Economics — confusing mathematical masturbation with intercourse between research and reality

7 March, 2017 at 13:53 | Posted in Economics | 3 Comments

There’s no question that mainstream academic macroeconomics failed pretty spectacularly in 2008 …

Many among the heterodox would have us believe that their paradigm worked perfectly well in 2008 and after … This is dramatically overselling the product. First, heterodox models didn’t “predict” the crisis in the sense of an actual quantitative forecast.

64f5d94d9836c6a09b5d2009f0d4634a845bb2d7ba56bbaa16176c2fd0e958c0This is because much of heterodox theory is non-quantitative. Basically, people write down English words explaining their conceptual ideas about how the economy works. This describes the ideas of mid-20th-century economist Hyman Minsky, who wrote books and essays about the instability of the financial system. Minsky, though trained in math, chose not to use equations to model the economy — instead, he sketched broad ideas in plain English …

At the end of the day, policymakers and investors need to make quantitative decisions — how much to raise or lower interest rates, how big of a deficit to run, or how much wealth to allocate to Treasury bonds.

Noah Smith

Noah Smith — like so many other mainstream economists — obviously has the unfounded and ridiculous idea that because heterodox people like yours truly often criticize the application of mathematics in mainstream economics, we are critical of math per se.

I don’t know how many times I’ve been asked to answer this straw-man objection to heterodox economics — but here we go again:

No, there is nothing wrong with mathematics per se.

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

amathMathematics 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”

As social scientists we should never equate science with mathematics and statistical calculation. All science entail human judgement, and using mathematical and statistical models don’t relieve us of that necessity. They are no substitutes for doing real science. Or as a great German philosopher once famously wrote:

There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.

Looking at what famous mathematical mainstream economists — like e.g. Paul Samuelson and Gerard Debreu — have come up with, there is no indication at all they produce rigorous and successful explanations or predictions of real-world phenomena. In physics it’s all different. There one has often been able to, by the use of mathematics, to produce both rigorous and successful explanations and predictions. But then, of course, the material world is something quite different from the social world …

Neoclassical economic theory today is 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 modeling activity is considered useful and essential. Since fully-fledged experiments on a societal scale as a rule are prohibitively expensive, ethically indefensible or unmanageable, economic theorists have to substitute experimenting with something else. 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 “analogue-economy models” rather than engineering things happening in real economies.

Formalistic mathematical-deductive “Glasperlenspiel” can be very impressive and seductive. But in the realm of science it ought to be considered of little or no value to simply make claims about the model and lose sight of reality.

With his profound knowledge of mathematics, Keynes realized the limits of its applicability to the real world — and that it was certainly not enough for a relevant social science to prove things about thought up worlds:

But I am unfamiliar with the methods involved and it may be that my impression that nothing emerges at the end which has not been introduced expressly or tacitly at the beginning is quite wrong … It seems to me essential in an article of this sort to put in the fullest and most explicit manner at the beginning the assumptions which are made and the methods by which the price indexes are derived; and then to state at the end what substantially novel conclusions has been arrived at … I cannot persuade myself that this sort of treatment of economic theory has anything significant to contribute. I suspect it of being nothing better than a contraption proceeding from premises which are not stated with precision to conclusions which have no clear application … [This creates] a mass of symbolism which covers up all kinds of unstated special assumptions.

Keynes to Frisch 28 November 1935

So — please — let’s have no more of this feeble-minded pseudo debate where heterodox economics is described as simply anti-math!

Mainstream economists love to depict heterodox economists’ views on the use of mathematics as coming from sadly misinformed and misguided people who dislike and do not understand much of it. This is really a gross misapprehension. We do not misunderstand the crucial issues at stake — and many of us have spent decades on using mathematics and statistics in our research and teaching.  To be careful and cautious is not the same as to dislike. Quite the contrary. We know the crucial issues all too well — and are not satisfied with the validity and philosophical underpinning of the assumptions made for applying mathematical methods in economics.

Without strong evidence all kinds of absurd claims and nonsense may pretend to be science.  So let us not forget what Paul Romer — someone I guess not even the most outré mainstreamer would call ‘anti-math’ — said in his masterful attack on ‘post-real’ economics last year:

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 the standard modeling assumption made in much of modern macroeconomics. The reason for this sad state of ‘modern’ economics is that economists often mistake mathematical beauty for truth.

russell_ackoffNo real problem worth solving can be solved without some basic research. Therefore the engagement of faculty and students on real problems yields basic research problems whose solutions are of practical significance. Furthermore, the validity of these solutions can be tested in the most effective way known: in application. This avoids one’s confusing mathematical masturbation with intercourse between research and reality.

Russell L. Ackoff

Advertisements

3 Comments

  1. “This avoids one’s confusing mathematical masturbation with intercourse between research and reality.”

    Welcome to the latest mathematics Bunga Bunga party where all intellectual pleasures and delights are permissable. Please provide your own prophylactic containment devices.

  2. I just spent a week modeling noise. I found very good linear relation in my 900 noisy variables, spectral data of 900 wavelength and one respons. The fit was great, but the models ability to predict really sucked. It got apparent that it was noise i modelled when I noticed that the models ability to predict got worse the more I added calibration points. At first it looked promising, with few calibration points over a wide span it looked as if the model only needed more calibration. But it was only guessing, but with responses wide apart the errors in guesses was relatively small, the large errors in guessing could be explained as ”outliers”. It looked as if the model only needed more calibration, but it was first after I was adding more and more calibration points that it got apparent that I was modeling noise. As the calibration points got closer and closer together, the errors of the model that first was easy to dismiss, now got so large relative to the distance between the calibration points that it was beginning to get hard to rationalize the errors. It was beginning to converge on the stock-monkey.

    I new that modeling could work, since what I was looking at was the spectra of water, and what I wanted to know was a solute that had no direct observable absorption, but it would affect the water spectra, it’s surroundings. But it failed with 900 variables as miserably as it would have failed with just one.

    The thing is, with enough variables in your data, with enough data, it becomes impossible to not find a nice linear fit. With enough data you are guaranteed to make an ass of yourself. The hardest part, the labour intensive part, it was to realize that I was the ass and that I had failed. Somehow the next calibration point would make everything all right was the driving force that wasted a lot of time.

    I had spent a week, and learned nothing, I did not learn how or why my solute affect the water spectra, i did not learn to quantify my solute. All I learned was that with enough data I was guaranteed to waste a lot of time demonstrating that I am an idiot.

    I, however, could go out on the lab and test my model, over and over, no one got hurt but my pride. Now imagine if people in social sciences does this, and imagine if politicians are impressed by my mathematics. Imagine if people got hurt. Imagine the difficulty in admitting that I was an idiot and my mathematics was bullshit? It was hard enough without the high stakes.

    • Ultimately, it was not mathematics that exposed the model for what it was. While the mathematics kept rationalizing itself, the monkey doing the maths started to doubt it. That was the death of the model, mathematics would have kept going.


Sorry, the comment form is closed at this time.

Create a free website or blog at WordPress.com.
Entries and comments feeds.