Wired.com has an article up about factors leading to the current economic crisis. Felix Salmon, in “Recipe for Disaster: The Formula That Killed Wall Street,” focuses attention on mathematical formula by David X. Li that Salmon suggests played a  pivotal role in the economic downturn. Speaking of Li’s formula, for example, Salmon writes:

His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored.

Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li’s formula hadn’t expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system’s foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.

While the article is interesting for its analysis of what happened, to me, as a sociologist, it is also interesting because it points to the limits of reliance on too narrow quantitative indicators for complex social phenomena. For example, Salmon writes:

During the boom years, everybody could reel off reasons why the Gaussian copula function wasn’t perfect. Li’s approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial.

And he later adds:

Bankers should have noted that very small changes in their underlying assumptions could result in very large changes in the correlation number.

And:

They didn’t know, or didn’t ask. One reason was that the outputs came from “black box” computer models and were hard to subject to a commonsense smell test.

One of the dangers of over-reliance on such quantitative indicators is failure to recognize their limitations. In this case it would appear that part of the problem was that many of those who used the formula either didn’t fully understand or underestimated such weaknesses. In practice, both quantitative and qualitative approaches are invaluable as tools to help us to better understand our social worlds, but any method we might use to collect data can only tell part of the story.

David X. Li's Copula Function Formula

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