Mathematician Michael Edesess has **a dose of reality for economists.**

“Economics pretends to be mathematics, but it is not mathematics,” he says. “There is a major difference. No mathematician uses a term in a formula, or a statement of a theorem, unless that term has first been defined with excruciating precision.”

And while economists may think they’ve defined terms like “aggregate demand” or “economic growth,” Edesess suggests they talk to a mathematician. “Economists may think they’ve defined them, but they should try reading some real mathematics to see what a precise definition truly is,” he says. “The economists, I think, leave the work of definition to be inferred from the way the terms are used in the formulas. This, to me, is weird.”

Using a recent blogosphere debate between Steve Keen and Paul Krugman as a jumping off point, Edesess offers a mathematician’s insight into some of the key problems with economic theory and economic debate. The lack of precise definitions produces some distinct symptoms, as the Krugman-Keen argument shows: “The amazing thing is that, in this debate, one side or the other will present what appears to be a very simple proof that they are right – and yet the other side is not persuaded in the least.”

He traces this problem back to what he suggests is the cause: “The source of all the confusion, in my view, is the idea that if you can’t measure something and model it mathematically, it has no meaning. There is too much mathematics used and expected in economics, and too much of it is of poor quality and distorts the ideas it is meant to undergird.”

This mathematical hubris is at the heart of the “the critical state of economic theory has been exacerbated by the financial crisis” – a crisis that was in part created by the overreliance on precise but not accurate mathematical models used as if the real world were made up of mere numbers.

This reliance on mathematics can be traced back to an economics that has falsely aspired to the certainty of a mathematical science like physics (which, in reality, is far less well-defined and precise than economists seem to believe). But, as Edesess also suggests in relation to a part of the Keen-Krugman debate, “causality runs both ways.”

The desire of the business community and society for the illusion of certainty has created significant short-term incentives for economists to provide this false reassurance. But the long-term costs were well demonstrated by the 2008 financial crisis and its aftermath, which we’re still dealing with. Economists too often ignored the real world – and key issues like inequality, financial instability, and innovation – in favor of precise but not accurate numbers, like, as Edesess notes, aggregate demand or GDP.

If economists want to remain relevant they have to return mathematics and the precision it offers to its proper place in the discipline. Math should be a tool that economists use, not an end goal in and of itself. And economists must focus on addressing humanity and morals and ethical dilemmas, which lie at the heart of it all.

## Comments

Great piece, especially when one reads the original Edesess post on his blog. I thought the mathematics would be beyond my limited understanding, but Edesess uses common sense arguments to show that economics is polluted by inaccurate, poorly defined math. I think he does a good job of clarifying the key issues in the Krugman-Keen debate. The air feels better after reading his post. Thanks!

You might look at the intro of a Tarski book (say, about the fifties) on logic (Tarski was a rather important mathematician...just recall the Banach-Tarski theorem/paradox...) by, no other than Keneth Arrow: one of the most influential (if not the greatest of all times) pioneers of modern economics!!!

Krugman is taking a lot of heat recently from all directions (Michael Hudson - Paul Krugman’s Economic Blinders and Krugman Reveals New, Flawed Definition of Austerity). At the heart of Edesess’ argument, however, is a deeper problem for economics that I attempted to address in my post, What is Austerity? The trouble arises from the simple fact that seemingly basic terms can mean wholly different things to individual economists or various sub-sects of the discipline.

Many in the profession may wish to further direct economics towards mathematics, but I fear that process will only further abstract economic thinking from application to the real world. In the realm of policy making and human interaction, individuals and groups will always hold nuanced views regarding the strict meaning of terminology, in part, because language is forever changing. Economics should embrace this social science aspect and, as Edesess says, “disdain the abstractions and think in more ordinary terms.”

http://bubblesandbusts.blogspot.com/2012/05/lack-of-clarity-in-economic-...

Thanks. I wrote about a related view of the problem in 2009. http://www.dailykos.com/story/2009/09/15/780776/-Mathematical-Economics-...

My point was that mathematical theorems prove results from given assumptions, and that one must either verify the assumptions, or take some action to make them true. Hence constant collection and publication of financial and economic data, regulation, the courts, and other processes such as consumer boycotts to get economic actors to behave according to the rules, where the laws and rules should be designed to prevent accumulation of undue economic power, or forbid its use.

That leaves us with a significant set of problems that the math cannot help us with.

