Tag Archives: nonlinear dynamics

Chaos theory and economics

I’m working on a long post on extending the implications of work done by Edward Lorenz (1963) on chaotic outcomes from deterministic systems to economics. For those of you unfamiliar with the subject (and who have an idea of fun that doesn’t include reading academic mathematical papers) Lorenz examines a simple system of 3 deterministic equations that describe convection in the atmosphere. His key insight in this examination is that changes in the parameters generate vastly different systemic behaviors, some of which are chaotic and unpredictable.

The general lesson for meteorologists that Lorenz isolates is that you can’t predict some of these weather systems past some specific time frame (I think a week or so). More generally, Lorenz’s work is foundational in chaos theory, fractal dynamics, and nonlinear systems.

Where I propose to extend this work is in following Benoit Mandelbrot (1963) who finds evidence of chaotic behavior in cotton prices. Mandelbrot was also Eugene Fama’s instructor at the University of Chicago and this work plays a key role in the development of theĀ  efficient market hypothesis. I also am inspired by Stephen Wolfram (2002, A New Kind of Science) who suggests that there are extensive applications for the tools used by nonlinear dynamical studies of cellular automata in modeling economies and interactions. I won’t delve into it here, but Douglas Hofstadter’s seminal text on Godellian incompleteness (1977, Godel, Escher, Bach) is also worth reading for the deep and rich insights into cognition and systems theory.

My interest in this subject was triggered from the notion that institutions are fundamental parameters in describing and understanding economic interactions. Rafael La Porta, Florencio Lopez-de-Silanes, Andrei Shleifer, and Robert Vishny (LLSV) are foundational in the study of legal origins and economic development but I am hard pressed to think of work outside of that literature that engages institutional interactions, development, and outcomes.

I suggest that properly understand the dynamics of interactions and change are key in understanding the nuances that make political ideologies untenable at the margin (and this is a statement that I want to make in context specifically of the 3 major strains of thought competing for space today: liberalism, conservativism, and libertarianism). There are many places where these ideologies allow for computationally equivalent outcomes but this is poorly understood.

Stay tuned. Oh and here’s the famous Lorenz Butterfly, which is the phase space portrait of the dynamical system that Lorenz (1963) analyzes:

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The Nonlinear Dynamics of International Conflict

Wolfson, Puri, and Martinelli write in the Journal of Conflict Resolution in 1992:

We propose a dynamic model of the interaction between two rival powers. It is not an easy model, because it involves nonlinear difference equations; yet it is simple in the sense that it involves only a few variables. Parsimony shows that complexity and apparent paradox need not arise from the multiplicity of factors but from their nonlinear connections. Complications certainly may be introduced such as considering more than two states and alliances among them (Wolfson 1973) as well as further specification of expectation formation. They might improve some future statistical investigations, but the theory has no need for those hypotheses to explain the complexity of the historical record. Occam’s razor suggests that small is beautiful.

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