Why testing axioms is necessary in economics
from Lars Syll
Of course the more immediate target of Davidson in his formulation of the argument in the early 1980s was not Samuelson, but Lucas and Sargent and their rational expectations hypothesis … This was indeed the period when new classical economics was riding at its highest point of prestige, with Lucas and Sargent and their rational expectations assumption apparently sweeping the boards of any sort of Keynesian theories. Curiously, they did not seem to care whether the assumption was actually true, because it was “an axiom,” something that is assumed and cannot be tested …
This matter of “testing axioms” is controversial. Davidson is right that Keynes was partly inspired by Einstein’s Theory of General Relativity that was based on a relaxation of the parallel axiom of Euclid. So, Davidson argued not unreasonably that he would also be inclined to wish to relax any ergodic axiom. However, of course, the rejection of the parallel postulate (or axiom) did come from empirical tests showing that it does not hold in space-time in general due to gravity curving it. So, the empirical testing of axioms is relevant, and the failure of the rational expectations axiom to hold empirically is certainly reasonable grounds for rejecting it.
On this Einstein and Keynes are of course absolutely right. Economics — in contradistinction to logic and mathematics — is an empirical science, and empirical testing of ‘axioms’ ought to be self-evidently relevant for such a discipline. For although the economist himself (implicitly) claims that his axiom is universally accepted as true and in now need of proof, that is in no way a justified reason for the rest of us to simpliciter accept the claim.
When applying deductivist thinking to economics, neoclassical economists usually set up “as if” models based on a set of tight axiomatic assumptions from which consistent and precise inferences are made. The beauty of this procedure is of course that if the axiomatic premises are true, the conclusions necessarily follow. The snag is that if the models are to be relevant, we also have to argue that their precision and rigour still holds when they are applied to real-world situations. They often don’t. When addressing real economies, the idealizations and abstractions necessary for the deductivist machinery to work simply don’t hold.
The logic of idealization is a marvellous tool in mathematics and axiomatic-deductivist systems, but a poor guide for real-world systems. As Hans Albert has it on the neoclassical style of thought:
Science progresses through the gradual elimination of errors from a large offering of rivalling ideas, the truth of which no one can know from the outset. The question of which of the many theoretical schemes will finally prove to be especially productive and will be maintained after empirical investigation cannot be decided a priori. Yet to be useful at all, it is necessary that they are initially formulated so as to be subject to the risk of being revealed as errors. Thus one cannot attempt to preserve them from failure at every price. A theory is scientifically relevant first of all because of its possible explanatory power, its performance, which is coupled with its informational content …
Clearly, it is possible to interpret the ‘presuppositions’ of a theoretical system … not as hypotheses, but simply as limitations to the area of application of the system in question. Since a relationship to reality is usually ensured by the language used in economic statements, in this case the impression is generated that a content-laden statement about reality is being made, although the system is fully immunized and thus without content. In my view that is often a source of self-deception in pure economic thought …
Most mainstream economic models are abstract, unrealistic and presenting mostly non-testable hypotheses. How then are they supposed to tell us anything about the world we live in?
Confronted with the massive empirical failures of their models and theories, mainstream economists often retreat into looking upon their models and theories as some kind of “conceptual exploration,” and give up any hopes/pretenses whatsoever of relating their theories and models to the real world. Instead of trying to bridge the gap between models and the world, one decides to look the other way.
To me this kind of scientific defeatism is equivalent to giving up on our search for understanding the world we live in. It can’t be enough to prove or deduce things in a model world. If theories and models do not directly or indirectly tell us anything of the world we live in – then why should we waste any of our precious time on them?
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How many times can one actually see the stark naked emperor … and still believe the dogma of his clothing? Perpetually, apparently, because disbelieving carries the penalty of ‘hell’… as we are taught. It could make one weep. When will ‘we’ be able to actually ‘see’ a viable alternative…. Bitcoin? or only when havoc reigns?
