Maths, Economics, and pseudo-science

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.”