) Such systems have many levels of organization, with agents at any one level serving as building blocks for agents at a higher hierarchical level; (4) The systems are constantly revising and rearranging their building blocks, as they anticipate the future; (5) They anticipate the future and they are constantly making predictions based on their various internal models of the world; (6) They can be best understood through inductive rather than deductive logical processes (hence the use of clinical studies); and (7) finally, such systems possess emergent properties.

Based on the above attributes, it appears that the complexity embedded in the WTO regulatory and Governance Dynamic in the future displays ideal conditions for analysis within the framework of “Complex Adaptive Economic Systems.” Indeed both Regulatory and Governance Dynamics are characterized by non-linearity, path dependence, feedback, lock in, feedback loops, endogenous change and non-stable interactions between variables.

2.2 Complexity and Mathematical Solutions

The greatest problem with the theory of complexity is that economists must now abandon the mathematics that has served us well in the past. The problem can best be illustrated with the Lorenz equation.

The Lorenz equation was originally produced to attempt to simulate weather patterns and try to predict the weather. Its basic equations are a set of three derivatives:

[pic]

where r, b and δ are parameters that change the behavior of the system while x, y, and z are constants. More formally, these are known as:

δ = the Prandtl number[2]

r = the Rayleigh constant[3]

b = The physical proportion

When these parameters are at fairly low levels they will converge around two fixed points in a rather stable pattern. When the numbers are increased they tend toward chaos, where the resulting paths are unpredictable. In this state of chaos any minute change will set the model off in an unpredictable direction. While these changes may seem small and at first very little difference is seen the two conditions will eventually diverge. The following is an example of this divergence:

[pic]

Source: The Non-Linear Lab at

In the example of the WTO we have three parameters, the WTO’s original mission of promoting free trade, the influence of the developed nations to protect copyright and patents while continuing to stem imports of agricultural products through subsidization of their agricultural sector, and the influence of the LDC’s to allow copying of drugs and copyrighted material and open the developed world to their agricultural goods. As long as these influences remain small the WTO will oscilate in its mission in a rather predictable manner. If, however, these influences grow chaos may be expected. Before 1995 the WTO had little enforcement authority and could be safely ignored by most nations. Now they have actual authority to impose sanctions and pressure from all parties to the WTO should be expected. The recent “Battle in Seattle” and complete breakdown of talks in Mexico may be examples of the chaos in the system.

The chart above also points out the fact that if someone knows the approximate parameters and constants of the system it might be possible to predict the short run consequences of certain actions but a long run prediction of the results will be impossible. A meteorologist may be able to give a fairly accurate seven-day forecast but will fail in a twelve month forecast.

The future of the complexity discipline in the field of International economics is certain and uncertain. The certainty is chaos and complexity. The uncertainty is how it is to be measured and dealt with by economists. Arthur (Waldrop, 1992) believes one path is through computer simulations of economic systems in which the agents, be they nations or multinationals, are intelligent, having the capacity to learn and adapt to the forces unleashed on them.

References:

[1] Arthur W. Brian, “Increasing Returns and Path Dependence in the Economy,” University of Michigan Press, 1994.

[2] Arthur W. Brian, “Increasing Returns and the New World of Business,” Harvard Business Review, July-August, 1996, pp. 100-109.

[3] Arthur W. Brian, “Positive Feedbacks in the Economy,” Scientific American, February 1990, pp. 92-99.

[4] Arthur W. Brian, “Competing Technologies, Increasing Returns, and Lock-in by Historical Events,” Economic Journal, 1989, Vol. 99, N. 394, PP. 116-131.

[5] Waldrop, M. Mitchell, Complexity, Simon and Schuster, 1992

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[1] It may be worth noting here that the majority of WTO members have developing economies that exhibit Marshallian diminishing returns. This magnifies the disparity of the “haves” and “have nots” of the world in modern information-and-technology-based economics.

[2] This is a dimensionless parameter in convection proportional to (momentum diffusivity) / (thermal diffusivity)

[3] Governs the onset of convection when it reaches a critical value. Contains the thermal expansion coefficient and kinematic viscosity.

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