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On technical and moral equilibrium

by Robert Teitelman | Published September 6, 2011 at 12:57 PM

Mark Thoma at the Economist's View Monday linked to a post with the provocative headline: "What if Equilibrium Never Existed? The Crisis in Economic Theory." The post, by Alejandro Nadal, argues against the standard proof of the existence of competitive equilibrium by Kenneth Arrow and Gerard Debreu in 1954. The Arrow-Debreu model is pretty old hat in mathematical economics; it underpins much of what's known as competitive equilibrium analysis. What's striking about the piece for a layperson (that would be me) is less the technical argument itself, which I lack the tools to adequately judge, and more the context in which Nadal, a professor at the Centre for Economic Studies of El Colegio de Mexico, places the proof. "The existence question is not only a technical question (i.e., finding out if a system of equations has a solution). In the grand narrative of market theory, the issue of existence of equilibrium is relevant because it concerns the reference point towards which disequilibrium prices (and allocations) are supposed to converge. The idea of market forces leading an economy to a point of equilibrium would be meaningless without certitude about the existence of the promised land. In macroeconomic theory, this is so important that in some extreme cases (i.e., dynamic general equilibrium models), it is assumed that the economy is always in an equilibrium position."

A few preliminary observations. With "the crisis in economic theory," Nadal is signaling that he's part of a larger insurgency in economics. It's clear as well that Thoma is also harboring some fundamental doubts and is not only willing to link to what might have once seemed a heretical position, but to write openly about that doubt himself. Last week, I discussed pieces by the Financial Times' John Kay and Thoma himself laying out their own views on the "crisis."

Nadal is right about one thing: The idea of equilibrium is a powerful one, and not just in a technical sense. In fact, it's difficult from a lay perspective to imagine a market that lacks an equilibrium; the belief that markets are constantly struggling toward some Platonic point -- what Nadal calls a reference point -- seems to be an embedded feature of any market. What's the larger point of a market if prices over the long run do really resemble a kind of random walk? Lacking an equilibrium, whether for the market as a whole or for individual securities, suggests that there is no meaning beyond prices set by the market. Prices are simply set by supply and demand, and by whatever combination of rational and irrational decision-making investors possess that day. Markets would thus be robbed of their moral underpinning; the idea going back to Adam Smith that the confluence of individual self-interests combine in the market to create an invisible hand that produces overall social good. And it raises questions about the morality of value creation -- the notion, associated in our own day with that sage moral exemplar Warren Buffett, that stocks will eventually discover value -- a "fair" price -- by reaching their equilibrium or at least attempting to reach it. The concept thus represents an escape from the nihilistic relativism that markets often seem to embody.

Equilibrium is thus larger than just a model, some equations and a set of proofs; it's a powerful metaphor that has shaped the way we think not only about markets but about politics and society, particularly after a period where the market was so effectively deified, at least in part because of proofs such as Arrow-Debreu. As a people we believe that good people will get their just desserts, even if it's in heaven, and that bad people will be punished, at least in hell and Hollywood movies. We discriminate (though less so these days) between investment (good) and speculation or gambling (bad). We believe instinctively that there is some general accounting of personal rectitude; we resist the idea that the universe is not, to some degree, accountable. Americans were never devotees of fashionable post-World War II existentialism -- it was, popularly speaking (if you can think of elite philosophies as part of the popular culture), a French thing -- with its human actions taken in a hostile, absurd universe. Democracy in America resembled an equilibrium-seeking marketplace: The short term always seemed gloomy, the populace clueless, but that was the magic of democracy: somehow, in the longer run, the citizenry roused itself to display a degree of wisdom, even valor. The New Deal. The Greatest Generation. Civil Rights. Equilibrium was thus a component of that very 19th-century notion of Progress. But of course this variant of equilibrium grows more elusive the more you think about it. John Maynard Keynes' epigram, "in the long run we're all dead," keeps recurring. We can't prove that certain policies, certain actions, were a distortion from a reference point. And even if we could -- politics, after all, is a lot more arbitrary, that is has fewer rules, than mathematical economics -- how do we calculate what occurs between the short and long term? We can't magically return to Bill Clinton's surpluses or the day before Sept. 11. We can't bring back the dead; we can't re-run history.

Yes, this is far afield from Arrow-Debreu. But whether Nadal is right or wrong, he is clearly correct in the enthusiasm that greeted a proof of equilibrium (under very finite conditions, mind you). Such a proof offers an escape from complex systems -- the markets, history itself -- that often seem to have a mind of their own, or far worse, no mind at all. Perhaps Nadal is right. But if that's the case, and Arrow-Debreu is robbed of its status, something tells me that other means to provide meaning and equilibrium to the markets, and to life itself, will emerge. - Robert Teitelman

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