UPDATE: See the follow-up article here.

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In a recent methodological flare-up among economists, Paul Romer accuses Robert Lucas , among others, of "mathiness."

In an unceremonious outburst, Romer accused several colleagues -- including Lucas and Prescott -- of using mathematics dishonestly to support their ideological beliefs. In constructing theories about how economic growth happens, he suggested, they slipped preposterous assumptions into their economic models to guarantee the results they wanted. His denunciation of such “mathiness” has triggered a storm of commentary to which my Bloomberg View colleagues Justin Foxand Noah Smith have made noteworthy contributions.

The problem Romer identifies, though, goes far beyond the growth theory in which he specializes, and runs deeper than a mere squabble between academic camps. He is objecting to the way many economists use mathematics, which is different from the way physicists or biologists or engineers use it.

There"s some weird history here. In its style, a great deal of modern economic theory follows the norm established in the 1950s by Kenneth Arrow and Gerard Debreu. They started with an extremely abstract mathematical model of an economy -- a set of producers, consumers and commodities -- and then built theorems about its properties. Their famous result was that, under a gamut of conditions, this imaginary economy would possess a unique equilibrium, one set of prices that would perfectly match production and consumption.

Debreu held a position at the Cowles Commission at the University of Chicago -- a research institute devoted to linking economics with mathematics and statistics -- where he helped educate a flock of young mathematical economists in this approach. They spread it through the profession, where it still prevails, with economists setting out axioms and assumptions, making propositions and proving them. As a result, many of their papers end up reading like lectures in pure mathematics.

This mathematical-purist approach came from a rather odd place. As Roy Weintraub relates in his excellent book "How Economics Became a Mathematical Science," Debreu took his perspective from a secret group of French mathematicians who, starting in the 1930s, worked under the pseudonym “Nikolas Bourbaki.” The Bourbaki group thought mathematics should have an almost religious purity, refined and unsullied by contact with the practical. Educated in Paris, Debreu came under their influence, and then shifted from mathematics to economics.

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Weintraub argues that Debreu played a decisive role in transforming economics -- “not only the field"s self-image, but its concept of inquiry itself.” Ever since, economic math has been Bourbakian, primarily concerned with formal structure. Practitioners downplay the need for realistic assumptions, as Paul Fleiderer noted in his brilliant essay onchameleons. They use highly dubious suppositions to generate a result, which they then use as a foundation for giving advice to policy makers. This is pretty much the opposite of good science.

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Those of us who have been workaday non-academic economists have all used math (including the use of regressions and similar methods) to make observations and check the plausibility of claims. This is *totally* different, however, from how some academic economists use math to create complex models that may or may not have anything to do with observations in the real world.