Economics and Math – A Delicate Balance

Photo / Joao Trindade

Photo / Joao Trindade

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.”

5 responses to “Economics and Math – A Delicate Balance

  1. Provocative post. I read Gibson’s article. I’m reminded of when I earned my Economics BA. The final class I took was on development growth models, starting with the Solow curve and tweaking it to account for different inputs. I think there’s great value to that kind of work when it is describing readily discernible things.

    Your thesis also calls to mind various explanations of big bang cosmology, such as Hartle-Hawking, quantum vacuums, and multiverse scenarios. In some cases, mathematicians and theoretical physicists appeal to irrational numbers or metaphysical explanations to support the superiority of their models.

    I would say math shouldn’t be underestimated as a tool for discovering objective realities. It seems you’re proposing a practical division between data and equations, but I don’t think that kind of division exists. Even in Gibson’s example of the used car sales model, the economist had to start with a set of data around which to build his mathematical model. Gibson appeals to common experience about when cars start needing repair or when the engine gives out. But future changes in manufacturing techniques, quality expectations, consumer lifestyle, and so on might be better understood because of the mathematical model he criticizes.

    Ultimately, the problem of frivolous research comes down to how the academic knowledge market is structured. When grant givers have bad ideas about what kind of knowledge is important, then we’ll get wasteful research. Truth be told, lots of granting institutions have bad ideas about what is valuable new knowledge.

    • Point taken. Obviously, I don’t hate math either – I am a math minor after all. I understand how the complexities can have very important real-world effects. It seems, however, that the basic models we have considered require so many assumptions that we never did anything that included more fundamental economic ideas. It was difficult to apply any of the old, historical models to modern ideas.

      • Ha! I actually never liked math in school. It was too abstract. Social sciences were much more fascinating. But now things are coming full circle. I appreciate arithmetic, calculus, etc as forms of sentential logic.

  2. It seems to me that, perhaps, there is broad confusion about two separate issues (or of them). It may well be the case that progress in understanding economics depends on continued and increased reliance on mathematics. There could be several reasons why this is so. One of those reasons is that all words carry baggage that interfere with clarity. That’s on the one hand. On the other hand, the few and modest ideas one can hope to impart undergraduates (and politicians) may be best communicated purely with words . That’s because many people don’t like math (for whatever reason).

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