## Economists — not mathematics — solve economic problems

6 Nov, 2014 at 17:20 | Posted in Economics | 3 CommentsA common mistake amongst Ph.D. students is to place too much weight on the ability of mathematics to solve an economic problem. They take a model off the shelf and add a new twist. A model that began as an elegant piece of machinery designed to illustrate a particular economic issue, goes through five or six amendments from one paper to the next. By the time it reaches the n’th iteration it looks like a dog designed by committee.

Mathematics doesn’t solve economic problems. Economists solve economic problems. My advice: never formalize a problem with mathematics until you have already figured out the probable answer. Then write a model that formalizes your intuition and beat the mathematics into submission. That last part is where the fun begins because the language of mathematics forces you to make your intuition clear. Sometimes it turns out to be right. Sometimes you will realize your initial guess was mistaken. Always, it is a learning process.

Good advice — coming from a professor of economics and fellow of the Econometric Society and research associate of the NBER — well worth following.

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Farmer is repeating what Marshall said before him

“I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypothesis was very well unlikely to be good economics: and I went more and more on the rules – (1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This last I do often.”

Letter to A.L. Bowley, 27 February 1906, cited in: David L. Sills, Robert King Merton, Social Science Quotations: Who Said What, When, and Where Transaction Publishers, 2000. p. 151

Comment by Tom Hickey— 6 Nov, 2014 #

Economists do not solve problems, they are the problem

Comment on Roger Farmer’s ‘Economists — not mathematics — solve economic problems’

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It is widely known that the representative economist does not understand how the economy works. Many explanations have been advanced. One of them is that economists have serious troubles with mathematics. The trouble, though, is twofold: economists either reject or accept mathematics but always for the wrong reason.

When economics was young, calculus was the new and tremendously successful tool. So economists copied it (Mirowski, 1995) and this is how marginalism became the chief tool of explanation. This was the first methodological mistake.

“The mathematical language used to formulate a theory is usually taken for granted. However, it should be recognized that most of mathematics used in physics was developed to meet the theoretical needs of physics. … The moral is that the symbolic calculus employed by a scientific theory should be tailored to the theory, not the other way round.” (Wittgenstein, quoted in Schmiechen, 2009, p. 368)

It has been realized by many observers that utility maximization, equilibrium, perfect competition, etcetera was the unacceptable part of economic theory and not the application of mathematics.

“When very sound and proper mathematics is misused and misapplied to fairyland problems without any basis in the real world, that fact that the mathematics itself is impeccable makes the whole obnoxious game just that more offensive.” (Blatt, 1983, p. 173)

To blame mathematics for its abuse in economics is simply wrong-headed.

“Mathematics is not really of much fundamental use in a science unless that science is able to constitute its basic concepts with “exact axioms” and precise numerical results.” (Weintraub, 2002, p. 26)

Ultimately economists got the basic concepts wrong. Conventional economics rests on behavioral assumptions that are formally expressed as axioms (McKenzie, 2008). Axioms are indispensable to build up a theory that epitomizes formal and material consistency. The fatal flaw of the standard approach is that human behavior does not yield to axiomatization.

As a matter of fact, no way leads from psychologism of any sort to the understanding of how the actual economy works. The solution consists in replacing behavioral axioms by objective structural axioms (2014).

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Egmont Kakarot-Handtke

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References

Blatt, J. (1983). How Economists Misuse Mathematics. In A. S. Eichner (Ed.), Why

Economics is Not Yet a Science, pages 166–186. Armonk, NY: M.E. Sharpe.

Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics:

Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2489792.

McKenzie, L. W. (2008). General Equilibrium. In S. N. Durlauf, and L. E. Blume

(Eds.), The New Palgrave Dictionary of Economics Online, pages 1–18. Palgrave

Macmillan, 2nd edition. URL http://www.dictionaryofeconomics.com/article?id=

pde2008_G000023.

Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University

Press.

Schmiechen, M. (2009). Newton’s Principia and Related ‘Principles’ Revisited,

volume 1. Norderstedt: Books on Demand, 2nd edition. URL

http://books.google.de/books?id=3bIkAQAAQBAJ&printsec=frontcover&hl=

de&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false.

Weintraub, E. R. (2002). How Economics Became a Mathematical Science. Durham, NC, London: Duke University Press.

Comment by Egmont Kakarot-Handtke— 7 Nov, 2014 #

I worry that saying this sort of thing will put economists off from properly formulating what they think. Maths is just a way of formulating the issue – if you get it right it can help work out possible solutions to problems – but if you get it wrong you can end up dealing with problems that dont exist.

Perhaps more important is getting the language of economics right – otherwise it is all written down in dense incomprehensible text which no-one understands (not even the author when he has had a few nights to forget the thread of his arguments).

Comment by Huw Williams— 18 Nov, 2014 #