The misuse of mathematics in economics
from Lars Syll
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 assumptions 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 to 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 quixotic 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 good – not even as a ‘successive approximation’ – modelling strategy.
Mainstream economic theory today is still in the story-telling business whereby economic theorists create mathematical make-believe analogue models of the target system – usually conceived as the real economic system. This mathematical modelling 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 modelling 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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Real-World Economics Review Blog 
The ending of the article immediately reminded me of the ending of Keats’ Ode on a Grecian Urn:
“Beauty is truth, truth beauty,—that is all Ye know on earth, and all ye need to know.”
The equations in physics are excellent (Newton, Maxwell, Heisenberg).They describe reality when the parameters of the environment are within certain limits on planet Earth.
The same is true of the social sciences and economics. Equations are used to describe the processes of the financial market when the parameters of societies are within certain limits. That is why it is necessary to constantly monitor the parameters. The strategies and models are good, but they require criticism.
László Kulin
social expert
Hungary
Had you written about the use of logical argument I would very strongly disagree, however since much logic does require mathematics, it does have its benefit. Not every kind of mathematics involves numbers, statistics nor algebraic formulations and you may be surprised to find that some of it has some other ways for use in modelling the situation in macro that is getting attention. If you look in my short working papers such as SSRN 2865571 “Einstein’s Criterion Applied to Logical Macroeconomics Modelling”, you can get a feel for it.
I see that the mathematical sin of economics goes much beyond a certain hubris or misuse. It has to do with the central role economics plays in our market-centred economic practice and how given development models and power structures are legitimized by economics the way it is presented – and here mathematics plays a central role and has, indeed, become the new Latin and a major tool whereby economists have, in a paradoxical way, replaced Medieval Theology as guardians of dogma-based models who legitimize and promote free-markets and what Polanyi called the utopian character of free-markets who never have and, as Polanyi showed, cannot exist without imperilling the social, ecological and financial ground of society.
Galileo’s challenge to the Church went much beyond a simple astronomical question. In the same way, challenging the use and abuse of mathematics in economics goes much beyond a simple methodological question. It touches the core of our present development practice and power structures. In my article, I go deeper into this crucial question. It can be found here at RWER: http://www.paecon.net/PAEReview/issue97/whole97.pdf
I have read you paper in RWER #97. I agree with you that actual economics is in a rough comparison theology of the Middle Ages. More precise comparison would be compare modern economics with astrology. I once posted the following:
I have forgotten to put closing “blockquote” tag before the last paragraph, which is a new text for the above post.
In other words,
(misguided faith in math + hubris – broad human understanding) x years in the profession = tendency to misuse math in economics.
Maths is a tool that can be misused. Economic theory as taught, apparently, in higher degree courses in he U.S. is no more than the arid application of the maths of optimisation to artificial worlds. I have a question for those who want to do better.
We have a complex social system in which any variable we wish to define and measure will be influenced by a host of other variables and will influence them in return. There is a dense web of causal influences, which is extremely difficult to untangle. People use temporal ordering to try and distinguish cause and effect but this often fails in multivariate systems where important variables may be uncontrolled. A difficult situation but it gets worse. The system under analysis is not entirely stable. You can regard many aspects as enduring for years but probably not for decades and some aspects change even more quickly.
How do you untangle what is going on? How do you test hypotheses and knock out ones that are not useful? It is usually impractical and unethical to carry out controlled experiments and if you do Lars Syll will tell you that you cannot know whether you have controlled for everything anyway.
Some orthodox economists are shysters but most are simply clinging to a method and its conclusions like drowning men holding driftwood in a whirlpool. Anyone can dream up a theory. If we have no technology to look at complexity and filter error from tenable hypotheses, one half-baked notion may be as durable as another. And inadequate generalizations will survive indefinitely.
As well as repeatedly denouncing error, would the local methodologists address the issue of how to assemble evidence and distinguish useful generalizations from misleading ones? The assumption that blind economists are missing the obvious ignores the fact that there is no drawback to being blind in the pitch dark. How do we turn on the light?
I don’t think I’ll bother to read any more ritualistic denunciations of “mainstream” economics on this blog until someone at least tries to address the question above. Inventing words like “abduction” which cannot be given precise meaning is not good enough. The arguments that Lars advances, dismissing both experiment and statistical analysis have a logical conclusion in nihilism: it really is all too difficult. Indeed perhaps it is. So is the conclusion :let’s not bother? After all, bridge and chess are fun..
It is sad to read this kind of feeling from one of most serious discussants in this Real-World Economics Blog.
Lars Syll likes to cite a phrase of Paul Romer, as if he has found a supreme verdict:
He repeats citing it in various posts of the same theme. See for example,
Paul Romer explains what went wrong with economics on February 22, 2020 and Paul Romer’s critique of ‘post-real’ economics on October 18, 2018.
It seems that Lars Syll does not acknowledge that Paul Romer is one of mainstream (or neoclassical) economists with some dissident political ideas, like Joseph Stiglitz and Paul Krugman. When Romer got the Nobel Prize in Economics in 2018, Lars Syll was rejoiced with the news and posted a welcome letterAt last – Paul Romer got his ‘Nobel prize’ in this blog. (See my comment on October 11, 2018 at 4:01 pm on Lars’s post. Romer’s endogenous growth theory is but a small innovation within the framework of Solow-Swan growth theory or a typically neoclassical growth theory.)
The dictum that Syll cites as if it is a new philosopher’s stone is just an expression of feeling of most of conscientious mainstream economists. It signifies that a simple rejection of mathematical theorizing does not work for a reconstruction of new alternative economics. Syll’s criticism is aimed at a wrong direction.
Compare Syll’s post with a citation from a post-Keynesian methodologist: