Monday, August 11, 2014

Mark Buchanan — Arrow-Debreu Derangement Syndrome

Imagine you had never read any textbook economics, or studied any academic research papers. You didn't know the THEORIES of economics, especially in their mathematical form. But suppose you did know some mathematics, and were also generally well informed about the realities and complexities of real world economies. Now, suppose a demon sat you down and made you read and study the famous theorems concerning the existence of a competitive economic equilibrium as developed in the 1950s by Ken Arrow and Gerard Debreu. What would you think? 
My belief is that you would quickly conclude that these theorems probably held little or no importance for understanding any real world economic system. If the demon tried to tell you that these theorems were at the very core of today's theoretical approach to (much of) economics, you'd think he or she was joking. If the demon insisted, you'd suspect you were dealing with an insane demon; and if you discovered the demon was right, you suspect the economics profession of being deranged. At least I would...
I've never yet been able to understand why the economics profession was/is so impressed by the Arrow-Debreu results. They establish that in an extremely abstract model of an economy, there exists a unique equilibrium with certain properties. The assumptions required to obtain the result make this economy utterly unlike anything in the real world. In effect, it tells us nothing at all. So why pay any attention to it? The attention, I suspect, must come from some prior fascination with the idea of competitive equilibrium, and a desire to see the world through that lens, a desire that is more powerful than the desire to understand the real world itself. This fascination really does hold a kind of deranging power over economic theorists, so powerful that they lose the ability to think in even minimally logical terms; they fail to distinguish necessary from sufficient conditions, and manage to overlook the issue of the stability of equilibria.
The Physics of Finance
Arrow-Debreu Derangement Syndrome
Mark Buchanan

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