What are the best conditions to aim for? How do we set values on such considerations as productivity, efficiency, fairness, reasonably full employment with adequate compensation, and avoidance of regulatory capture by corporations?

Can we get laws and regulations that will allow us to approximate those conditions? What are the requirements for doing so?

Can we enforce such laws and regulations? What are the requirements for doing so?

Currently, politicians can claim that math justifies economic Voodoo without being laughed out of elections, so clearly the math and the politics can only be claimed to be working as intended by those with a vested interest in their failure. Common names for such people include liars, robber barons, kleptocrats, the 1%, Thorstein Veblen's Leisure Class and absentee owner class, the self-proclaimed Southern Aristocracy, or worse.

All for ourselves, and nothing for other people, seems, in every age of the world, to have been the vile maxim of the masters of mankind.--Adam Smith, Wealth of Nations

I frankly admire [Cecil Rhodes], I freely admit it, and when his time comes I shall buy a piece of the rope for a keepsake.--Mark Twain, Following the Equator

This type of observation about economics makes me feel a whole lot better about myself. I was worried that I was just too stupid to understand economic theory. However, it makes me feel pretty badly for our society, and the planet on which we live.

I have spent some time recently trying to understand where PROFIT comes from and who pays it. Its a little word somehow at the heart of economic theory, defined simply as the difference between exchange value and the input costs.

P = V - C

Its a tidy little equation that even a tenth-grade student can comprehend. But that little piece of mathematics does not say from where comes the ability to pay profits year after year.

As a project manager, I learned about the "time value of money" and used its related mathematical formulae to forecast costs and benefits in cash flows in the distant future. But one has to ask just how this works.

At first, the statement that profit results from "agricultural surplus" is somewhat satisfying, but that idea does not, in the end, really stand up to scrutiny. One ponders and staggers at the scale of the ripoff that that implies is being born by modern farmers. If the benefits to business arise from farmer's activities, the farmers see little of it.

A more intellectually satisfying idea, but a little less obvious in connection, is that it comes from surplus energy arising from fossil fuels via EROEI. This is more intellectually satisfying, since a large-scale transfer of value from consumers to the oil magnates (rather than the farmers) does not challenge credibility quite so much.

However, the point is well made that just because "economic theory" includes a mathematical definition of profit based on input costs and exchange values, it does not imply that economists have any real understanding about how profits arise in our modern society.

I am coming to the conclusion that profits arise from (a) a small agricultural surplus of energy; (b) a large surplus of energy coming from the fossil fuel industry; and (c) a massive surplus of cash coming from the debt/credit industry.

This type of economy cannot be sustainable.

Please tell me I am wrong.

Garvin H Boyle

No sane economist claims that "that if you can’t measure something and model it mathematically, it has no meaning." That is a complete misrepresentation of the motivation for using mathematics in economics.

One motivation is simply that it is often a better way to present ideas. First because it forces the author to clearly define underlying assumptions and relationships between different parts of the idea. Second, because once an idea becomes sufficiently complex, formulas are far easier to read for trained readers than long verbal discussions.

That doesn't mean that we can capture every good idea into a mathematical model. It just means that it is a good thing if we can, so we should try. Often the reason that we can't is because an argument is too fuzzy - so then the whole process of trying to put them into a model is quite informative. I usually find out if my ideas have major holes once I try to write them down into a model.

The rest of Edessess opinion can be summarised as "my math is bigger than your math" - sure, but as long as economists understand each others ideas sufficiently well our type of math serves its purposes.

The biggest problem with posts like these is the negative impact they have on young students in the field. Many are initially struggling with maths and statistics, and some of them will happily follow any argument that implies that learning these languages is anyways a waste of time.

Prof M. Edesses hit it exactly. His points are exactly what Prof Michael Fast and I wrote about in our book, Qualitative Economics (Coxmoor Press, 2008) whose subtitle is "toward a science of

economics" makes these same points. I have several other articles and

book chapters out now on these every issues. And even notice that the

Economist even admires that economics is a "field of study" implying that it is NOT a science. NOTE their July 16, 2009 with a Bible melting on the cover with the Title: "Modern Economic Theory".

Check even two other issues earlier this year (2012) on "State Capitalism" and more recently on The Third Industrial Revolution (which they took from Prof Jeremy Rifkin and his latest book on that topic. However, my last book and talks are all about The Green Industrial Revolution (Praeger Press) in which China has "leap frogged" --- including the USA which is NOT there yet.

