The misuse of mathematics in economics

8 Dec, 2022 at 23:32 | Posted in Economics | 2 Comments

Many American undergraduates in Economics interested in doing a Ph.D. are surprised to learn that the first year of an Econ Ph.D. feels much more like entering a Ph.D. in solving mathematical models by hand than it does with learning economics. Typically, there is very little reading or writing involved, but loads and loads of fast algebra is required. Why is it like this? …

One reason to use math is that it is easy to use math to trick people. Often, if you make your assump-tions in plain English, they will sound ridiculous. But if you couch them in terms of equations, integrals, and matrices, they will appear more sophisticated, and the unrealism of the assumptions may not be obvious, even to people with Ph.D.’s from places like Harvard and Stanford, or to editors at top theory journals such as Econometrica …

Given the importance of signaling in all walks of life, and given the power of math, not just to illuminate and to signal, but also to trick, confuse, and bewilder, it thus makes perfect sense that roughly 99% of the core training in an economics Ph.D. is in fact in math rather than economics.

Douglas L. Campbell

Indeed.

No, there is nothing wrong with mathematics per se.

No, there is nothing wrong with applying mathematics to economics.

Mathematics is one valuable tool among other valuable tools for understanding and explaining things in economics.

What is, however, totally wrong, are the utterly simplistic beliefs that

• “math is the only valid tool”

• “math is always and everywhere self-evidently applicable”

• “math is all that really counts”

• “if it’s not in math, it’s not really economics”

• “almost everything can be adequately understood and analyzed with math”

Mainstream economists have always wanted to use their hammer, and so have decided to pretend that the world looks like a nail. Pretending that uncertainty can be reduced to risk and that all activities, relations, processes, and events can be adequately converted to pure numbers, have only contributed to making economics irrelevant and powerless when confronting real-world financial crises and economic havoc.

How do we put an end to this intellectual cataclysm? How do we re-establish credence and trust in economics as a science? Five changes are absolutely decisive.

(1) Stop pretending that we have exact and rigorous answers on everything. Because we don’t. We build models and theories and tell people that we can calculate and foresee the future. But we do this based on mathematical and statistical assumptions that often have little or nothing to do with reality. By pretending that there is no really important difference between model and reality we lull people into thinking that we have things under control. We haven’t! This false feeling of security was one of the factors that contributed to the financial crisis of 2008.

(2) Stop the childish and exaggerated belief in mathematics giving answers to important economic questions. Mathematics gives exact answers to exact questions. But the relevant and interesting questions we face in the economic realm are rarely of that kind. Questions like “Is 2 + 2 = 4?” are never posed in real economies. Instead of a fundamentally misplaced reliance on abstract mathematical-deductive-axiomatic models having anything of substance to contribute to our knowledge of real economies, it would be far better if we pursued “thicker” models and relevant empirical studies and observations.

(3) Stop pretending that there are laws in economics. There are no universal laws in economics. Economies are not like planetary systems or physics labs. The most we can aspire to in real economies is establishing possible tendencies with varying degrees of generalizability.

(4) Stop treating other social sciences as poor relations. Economics has long suffered from hubris. A more broad-minded and multifarious science would enrich today’s altogether too autistic economics.

(5) Stop building models and making forecasts of the future based on totally unreal micro-founded macro models with intertemporally optimizing robot-like representative actors equipped with rational expectations. This is pure nonsense. We have to build our models on assumptions that are not so blatantly in contradiction to reality. Assuming that people are green and come from Mars is not a good – not even as a ‘successive approximation’ – modeling strategy.

Mainstream economic theory today is still in the story-telling business whereby economic theorists create mathematical make-believe analog models of the target system – usually conceived as the real economic system. This mathematical modeling activity is considered useful and essential. To understand and explain relations between different entities in the real economy the predominant strategy is to build mathematical models and make things happen in these ‘analog-economy models’ rather than engineering things happening in real economies.

Without strong evidence, all kinds of absurd claims and nonsense may pretend to be science. Let us not forget what Paul Romer said  in his masterful attack on ‘post-real’ economics a couple of years ago:

Math cannot establish the truth value of a fact. Never has. Never will.

We have to demand more of a justification than rather watered-down versions of ‘anything goes’ when it comes to the main postulates on which mainstream economics is founded. If one proposes ‘efficient markets’ or ‘rational expectations’ one also has to support their underlying assumptions. As a rule, none is given, which makes it rather puzzling how things like ‘efficient markets’ and ‘rational expectations’ have become standard modeling assumptions made in much of modern macroeconomics. The reason for this sad state of ‘modern’ economics is that economists often mistake mathematical beauty for truth.