Tuesday, September 8, 2009

Economics and Jurassic Park

In this past Sunday's NY Times Magazine, economist Paul Krugman has an interesting article "How Did Economists Get It So Wrong?"; it can be found here:


It is incredible that economists could believe that they could use mathematics to "prove" anything beyond the simplest and most basic propositions about very simple systems. First of all, the factors that contribute to the behavior of anything of any real interest in macro-economic (large-scale state or national) systems are huge in number and interact in very complicated ways. Some of this is psychological (the minds and fears of investors), some of it is physical (time-related interactions of supplies, demands etc.) and some of it is the interrelation of the two (fads and panics caused by perceptions of actual fluctuations).

Now it is true that we are not talking about trying to understand, mathematically, the behavior of individuals or individual commodities or economic quantities. Just as fluid or statistical dynamics in physics tries to understand the overall gross behavior of gases and liquids, so economists try to understand the overall behavior or interactions of large economic groups and quantities. Just as in physics, however, the mathematics nearly always leads to equations (actually, differential equations) that are non-linear, hence "unstable" or chaotic. This means that the solutions of the equations, describing the evolution of the system, depend on knowing the initial state of the system in excruciating detail. In fact, as in weather forecasting (an application of fluid dynamics), knowing anything even modestly far into the future (more than a few days) requires initial knowledge so precise as to be impossible in practice or in theory to obtain. We will never be able to predict weather accurately more than a week or so in advance.

Thus, the second reason why mathematics can't "prove" complicated theorems in economics is that economic prediction is inherently non-linear, hence inherently chaotic. Without theoretical stability, even defining things such as the true or exact worth or value of a product or commodity is not really possible. One has a way out by simply stating that a quantity is worth what the market at any time says it's worth, but this removes any content from the statement that "the market always values a quantity at exactly its worth". The only way such a tautological statement could be of use would be if one could predict, with accuracy, what such a value would be in the future. But this prediction is exactly what can't be done -- as we've seen recently in the case of house prices, which weren't supposed to be so unstable, and the predicted values of certain bundled mortgages say, or credit default swaps and other financial constructions, which are even now unknown.

The problem is a little like the situation in the book/movie "Jurassic Park" where the scientists and engineers theorized that they had figured out exactly what could or couldn't happen to the dinosaur clones. The mathematician Ian Malcolm pointed out that such a theory could not hope to be 100% correct because of the chaotic element in such a complicated system; hence, their complacency was dangerous. Sure enough, aberrant human behavior plunged the system into chaos, and the proof that the number of velociraptors was limited -- depending on the sterility of an all female population -- turned out to be exactly wrong. While calling this application of "Murphy's Law" Chaos Theory is perhaps a bit overblown, there is nevertheless a strong germ of mathematical truth in it.

Whatever hope there might be in protecting us from economic disaster (or from T. Rex clones) lies in vigilance and multiple layers of protection. "Jurassic Park" is just a story, but we have yet to learn this lesson on the very real economic front.

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