Does economics rely too much on math?

A fellow blogging friend recently pointed me to a scholarly article discussing the increasing reliance of economics on mathematical models.

Dr. Gibson, an engineering and economics expert, takes a strong stance against the “allure” of mathematical models, arguing that they offer no significant contribution if the importance of common sense and human interaction is ignored. He argues,

“But while the mathematicians, some of them at least, are explicit about doing math for its own sake, engineers are hired to produce results and economists should be, too.”

According to Gibson, engineers realize that data and real-life experiments are the most important. A study reveals a different focus in economic papers.

“Perusing the contents of the

American Economic Review, [Wassily Leontief (1982)] found that a slight majority of the [economic] articles presented mathematical models without any data, just 12% presented analysis without any math, while the rest were mainly empirical studies.”

I just completed an undergraduate economics course, Intermediate Macroeconomics. The course was almost entirely mathematical, relying on calculus and algebra techniques to find solutions for theoretical problems related to consumption, investment, and taxation. With almost every model we considered, however, there were notable flaws once applied to real-life situations. There’s a famous quote by mathematician George E.P. Box,

“All models are wrong, but some are useful.”

To be sure, we shouldn’t try to dissociate mathematics from economics. Economic theory and so-called “common sense” are no good if the facts tell a different story. However, there is a difference between data and mathematical models. The data, or numbers, of economics will always be undeniably vital to any conclusion. The problem arises when the underlying economic problem is lost amid the cacophony of additional formulas and derivatives.

As economists realize, mathematical models can explain trends with some degree of confidence, but there will always be outlying observations. Furthermore, almost every model relies on core assumptions in order to be useful. There are simply too many variables in the real world to completely explain any economic trend.

Essentially, applying mathematical formulas to economics can tell us if one event *should* happen, given a set of conditions. Sometimes these conditions, such as assuming consumers always optimize their money, do not translate well into the real world. This may lead to contradictory conclusions.

The human aspect of economic decisions must be first considered. If we primarily understand how economic problems affect real people, the math takes on a purely supporting role.

Gibson urges clarity for economists, hoping to make the conclusions more applicable to the everyday American.

“What if real answers to urgent problems could be delivered in plain English? Do economists have the courage to shun the romance of mathematics and produce such answers? Let us hope so.”

Danny Huizinga | Baylor University | @HuizingaDanny

I majored in econ at Carleton in 1978: I flunked the comp exam the first time, boned up for a couple of weeks, and passed it. That shuould tell you something about the rigor of the discipline. I subsequently got another BA in Biology (the Econ was doubled with Urban Studies, with a separate Comp exercise, which Paul Wellstone approved as “damn near Distinction”), and a law degree. I’m left with the general sense that academia is an easily corrupted institution. The very idea of a school as a “marketplace of ideas” (Holmes is credited with the term, but the idea is his: he had a knack for grasping the essentials) is a wonderfully rich concept. That is, markets run on information, but you have to pay to learn stuff. Generally, you have to trade truth for truth, because, on your own, you don’t know enough. But, but, never reject the evidence of your senses. That way leads madness albeit perhaps as a US Senator.

The nice thing about Econ at Carleton was that there was a capstone course where you looked, at least with Ada Mae Harrison in charge, at the structure of the science. “There are perhaps eight key concepts in economics, none of which make sense without the rest: it’s like juggling: they all have to be in the air at once.” She recommended Joseph Schumpeter, which I read. A critique of “neo-classical economics” is remarkably easy to at least start. Like, what does “rational” mean? This segues nicely into a critique of law. What is a fact? You use the term “empirical”, based on the Greek term for “attempt”. Who attempts what when where and how?

You end up having to make assumptions. So the capstone course tries to set out two or three, like “perfect competition”, which, in hindsight was probably supposed to mean the persons are not prejudiced. It all revolves around the idea of information. My assumption is that there is an “out there” beyond imagining (Holmes’ “the unimaginable whole”), but we only understand what we imagine, based as much or as little as we desire on what we experience. (Same route as “empiric”).

So to sum off this little sermonette, it’s all a matter of what you’re willing to risk, but results speak for themselves. I was just reading about the origin of FedEx in a Yale student’s essay. Now they own six hundred corporate-industrial-size aircraft. He sort of met one early payrool by winning 27,000 dollars at a blackjack table. It took five years to become profitable. They started off with 18 corporate-sized jets, first day’s traffic: eighteen parcels.

Finally, a note from my micro-economics textbook (I remember now that there were three capstone courses: one in macro, one in micro, and then a final, so what, one). The footnote mentioned that maybe once, as of 1978, had anyone matched data to the claim that a firm’s cost curves showed anything at all about reality. You know, raise price and what does output do, either on supply or demand sides. It had been tested as far as field observations (an actual experiment would be harder to imagine) go exactly once. And with two or three observations, not the hundreds or millions that you’d expect after taking a course in statistics or watching a show on “hard science” research. Imagine drawing a curve through two or three points on a graph.

Happy studying.