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One salutary side effect of economic collapse: it gets people thinking. Or, rather, rethinking.

Case in point: "Recipe for Disaster: The Formula That Killed Wall Street," a fascinating story in Wired magazine that traces much of the blame for our current financial mess back to a highly abstruse mathematical formula, invented in 2000, that allowed Wall Streeters to easily model the complex risks of mortgage derivatives and other big messy investments.

Trouble was, the formula -- known as a "Gaussian copula function" -- wasn't quite as magical as it appeared to be, and in the end left investors blind to the dangers that came up and bit them -- bit all of us -- on the behind.

Wired attributes rather too much of our current mess to this one equation; there were many other factors as well, the same mixture of greed and shortsightedness found in every financial bubble we've seen from the Tulip Mania onwards. But the article's conclusion is dead-on:

“In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years' worth of data and come up with probabilities for things that may happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense at all.”

Speaking of which ...

Case in point number two: "The Financial Crisis And The Systemic Failure Of Academic Economics," a manifesto of sorts recently formulated by a bunch of (mostly European) economists at an academic conclave called the Dahlem Workshop. (You can download a pdf of the paper here.)

As you might have gathered from the document's cumbersome title, economists aren't natural manifesto-writers -- heck, legendary commie economist Karl Marx turned to journalist-cum-philosopher Friedrich Engels when it came time to write the Communist Manifesto. The Dahlem paper is filled with references to "'fat-tailed' Levy processes" and "the Arrow-Debreu two-period model."

While lacking something in style, the paper presents an argument that is blunt and convincing: while developing more and more abstruse mathematical models, economists ignored the glaringly unreliable (or just plain incorrect) assumptions upon which these models were based, leaving the economic profession as dumbfounded as the rest of us when the financial system came tumbling down.

Without the data they needed to prove their arguments, the paper notes, economists resorted instead to "simulations with relatively arbitrary assumptions on correlation's between risks and default probabilities. This makes the theoretical foundations of all these products highly questionable – the equivalent to building a building of cement of which you weren’t sure of the components."

On a more basic level, most models simply ignored the -- seemingly theoretically remote -- chance that everything could fail at once. "If one browses through the academic macroeconomics and finance literature, 'systemic crisis' appears like an otherworldly event that is absent from economic models," the Dahlem economists note. "In our hour of greatest need, societies around the world are left to grope in the dark without a theory."

Meanwhile, the economists themselves "have had no choice but to abandon their standard models and to produce hand-waving common-sense remedies. Common-sense advice, although useful, is a poor substitute for an underlying model that can provide much-needed guidance for developing policy and regulation. It is not enough to put the existing model to one side, observing that one needs, 'exceptional measures for exceptional times'. What we need are models capable of envisaging such 'exceptional times.'"

I think I speak for many when I say: I wish you guys had told us that a little bit sooner.

--David Futrelle