Our buddy Stickman has a post over at his blog about the virtues of maths in economics. In his very pragmatic way the Stickdude basically argues that yes, maths has its limitations, but that it is nonetheless an indispensible tool of the truly serious economist.

Those of us less enamoured of the value of maths in economics and who rely on basic axioms of human action are hiding from the virtues of maths, perhaps because we do not understand it, or perhaps even fear it? This, he argues, is folly. How can serious theoreticians such as Mises, Hayek, Rothbard etc dismiss the mathematical method and still be expected to be taken seriously?

However, the nub of Mr. Stickman’s argument is that mathematics helps us understand complex dynamics that are not apparently intuitive to the good, rational brain. But this immediately is to confer upon maths the ability to a) think for us, and b) to achieve the same or similar utility as it does in the hard sciences.

As many have pointed out however, economics is not a hard science and never will be. Moreover, even to the extent that it might be deemed a semi-science, it is fundamentally different in its objectives and measurable abilities than are the true sciences.

This is why the great praxeological thinkers of the Austrian tradition realised early on that good economic theory had to be built in a fundamentally different way to theories in the hard sciences. And so from the ground up they constructed theory in a fundamentally different way to the other economists of their time, and of course from the hard scientists.

Moreover, as Hayek pointed out, the praxeological thinkers recognise the limitations of what is even measurable in the first place. We can only apply quantitative scientistic methods to MEASURABLE THINGS. But then we have to acknowledge that MOST things are un-measurable, and therefore that indeed most causality is likely to be fundamentally un-measurable.

In fact the modern day economist is practically constrained in his or her quantitative techniques by the data government statistical departments want to, or simply are able, to produce. Not only that, the quantitative economist is also subject to the quality of said data, which tends to be poor. That is hardly a sound basis from which to determine economic truth!

Indeed, this brings us back to assumptions, for absent measurable data, mathematics hinges upon sound equations. But in the economic sense these equations hinge upon assumptions, even, dare we say, known axioms. Where they cannot hinge upon measurable data or assumptions, they tend to be identities that must necessarily be true and therefore of little deductive or theoretical value other than to tell you something you already know.

The best example of this is the Fisher equation of money and money velocity. MV=PT. Fisher produced this equation to describe and prove his ”Quantity Theory of Money”. Mathematical economists have used this equation to derive erroneous theories about price inflation, when in fact the equation is an identity that only tells you something that could logically be deduced anyway without the help of mathematics, simply using sound reasoning. MV=PT is a ruse.

Original assumptions matter, and as even Stickman writes concedingly,

“By any reasonable account, many an economist has become enamoured of their elegant theoretical models and abstract equilibria points, all the while ignoring the implausibility of their founding assumptions and the unpredictability of real-life phenomena.

But he then shrugs this ‘minor’ issue off…

Point made, let’s correct for these imbalances and move on.

Correct the imbalances? Just tweak the dial a little then shall we?

In fact this is the very core of the issue – conferring too much importance to the scientistic mathematical method. But it is less a case of “getting the balance right” per se than it is about rethinking the very essence of mathematical economics, its value in building theory, and its value in verifying theory and testing hypotheses.

From F.A. Hayek’s 1974 Nobel acceptance speech:

“…allow me to define more specifically the inherent limitations of our numerical knowledge which are so often overlooked. I want to do this to avoid giving the impression that I generally reject the mathematical method in economics. I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation. We could scarcely have achieved that comprehensive picture of the mutual interdependencies of the different events in a market without this algebraic technique. It has led to the illusion, however, that we can use this technique for the determination and prediction of the numerical values of those magnitudes; and this has led to a vain search for quantitative or numerical constants. This happened in spite of the fact that the modern founders of mathematical economics had no such illusions. It is true that their systems of equations describing the pattern of a market equilibrium are so framed that if we were able to fill in all the blanks of the abstract formulae, i.e., if we knew all the parameters of these equations, we could calculate the prices and quantities of all commodities and services sold. But, as Vilfredo Pareto, one of the founders of this theory, clearly stated, its purpose cannot be “to arrive at a numerical calculation of prices,” because, as he said, it would be “absurd” to assume that we could ascertain all the data. Indeed, the chief point was already seen by those remarkable anticipators of modern economics, the Spanish schoolmen of the 16th century, who emphasized that what they called pretium mathematicum, the mathematical price, depended on so many particular circumstances that it could never be known to man but was known only to God. I sometimes wish that our mathematical economists would take this to heart. I must confess that I still doubt whether their search for measurable magnitudes has made significant contributions to our theoretical understanding of economic phenomena — as distinct from their value as a description of particular situations.”

