## The misuse of mathematics in economics

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

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.

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From today’s slashdot:

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《Theoretical physicist Sankar Das Sarma wrote a thought-provoking essay for New Scientist magazine’s Lost in Space-Time newsletter: I was recently reading an old article by string theorist Robbert Dijkgraaf in Quanta Magazine entitled “There are no laws of physics”. You might think it a bit odd for a physicist to argue that there are no laws of physics but I agree with him. In fact, not only do I agree with him, I think that my field is all the better for it. And I hope to convince you of this too. […] Despite many scientists viewing their role as uncovering these ultimate laws, I just don’t believe they exist…. I know from my 40 years of experience in working on real-life physical phenomena that the whole idea of an ultimate law based on an equation using just the building blocks and fundamental forces is unworkable and essentially a fantasy. 》

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And from the Quanta Magazine article cited:

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《On the one hand, particle physics is a wonder of elegance; on the other hand, it is a just-so story.》

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《[…] the basic models that we fully understand […] are of little value in describing the real world […]》

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Does this sound similar to point (3) in Lars’ post, except about physics?

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Thus, why envy physics?

Comment by rsm— 12 Dec, 2022 #

《No, there is nothing wrong with mathematics per se.》

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《Mathematics gives exact answers to exact questions.

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Did Gödel ask exact mathematical questions that had no answers? Does the Banach-Tarski paradox ask if 1 = 2 and prove the answer is yes? Are mathematicians wilfully ignoring the blatant Trivialism their own assumptions lead to?

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《There are no universal laws in economics. Economies are not like planetary systems or physics labs. 》

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Why do the “universal” laws of planetary systems not apply to all galactic systems in the rest of the universe, without positing an aether-like Dark Matter that conveniently appears just where it is needed?

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Regarding labs, From wikipedia:

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《In the laboratory, Latour and Woolgar observed that a typical experiment produces only inconclusive data that is attributed to failure of the apparatus or experimental method, and that a large part of scientific training involves learning how to make the subjective decision of what data to keep and what data to throw out. Latour and Woolgar argued that, for untrained observers, the entire process resembles not an unbiased search for truth and accuracy but a mechanism for ignoring data that contradicts scientific orthodoxy.》

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Why envy physics?

Comment by rsm— 9 Dec, 2022 #