Tuesday, July 28, 2009

Economic Equilibrium, Chaos and the Malcolm Effect


By: Carlos Pedro Gonçalves
The notion that economic equilibrium leads to a fixed point dynamic equilibrium and that all randomness, and, therefore, uncertainty and risk come from exogenous shocks that change the equilibrium from one (attracting) fixed point to another (attracting) fixed point was a useful argument in justifying a neoclassical economic discourse of power that defends the idea that a self-regulating free market does not produce bubbles and crises, the crises being produced, according to this perspective, by inefficiency sources such as transaction costs, market regulation, State intervention.

This argument allows one to confabulate a market economy as something that is completely controllable, with a predictable mechanics, and a manageable exogenous risk of a mild nature.

This "useful" reasoning about the equilibrium was, however, put into question by the applications of chaos theory to economic dynamics. In the book Cycles and Chaos in Economic Equilibrium, edited by Jess Benhabib (1992), it is shown, through several examples, that the very same homeostatic mechanisms that lead to an economic equilibrium can also lead to a dynamic instability, the conditions of economic equilibrium and the dynamics at the economic equilibrium may, thus, produce complex chaotic motion. A market economy may, therefore, be in economic equilibrium and, at the same time, not in a fixed point equilibrium.

The endogenous risk that occurs from chaotic dynamics falls into a notion of deterministic risk that may coevolve with external shocks.

In a model proposed by Tönu Puu (1997), in the book Nonlinear Economic Dynamics (pages 240 to 243), it is assumed that the investment is adaptive, in such a way that a period of rapid growth and the formation of a bubble may become unstable and, thus, lead to an economic crises (see figure 1 below). Similarly, when a crisis occurs there is a limit below which it becomes advantageous to invest due to low costs.

Fig.1 - Bubbles and crashes (example near t=600 and t>=850) in simulated income


The video, below, is an example of the Malcolm effect (Crichton, 1991) taking place in Puu's model. There is economic growth up to a point where the system is at its highest growth rate, at that point there is a quick fall, and a crisis takes place with large swings in the growth, accounting for a high variability.

This effect is described by Crichton in the book Jurassic Park, the name Malcolm effect being attributed to the fictional chaos theorist Ian Malcolm.

The Malcolm effect is a general crisis dynamics where the system suddenly crashes exactly when it is functioning at its highest performance.

For the Malcolm effect to occur it must be possible for the system to produce a sharp jump. In economics this means that a bubble would not be followed by a corrective slow fluctuation showing convergence to a period slower economic activity, instead the bubble would burst into a period of high volatility and a few large downward swings that would characterize an economic crash and a period of economic crisis (as it takes place in the video below).

The occurrence of bubbles, crisis and phenomena like the Malcolm effect are not accounted for in the traditional equilibrium models but they are shown to occur in simple nonlinear models of market economies functioning in economic equilibrium, which puts into question the neoclassical argument that if the markets were left on their own all would go well and no bubbles and crashes would ever occur.

Economic equilibrium cannot be taken as a synonym of attracting fixed point dynamical equilibrium.


video

The video is also available at:

http://www.youtube.com/watch?v=Qf-2pEP6HVg

The figure and video were produced with the software EF Chaos 101.

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