Don’t blame mathematics for the dismal state of the dismal science

Ridiculing the state of economics has been in vogue for quite some time, especially since the last crisis hit. Even before that, we have seen attempts to reform the discipline from students as well as from vocal minorities in the profession. This is a necessary and healthy discussion, and a little bit of new fuel was recently added to the fire.

In his long and deceptively well-argued aeon-piece, Alan Jay Levinovitz attempts to solve the riddle of why economics as an academic field has often failed spectacularly in delivering predictive capacity, even on some of its most fundamental objects of study, but is still by far the most well-regarded social science discipline, and has been left completely unscathed when other social science departments have seen their budgets slashed. Levinovitz goes as far as dubbing the discipline a form of modern-era astrology for its ability to dupe public and politicians alike, an epithet which, of course, is a deliberate (and perhaps unfair) insult.

The solution to the riddle, according to the piece, is excessive mathematization. The parallel with astrology lies in a high level of formalization, used to clad theories in a largely impenetrable language and an air of scientific precision. Levinovitz’s argument thus boils down to a simple logic of deception (and perhaps self-deception): the mathematics look impressive, and few people understand what it actually means, and so economists (as formerly astrologers) are given an undeserved amount of credibility, influence and – tadaa – money.

There is something intuitively convincing about this parallel. Mathematics indeed manages to put some sort of spell on people (myself included, much to my dismay). As a particularly telling example, it has been shown that when an abstract to a scientific paper is accompanied by a totally meaningless equation, the credibility of the paper is consistently rated higher (even by academics) – but not among people who actually understand mathematics. And yes, undoubtedly the high level of formalization of economic theory makes it difficult (read: impossible) for lay people (or even highly trained social scientists from other disciplines) to even get a basic grasp of what the models actually mean.

So the question arises – is mathematization inherently bad? If we were to follow Levinovitz argument to its logical conclusion, it would appear that the solution to the occasionally poor state of economic theory is to abandon formalization. Could this possibly be correct?

The answer has to be no. To see why, it helps to understand 1) why we may want to use mathematics in the first place, and 2) why economics still often fails. Recall that physics is a discipline that relies heavily on mathematics as well, and heaven knows that physics puts a spell on people too. If formalization was really a problem per se, there is no reason why abandoning mathematics should be limited to economics. Yet, physics is a scientific enterprise with completely unprecedented success in terms of predictive capacity.

So why do we need mathematics then? We resort to mathematics because the analysis of certain questions and certain systems is simply too complex to be left to unaided human reasoning. Humans are equipped with a number of evolved computational rules of thumb that work well in approximating answers to calculations of a kind that we would encounter as hunter-gatherers. These rules of thumb often fail us, and fail us spectacularly, when dealing with the computational complexity of understanding how societies, economies, ecologies or atoms work (have a look at this article, for some famous and accessible examples). Thus, we often need mathematics.

Even in cases where mathematics may not be necessary to explain a particular theoretical relationship, it is not clear that the argument could have been made equally well without a formal model, had there been no modeling done. In my own experience, putting an argument on formal basis can make a mechanism that seemed confusing and tedious at first become at once completely clear and easily explainable even with verbal reasoning. The puzzle comes together. Further, relying on the mathematical formalization, we can be sure that such a verbal argument really is internally valid and actually follows from the premises, rather than having to rely on intuition.

In short, the reason why economic theory often looks perplexingly complex is not necessarily because of superfluous formalization, but because its subject matter is complex. So why does it too often fail? The great irony is that the state of economic theory is not complex enough. Rather, it is in many cases much too simplified. The assumptions of optimizing, rational, self-interested, atomistic agents and micro-macro structural uniformity make economic models tractable. Unfortunately, it also often makes them false. Real-world agents rarely conform to these micro-level assumptions, and economic systems are probably strongly dependent on emergent phenomena that cannot be accurately captured with the traditional micro-foundations approach.

Here is an admittedly ad-hoc and perhaps utopian two-pronged solution: 1) Other social scientists need to learn mathematics instead of deriding its use in economics. Not understanding mathematics amounts to leaving the economic theorists alone with their models in their ivory towers – the state of affairs we’ve already witnessed the results of. If, for example, academic psychologists had been on the formalization train earlier, I don’t think we would have had to wait until the last few decades to see the behavioral econ paradigm making serious headway in the discipline. 2) The solution to some of the endemic problems in economic theory is to replace faulty axioms of individual atomistic rationality etc, not to abandon mathematics. On the contrary, it seems likely that this will require more sophisticated mathematics, if anything.

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