Look at China, but especially the EU, Japan and S.Korea.

For more information and details on how economics can become (and should become) a science, look at my books on sustainable communities, but especially my forthcoming one on The Next Economics (Springer Press) this fall.

Hmm, at the end of the blog post it is said that Edesses is "an accomplished mathematician." He got his Ph.D. in 1961 from Northwestern. But he doesn't seem to understand much about mathematical systems. Chaotic systems have complicated blends of equilibrium and non-equilibrium behaviors. I guess I should just sigh and know that it will be a hundred years or more before economists catch up to this fact. Krugman's IS-LM model is oversimple but useful; Keen's recognition that the model can fail under special circumstances is to be applauded. But neither of those guys are math whizzes, not really. There's a whole lot more to understanding systems than either of them, or even Dr. Edesses, can imagine. What won't happen, as Mr. Soros says, is a simple axiomatic explanation of how an economy works. The micro people need a lot more humility, too.

It has been a cothurnus of economics to be overreliance on math for almost a century.

Thank your for your perspective. Teaching economics for IB means it is essential to remind students that economics is about people and not maths. What would be of great value if you could in a more detailed yet understandable form for those of us with less than advanced mathematical knowledge develop your critique using actual example and names and indeed theory.

Has anyone ever shown that there is an economic system that is equilibrial using assumptions that are not silly? Therefore, they are not allowed to use the assumption of efficient markets, rational agents, etc.

If it cannot be shown that the system is equilibrial, then one would assume that it is a multiple equilibrium system which moves between the various equilibria depending on driving variables. Phenomena to be exhibited being cascades, regimes changes, non-equilibrial dynamics, threshold effects and tipping points, etc. the literature is quite substantive in relation to other complex adpative systems. For a long time ecologist held to the equilibrial viewpoint, e.g. Clementsian Theory with a vengeance. Fortunately, it is now disposed of in favour of a more rational assessment of how ecossytem works based on evidence as opposed to ideology. Maybe by embracing evidence and brutally realistic assumptions economics can also move forwards.

If the output is a number and you think you are not using math, you are confused at a basic level.

"If economists want to remain relevant they have to return mathematics and the precision it offers to its proper place in the discipline. Math should be a tool that economists use, not an end goal in and of itself."

Well...yes, but math is not an end-in-itself in economics, it's more rhetoric than anything else. It's used to give a scientific air to the subject. All this was addressed by Keynes and others a long time ago, and it's very simple: economics is a moral and not a natural science. Admit that, and everything else follows.

What puzzles me no end is, why is INET repeating the mistake of the neo-classical synthesis of Samuelson et al. by taking complexity economics seriously? Math(and certain areas of physics adapted to economics) can only ILLUSTRATE or DESCRIBE economic ideas. Mathematical models, even ones with correct predictions, do not provide a "proof" of the validity of an economic idea. I'm sure that Samuelson's or even Lucas' models made correct predictions some of the time, but did that mean their understanding of the economy was correct? The same thing, in my opinion, would hold for Keen's work.

Gavin - - -

I think you have a pretty reasonable assessment. I would parse your statement "a massive surplus of cash coming from the debt/credit industry." Since "cash" may be considered to mean "currency" I would suggest that the term "money" be used which would commonly be interpreted to cover both currency and bank credits.

You conclusion is a simple truth: This type of economy cannot be sustainable.

How can it be sustainable when "growth" reflects predominantly the increase of surplus money from financial transactions without a significant surplus of physical and service production that advances the well being of society?

The creation of an expansion of credit in the hands of a few with no corresponding expansion of "real" production and utility for a broader population is clearly not sustainable.

In his Nobel Prize for Economics acceptance speech F A Hayek warned against trying to apply methods of the natural sciences in the social sciences, what he referred to a scientism. Too much is subjective to create the neat formulas of physics. There is strong evidence of economic growth the last 200 years and that that growth is much faster in free economies, but their are too many factors too have a formula for the rate of economic growth over time. A basic position in economics going back to Adam Smith is that society evolves as the result of human action, but can not be designed. Economists can demonstrate that free markets grow, but they can't predict the exact rate of growth or create absolute certainty, they can explain how free individuals interact better than central planers but can't create a scientific central plan. As Hayek put it "The curious task of economics is to explain to men how little they know about what they think they can design."

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