Maths is a beautiful discipline. Mathematical economics shows its limitations. Very good maths can proceed from very poor assumptions. Some of the most genius econometricians I know develop the most mathematically awe-inspiring models and produce the biggest load of economic explanatory drivel.

I echo Hayek: has maths in economics really enhanced our fundamental theoretical understanding of human action? Has it really built on the basic analyses of classical economists or even the pre-classicals? Has it not just helped us gain some understanding of specific cases rather than general theory?

For all the proliferation of maths in economics we have mass unemployment, persistent and pernicious inflation, poor resource management, fragile banking systems…and fallacial Keynesian pump prime spending to fix the mess.

A beautiful and simple mathematical equation has value. All the great Austrian thinkers have drawn on such equations when required to convey key, fundamental ideas. But these equations rested on the “plausibility of their founding assumptions”, not the other way around. And it is plain to see that much of the raft of bad economic theory (and I’m talking here about bad theory that BOTH Austrians and the Mainstream would recognise as such) rests on perfectly sound mathematics. Keynes was able to ‘prove’ mathematically some of the world’s greatest economic fallacies. Because maths is merely the tool of the mathematician, or the economist in this case, it is necessarily servant to him. The economist is not servant to mathematics.

Hard science has the luxury (mostly), of forming hypotheses based on heuristics, rules of thumb, estimation, guestimation, speculation, hope, and fear, then testing these hypotheses in controlled environments with clearly measurable material and defined objectives, and therefore then disproving or confirming the hypothesis.

Science becomes “softer” the more complex and dynamic the system being tested. Climate science is a perfect example of a soft science. The micro elements of climate science sometimes approach a hard science, but only because we can test various hypotheses of weather patterns day in and day out using a myriad of reliable data sources. Each test is flawed, but the ability to do it over and over, day in day out, year in year out, allows us to infer some scientific conclusions about cause and effect. We then use these conclusions to predict short term weather patterns, and our repeated accuracy (not perfection) confirms that our theories must be true, or at least very accurate for our purposes. If our short term predictions become increasingly less accurate and eventually fail altogether, we must conclude that their theoretical basis was only partially, specifically or temporarily applicable, not generally applicable.

Micro climate theories that prove resilient to repeated testing at multiple weather stations Over a long period of time around the globe will become accepted scientific truth. Those that do not, will not.

But this begins to break down when we get into what causes the cause? In South Africa cold weather tends to be the result of cold fronts that come from the Atlantic Ocean. Those fronts originate in the Antarctic, but the Antarctic itself is fed by moisture and air patterns from other parts of the globe. If we were able to follow this trail for long enough we could probably end up concluding that cold fronts in South Africa are partly caused (ultimately) by…cold fronts in South Africa! We start to run into problems of complexity.

The macro system of global climate is one such ultra-complex system that cannot viably be scientifically tested. Why not? Because while we can infer fairly good results from micro climate science, macro climate science requires longer time periods of testing, often far longer than the span of a human life. This means we then need to dig into past data, but past data is a) imperfect and b) only partial to the system. If we measure variable X and see it has a good correlation to variable Y, we might try to infer causality using supposedly sophisticated statistical ‘techniques’. But we immediately have a major selection bias, because we are only measuring that data that we can acquire and use. So we become limited to what is obtainable in terms of historical data, and then even what we have we cannot be certain is good data.

And thus macro climate ’science’ is a very weak science. Its hypotheses cannot be suitably tested, and nor can these ‘tests’ be repeated. It draws on weak, but more importantly, partial data sources. The variables in the system are completely unpredictable, such as human emissions, solar activity, cosmic ray activity, cloud formation, ocean currents etc. So dynamic is the system that we become confined to modelling only micro parts of it, but how each ‘micro’ interacts with other ‘micros’ to form the ‘macro’ we still haven’t figured out.

