## How could ‘testing axioms’ be controversial?

21 February, 2016 at 14:21 | Posted in Economics | 1 CommentOf 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 surrendering 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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Comment on ‘How could “testing axioms” be controversial?’

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Barclay Rosner writes “Curiously, they [Lucas and Sargent] did not seem to care whether the assumption was actually true, because it was ‘an axiom,’ something that is assumed and cannot be tested …” (See intro)

The first methodological idiotism consisted in Lucas’/Sargent’s idea of what an axiom is; the second idiotism consisted in the rest of the profession swallowing the first idiotism hook line and sinker.

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Every half-witted economist can know from the founding fathers that an axiom is defined by its ROLE in a consistent set of propositions, a.k.a. theory: “What are the propositions which may reasonably be received without proof? That there must be some such propositions all are agreed, since there cannot be an infinite series of proof, a chain suspended from nothing. But to determine what these propositions are, is the opus magnum of the more recondite mental philosophy.” (Mill, 2006, p. 746)

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To receive a proposition for the time being without proof never meant that any green cheese assumption is acceptable as axiom.

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As a rule, the proof of axioms is in the deductively derived conclusions. If what the theory says should be the case is actually the case, then the axioms are indirectly corroborated. If not, they are refuted qua modus tollens. “Whether an axiom is or is not valid can be ascertained either through direct experimentation or by verification through the result of observations, or, if such a thing is impossible, the correctness of the axiom can be judged through the indirect method of verifying the laws which proceed from the axiom by observation or experimentation. (If the axiom is deemed to be incorrect it must be modified or instead a correct axiom must be found.) (Morishima, 1984, p. 53)

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All this is well-known since Newton: “Could all the phaenomena of nature be deduced from only thre [sic] or four general suppositions there might be great reason to allow those suppositions to be true.” (quoted in Westfall, 2008, p. 642)

Not only physicists but mathematicians, too, have tested their axioms: “One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean.” (Brown, 2011, p. 565)

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No mathematician will ever accept the rational expectations assumption as premise of economic theory as Lucas/Sargent could have known from history: “Walras approached Poincaré for his approval. … But Poincaré was devoutly committed to applied mathematics and did not fail to notice that utility is a nonmeasurable magnitude. … He also wondered about the premises of Walras’s mathematics: It might be reasonable, as a first approximation, to regard men as completely self-interested, but the assumption of perfect foreknowledge ‘perhaps requires a certain reserve’.” (Porter, 1994, p. 154)

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What Walras and his neoclassical followers simply never understood was that the expression ‘… perhaps requires a certain reserve’ is a code among mathematicians which translates into ‘do not bother me with your brain-dead garbage’.

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So here is how to deal with economics from Walras to DSGE: “As with any Lakatosian research program, the neo-Walrasian program is characterized by its hard core, heuristics, and protective belts. Without asserting that the following characterization is definitive, I have argued that the program is organized around the following propositions: HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.By definition, the hard-core propositions are taken to be true and irrefutable by those who adhere to the program. ‘Taken to be true’ means that the hard-core functions like axioms for a geometry, maintained for the duration of study of that geometry.” (Weintraub, 1985, p. 147)

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To begin with, no one with an iota of scientific instinct will ever accept HC1 to HC6 as axioms. All the more so, as after the “duration of study”, that is, after more than 140 years of pointless model bricolage, even the dullest economists has now realized that this approach has failed in all methodological dimensions. The duration of acceptance of HC1 to HC6 is a simple metric for scientific incompetence.

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Walrasian axioms have never been acceptable and will never be. They have to be fully replaced.

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Egmont Kakarot-Handtke

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References

Brown, K. (2011). Reflections on Relativity. Raleigh, NC: Lulu.com.

Mill, J. S. (2006). Principles of Political Economy With Some of Their Applications

to Social Philosophy, volume 3, Books III-V of Collected Works of John Stuart

Mill. Indianapolis, IN: Liberty Fund. URL http://www.econlib.org/library/Mill/

mlP.html. (1866).

Morishima, M. (1984). The Good and Bad Use of Mathematics. In P. Wiles, and

G. Routh (Eds.), Economics in Disarry, pages 51–73. Oxford: Blackwell.

Porter, T. M. (1994). Rigor and Practicality: Rival Ideals of Quantification in

Nineteenth-Century Economics. In P. Mirowski (Ed.), Natural Images in Economic

Thought, pages 128–170. Cambridge: Cambridge University Press.

Weintraub, E. R. (1985). Joan Robinson’s Critique of Equilibrium: An Appraisal.

American Economic Review, Papers and Proceedings, 75(2): 146–149. URL

http://www.jstor.org/stable/1805586.

Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge:

Cambridge University Press, 17th edition.

Comment by Egmont Kakarot-Handtke— 21 February, 2016 #