Mathematics as a Signal

Some economists justify the use of math in economics as a means of keeping their model straight. What if it has another purpose? What if it’s a signal?

In economics, a signal is a means of communicating something to others. For example, suppose that a large group of employers is looking for candidates with a certain skill, say the ability to sit down, study a topic, and train themselves on it (e.g. if you’re a digital analyst, you may want to train yourself on JavaScript). Prospective candidates who can do that will want to separate themselves from prospective candidates who can’t, so the former develop a signal. Let’s, for the sake of an example, say that this signal is a degree from a four-year university. The degree shows that you can be given a book and you can attend a few hours of lecture every week, and that you can learn the material (supposedly, right?).

Ideally, the signal should have a cost. Restated, it should be costly for someone to attain that signal. In our example, the optimal cost is one that is costly enough to dissuade candidates who don’t fit the employers’ criteria and not too costly that it dissuades those who do fit the criteria.

Math could be interpreted as a signal, at least as far as its use in economics in concerned. Suppose we’re interested in differentiating good economic theorists who can make enlightening insights on complex topics from average economic theorists who aren’t so good at doing that. Math, specifically the kind of math you learn for economics, is not easy to learn. There’s a cost, and that’s the amount of time spent studying it (time you could have spent studying/doing something else). The cost is high enough to weed a lot of people out.

At my alma mater, math is used as a signal to differentiate those who intend to move on to grad school and those who don’t. You can get an economics degree from San Diego State University with only precalculus, trigonometry, and “business calculus.” But, if you want to go to grad school, the straightforward economics degree isn’t usually good enough. Instead, you get a “specialization is quantitative economics,” which necessitates a higher level calculus class and then a mathematical economics class, which pretty much sums up 13 semesters of math (derivatives, integrals, and matrix algebra, pretty much). That specialization serves as a signal to boards which regulate the entry of masters and PhD candidates.

In the academic world, perhaps math signals certain capabilities, including the ability to think about complex subjects and derive accurate results. Note, this is a generalization, and I’m sure there’s plenty of very good economists who aren’t so good at math, or at least don’t use math much in their work — in fact, I know good economists who fit this characterization. But, maybe they’re the exception to the rule?

3 thoughts on “Mathematics as a Signal

  1. Mateusz Wywiał

    That is clearly an interesting and insightful idea. Though, it rests on assumptions common to other applications of signaling theory – namely, that differentiation between good and bad economists (precisely, between good and bad economic publications) is difficult. While this may be true, it implies that the status of economic theorizing is not nearly the same as other theoretical enterprises to which we refer as ‘science’.

    If it is difficult to judge the body of theoretical work by itself and its results and need to rely on some kind of a signal or proxy, then it is difficult to speak about objective validity of that work, at least to the extent we need to rely on the signal.

    Or you are refering only to evaluating economic theorists and not their theories, e.g. when assessing them as universities’ and research centres’ potential employees?

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  2. Dave Marsay

    I agree with Keynes that we need a way to distinguish between different types of mathematics. He called the type that you refer to ‘pseudo-mathematics’. Strangely, this terminology didn’t catch on.

    In the 10 years in the run-up to the crisis of 2008 many proper mathematicians were advised that they were giving out the wrong signals and so would never be taken seriously by decision makers, who would only be confused. The most that such mathematicians could do would be to spoil the party. But while I agree with you that pseudo-mathematical bullshit is a problem, ‘proper’ mathematics could be a part of the answer.

    Incidentally, I saw the Turing film last night. In contrast to the film, I see Turing as a proper mathematician and suppose that proper mathematics helped the war effort, with any pseudo-mathematics being properly subordinated. Certainly, I consider that he would have been highly critical of economists’ pseudo-mathematics. Do we need another Turing film?

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