It is also a weak science because the historical record is up for debate. Various temperature records for example show a Medieval Warm Period, while others do not. This is not easily settled by science, because if it was it would already be! When the historical record is up for debate, the very record relied upon to conduct the science, you do not have viable scientistic method.

The best we can hope to achieve in macro climate science is best understand micro climate and then use logical reasoning to fill in the gaps. Such logical reasoning will not necessarily lead us to ultimate truth, but it can help our debate. For example, we may dispute climate data records for Medieval (warm) and Renaissance (cool) Europe, but we do know from written and pictorial human historical records (which tend to be far more reliable) that there were vineyards in London, signifying a strong possibility of a much warmer period than now. We also know from human records that people enjoyed skating on the Thames in London in 15th and 16th Centuries, denoting a very cool period, much cooler than today. We can then debate a whole host of non-scientific evidence and build our views from them.

However because we will largely be relegated to the realm of opinion in such fields as macro climate, we err in thinking we should listen to those who claim it to be a measurable science and therefore can be controlled by public policy, or indeed any other means of centralised or coordinated control. A scientist can say as fact that gravity will make you fall from high buildings at an accelerating rate, and therefore recommend that railings be fitted to the perimeters of building rooftops. But a macro climate scientist cannot factually claim that people are warming the planet, and much less that it is somehow undesirable that mean temperatures are rising, how far they will rise, or even whether they are higher than they have ever been in the history of the planet.

They cannot do this because their field is not a hard science.

More accurately, these ’scientists’ can by all means use a supposed scientific method in their chosen field, but it does not mean we should regard them as scientists, their findings as science, or their recommendations as sound.

Economics is not only a weak science, but something altogether different from the hard sciences, which is why the Austrians recognised the folly of the scientistic method. They reasoned instead that the scientistic econometric empirical method was inherently flawed. It would produce theories that might appear valid, but were only partially, specifically or temporarily applicable. If one arrived at a general theory via the scientistic method it was by luck, not design. Instead these folk decided to build up economic theory from the most basic building blocks of human action and incentive until fundamental theories presented themselves as self-evident.

And indeed they did present themselves, and so was built Mises’ theories of money and credit, Hayek’s theories on the business cycle, and Rothbard’s genius insights best expounded in Man, Economy and State (most notably his insights on natural interest rates), theories which are falsifiable only with weak empirical data, which is not really theoretical falsification at all.

Mathematics in economics has flown the coop and has come to dominate, and dare we say, ruin an entire profession. It is why mainstream economic theory is weak at best and often downright wrong, why mainstream economists almost ALWAYS make the wrong predictions, and why policy makers are going down exactly the same failed paths to fix their previous mistakes…

…as Stickman might say, “all the while ignoring the implausibility of their founding assumptions”.

Fittingly, we leave you with Mises himself from chapter 16 of Human Action,

“If this antagonism between the logical and the mathematical economists were merely a disagreement concerning the most adequate procedure to be applied in the study of economics, it would be superfluous to pay attention to it. The better method would prove its preeminence by bringing about better results. It may also be that different varieties of procedure are necessary for the solution of different problems and that for some of them one method is more useful than the other.

However, this is not a dispute about heuristic questions, but a controversy concerning the foundations of economics. The mathematical method must be rejected not only on account of its barrenness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena.”

Freeman (and JGalt),

Thanks for the props, chaps.

As you know, I am in the middle of exams so I do not have time to comment extensively on this post right now. I certainly hope to come back to it in two weeks or so, because there is a

tremendousamount that I have to say on what you have written. [SPOILER ALERT: I don't wish to give to much away about the direction that I will take, but reading the latter half of this post I was forced to spit my corn flakes all over my screen... And I had my breakfast about five hours ago!]Joking aside (although, seriously…), allow me some comments on the first section in the meantime:

1)

In his very pragmatic way the Stickdude basically argues that yes, maths has its limitations, but that it is nonetheless an indispensible tool of the truly serious economist.Thank you for referring to me as pragmatic :)

