**OpinionCommentary**

# What calculates isn't always right in economics

Some of the leading names in economics -- New York University's Paul Romer and Nobel laureates Robert Lucas and Edward Prescott -- have gotten into an unusually public tiff over the proper use of math. Academic as it may seem, the battle reveals a deeper rift in a discipline that is supposed to be aimed at making us all better off.

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.

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.

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 on chameleons. They use highly dubious suppositions to generate a result, which they then use as a foundation for giving advice to policymakers.

This is pretty much the opposite of good science.

Scientists generally enlist mathematics only as a tool, and ultimately value practical understanding above theoretical rigor. They care deeply about the plausibility of the assumptions used in any model. Models, of course, are always oversimplified -- one might say "wrong" -- but it's what they get right that matters. A sphere is a good model for the Earth not because it lacks any geographical detail, such as mountains or valleys, but because it gets the rough shape right.

The Bourbakian influence in pure mathematics actually caused a rift between physicists and mathematicians back in the 1980s. The formal and pure Bourbakian approach seemed useless to the physicists, whose more practical approach seemed suspect to the mathematicians. Since then, that rift has disappeared as math has moved on. Economics apparently hasn't recovered yet.

Romer's disagreement with Lucas and Prescott, then, might actually be about what economics should be. Like a physicist, chemist, or biologist, Romer wants to do economics of the real world. The others -- along with their colleagues in the more rarefied theoretical heights of economics -- want to do "mathematical economics," which they see as the study of a certain class of abstract mathematical models. If you were looking for advice on how to get out of a deep recession, whom would you call?

* Mark Buchanan, a physicist and Bloomberg View columnist, is the author of the book "Forecast: What Physics, Meteorology and the Natural Sciences Can Teach Us About Economics." *