Monday, August 11, 2014

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.

I just came across this old post from Yves Smith which makes the point rather nicely:


The scientific pretenses of economics got a considerable boost in 1953, with the publication of what is arguably the most influential work in the economics literature, a paper by Kenneth Arrow and G√©rard Debreu (both later Nobel Prize winners), the so-called Arrow-Debreu theorem. Many see this proof as confirmation of Adam Smith’s invisible hand. It demonstrates what Walras sought through his successive auction process of t√Ętonnement, that there is a set of prices at which all goods can be bought and sold at a particular point in time.42 Recall that the shorthand for this outcome is that “markets clear,” or that there is a “market clearing price,” leaving no buyers with unfilled orders or vendors with unsold goods.

However, the conditions of the Arrow-Debreu theorem are highly restrictive. For instance, Arrow and Debreu assume perfectly competitive markets (allbuyers and sellers have perfect information, no buyer or seller is big enough to influence prices), and separate markets for different locations (butter in Chicago is a different market than butter in Sydney). So far, this isn’t all that unusual a set of requirements in econ-land.

But then we get to the doozies. The authors further assume forward markets (meaning you can not only buy butter now, but contract to buy or sell butter in Singapore for two and a half years from now) for every commodity and every contingent market for every time period in all places, meaning till the end of time! In other words, you could hedge anything, such as the odds you will be ten minutes late to your 4:00 P.M.meeting three weeks from Tuesday. And everyone has perfect foreknowledge of all future periods. In other words, you know everything your unborn descendants six generations from now will be up to.

In other words, the model bears perilous little resemblance to any world of commerce we will ever see. What follows from Arrow-Debreu is absolutely nothing: Arrow-Debreu leaves you just as in the dark about whether markets clear in real life as you were before reading Arrow-Debreu.

And remember, this paper is celebrated as one of the crowning achievements of economics.