For the record, I certainly do regard Hayek as a serious economist and political scientist. I have deep respect for the body of his work and have been influenced by much of what I have read of his (e.g the value of decentralised information held within prices). One the other hand, I respectively disagree with some of his other prognostications. Nevertheless, among the reasons that I respect Hayek is his willingness to acknowledgement that any theory – including those in economics –

mustopen itself up to empirical testing and the possibility of falsification… Something undoubtedly influenced by his close friendship with Karl Popper. As I have pointed out in other places, the following interview elucidates very well Hayek’s view on non-falsifiable theories: http://hayek.ufm.edu/index.php?title=Leo_Rosten_Part_I(In answering a question starting about his intellectual development from the surroundings of Fabian socialism (+/- 3.55min mark), Hayek says: “

Both the Marxists and Freudians had the dreadful habit of insisting that their theories were irrefutable; they [were] logically and absolutely cogent… And that led me to see that a theory that cannot be refuted is not scientific…”)Sound familiar? Well, somewhat more obviously, here is Hayek in a letter to T.W. Hutchison (1983):

“I had never accepted Mises’

a priorism</i? …. Certainly 1936 was the time when I first saw my distinctive approach in full clarity – but at the time I felt it that I was merely at last able to say clearly what I had always believed – and to explain gently to Mises why I could not accept hisa priorism” (Caldwell, 2009: http://tinyurl.com/2w6857y)2)

[T]he Fisher equation of money and money velocity. MV=PT [..] Mathematical economists have used this equation to derive erroneous theories about price inflation, when in factthe equation is an identitythat only tells you something that could logically be deduced anyway without the help of mathematics, simply using sound reasoning.I agree and have said as much elsewhere. For instance, here: http://tinyurl.com/2w5jgjx

3)

But he then shrugs this ‘minor’ issue off [...] Just tweak the dial a little then shall we?Ha ha. This, I would contend, is taking an arm from a thumb. I believe my positions on the dangers of a maths fixation are well established. The post you are referring to was written in response to the reactionary swing of the pendulum the other way. I certainly believe maths can help us in many instances where words and intuition do not suffice (or, are simply overly cumbersome). My basic premise – which I’m sure you do not disagree with – is that we need to focus on when to use maths as much as how to use it. To illustrate my point, I provided two examples, which are linked at the bottom of the post. I encourage you to have a look over these and see whether you agree or not.

4)

Maths is a beautiful discipline[...] Very good maths can proceed from very poor assumptions. Some of the most genius econometricians I know develop the most mathematically awe-inspiring models and produce the biggest load of economic explanatory drivel.Once more, I do not disagree. However, that is precisely why we

needto seek empirical validation of our theories, whether it be derived mathematically or verbally.* My stance is that theory and empirics should necessarily be reinforcing. If there is a disagreement between the two, we are essentially left with three options: 1) Our model is wrong**, 2) Our data is flawed, or 3) Our application of empirical testing is faulty (e.g. not accounting for simultaneity bias when regressing co-determined equations). Whichever the case, this leads to refinement of our models, or improvements in our data collection and testing methods. In other words, general progress.* In the words of David Hume: “If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning, concerning matter of fact and existence? No. Commit it then to flames: for it can contain nothing but sophistry and illusion.”

** Taking an example from my own specialisation (natural resources): That is why we reject the simplistic notions of Hotelling’s Rule in modelling oil prices – i.e. that they should rise proportionally to the rate of interest – even though it has a crisp elegance and logical flow to its formulation. Unfortunately, the real world data simply do not support this claim.

5)

Last point:

Keynes was able to ‘prove’ mathematically some of the world’s greatest economic fallacies.I’m not a Keynes scholar, but I believe this assertion is quite false.*** Indeed, I seem to recall that Keynes himself deliberately eschewed the use of mathematics in, for example,

The General Theory. According to Hyman Minsky (thanks wikipedia!) “Keynes’s limited use of mathematics was partly the result of his scepticism about whether phenomena as inherently uncertain as economic activity could ever be adequately captured by mathematical models.” Actually, just doing a bit of googling, here’s direct passage from TGT:“It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis.[...] Too large a proportion of recent ‘mathematical’ economics are merely concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.”

*** Though you are, of course, entitled to your opinions on the man’s contributions to economics :)

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Okay, I’ve spent much more time writing this comment than I should have… Back to work! Anyway, as always, I enjoy our debates and look forward to seeing you both in the flesh when I get home in December…

Cheers,

o-[-<