It can be argued that the neoclassical paradigm in economic theory is as valid (or as «scientific») as the Euclidian paradigm is in geometry. They both depart from a set of axioms and as a result, some conclusions are derived as true and applicable to the «real world» out there. The fundamental difference, of course, is that Euclidian geometry deals with entities that are defined as static or permanent in time, whereas neoclassical economics is supposed to deal with phenomena that evolve along the axis of time. In that sense, some of the criticisms that are levelled at the neoclassical school reminds one of that old English language saying, «barking up the wrong tree».
Argh, such a scramble of terms misused, ambiguously used, inconsistently used, one doesn’t know where to start with something like this. Start afresh, perhaps.
An axiom is a thing of mathematics and logic. It is a founding assertion. One then uses deduction to deduce its implications. This builds an abstract logical structure. It may be interesting mathematically, connecting with other parts of mathematics’ very elaborate, abstract logical structures. All of this is independent of the observable world.
On the other hand if one wants to gain some insight into how the observable world works, one might make a founding *assumption* or *hypothesis* which one hopes captures some significant part of the observable world’s behaviour. One can then deduce the implications of the assumption, often with the help of pre-worked mathematical structures. This exercise becomes science when the logical structure is compared with observations. Any part of the structure – assumption, deduction – may be compared. If there is a useful resemblance, then the exercise might be declared to be useful, because it gives useful insight into how the observable world might actually work.
Notice I didn’t say anything about “truth”, “right”, “wrong”, “real”, “reality”. The criterion is “useful”, and that depends on context. You can say Einstein’s theory is more useful, because it applies to a wider range of conditions than Newton’s, but Newton’s theory is still very useful in many contexts.
Nor should economists be using the term “axiom”, it’s a product of the fundamental confusion they’ve had since the 19th century, when they never actually grasped the difference between mathematics and science.
No,fonseca, the difference is not the involvement of time. Euclidean geometry can be viewed as a mathematical structure. It can also be found to give a useful description of a lot of observations, in which context it is being treated as a scientific theory. Euclid becomes inaccurate at cosmological scales, and a more general geometry is found to be required to give a useful description of observations. All the same considerations apply to a time-dependent system.
Dear Geoff Davies, your comment is very interesting and quite to the point. However, it is not me who uses «axioms» (the term itself) when discussing matters that pertain to the Economy. It is the vast majority of mainstream economists. In fact there is a huge body of literature on the subject of «axioms in neoclassical economics»… On the other hand, if I remember correctly, at least one of the authors of reference in «economics methodology» is quite adamant about this (the use of «axioms»). Perhaps those economists should rather use the term «premises». Just to be clear, where I wrote «neoclassical economics is supposed to deal with phenomena that evolve along the axis of time», I should have written «the science of economy is supposed to…). According to my physicist friends there are no straight lines in the Universe, it’s all curves… Therefore Euclid becomes inaccurate (but still operative) at the planetary level. My point was (and is) that the methodology of study of the Economy is more akin to the methodology of study of Biology and/or Ecology, than to the methodology of study of celestial mechanics. But then, again, my physicist friends draw my attention to the fact that the Earth also evolves and so do the galaxies… Some go as far as contend that elementary particles «make decisions», in choosing the path of least resistance…
I totally agree that “study of the Economy is more akin to the methodology of study of Biology and/or Ecology, than to the methodology of study of celestial mechanics”. But that is because living systems are complex self-organising systems (“complex” in the technical sense) with many emergent levels of behaviour that make them unpredictable in detail. Celestial mechanics is predictable.
My terse comment seems to have been misunderstood. I merely meant that the key difference between what I call mathematics and what I call science is not whether the system evolves. The motion of a pendulum evolves, but it can still be described with some accuracy using a few founding assumptions. Similarly planetary orbits.
Again: the key difference between mathematics and science is that the former builds abstract logical structures whereas the latter is intended to be compared with observations to see if it gives a usefully accurate description.
For example, neoclassical economic theory is founded on patently unrealistic assumptions so it is an exercise in abstract mathematics, not a useful guide to observable economies. The behaviour it “predicts” (near-equilibrium oscillation) is wildly different from the far-from-equlibrium behaviour of real economies; for example an endogenous market crash is not possible in the neoclassical abstraction.
Let me react briefly to Nancy first. When will ‘we’ be able to ‘see’ a viable alternative? As it happens, ‘I’ can, because I have experienced the classical phenomena of thinking my railway train has started moving when actually the one that moved was going the opposite way on the adjacent line. So we see the banks give us money, but unless we are using a credit card we don’t see ourselves becoming indebted if we spend it. So what is money? It has long been known by a few and is now becoming obvious to many that – as created, whether as coins, paper money, cheques or bank credit transfers – all it is is an ‘IOU’ which is cancelled by ‘our’ earning it so it can be paid back. So the viable alternative is to be honest about money: to interpret it [and hence its possession] as having negative rather than positive value, so from those who have too much, much can be [if mercifully] demanded in the way of their earning it. One way of doing that was Keynesian progressive taxation, but it would be much simpler if financing business by credit card kept financiers and businessmen honest in the first place.
As between Fonsecca-Statter and Geoff, I agree with FC but sympathise with Geoff wanting to “start afresh, perhaps”. Actually, the same methodological issue arises in physics as we have just seen in my response to Nancy. We think of time moving forward, but cosmological observations in particular, though now, are very much of events in the past. Changes do occur in the cosmos, but these are only of academic interest to us, because in reality they are very much history. Economics as developed for the benefit of governments and other businesses (let me repeat that: “governments and other businesses”) would like to be able to predict what will happen in the future so they can avoid its problems and take advantage of its opportunities, but you can’t do that with static set theory and its corresponding quantitative logic, nor even with time-ordered generic logic and spatial metrics. All you can do is find ways to see the ‘type’ of events that are possible, and ways of observing them before they happen. Economic science should thus be reasonably like itself to weather forecasting, though I agree with F-C, we humans are not just physical particles and are animals as well as communicating humans, so that issues like epidemiology and the physiological causes of its illnesses should be very much centres of its interest.
Geoff, see the exchange between Yoshinori and myself on there being different types of logic, on July 19th at https://rwer.wordpress.com/2017/06/28/economics-10whatever/#comments.
Traditional quantitative logic is usually taken (if tacitly) as axiomatic, so that observations of time have to treated as a linear mathematical variable. However, if energetic motion is taken as axiomatic, time is built into the logic of evolution and, on timescales relevant to humanity, observations of it are cyclic, measured by e.g. solar days and years, sinusoidal radio waves. Is it really absurd to suggest that an economics which does not take account of cyclic variations in our food supplies and work patterns, enforcing constant “growth” via a monetary analogue instead of making the best of seasonal variety, really isn’t fit for purpose?
Thanks, Dave!! I (and most everyone I know) need ALL the clarification we can find. If you could suggest another website, source, etc. or two (I know this one is way over my head… but curiosity never dies :) , that offers more clarification, with ‘pictures’ and very ordinary language, I (and quite a few others) would be forever grateful. : )
Nancy, try googling for “elementary electric circuit theory”. I learned this at 16 in the first year of my apprenticeship. Its relevance to economics is that it gets you understanding how to think in terms of flows (and hence where the flows go) instead of exchanges between buyers and sellers (in which more abstractly there is a balance or equilibrium between supply and demand).
Imagine a river, then what happens if this flows round an island, falls down a waterfall or wells up through a crevice. Then not just the river powering a water-wheel but it conveying boats carrying people, goods and news… The theory I’ve developed from this boils down to different interpretations of a few simple pictures, but it seems to be unintelligible to people who can’t imagine flows and the rules governing their behaviour.