How could ‘testing axioms’ be controversial?

by
Lars Pålsson Syll
My articles My siteAbout meMy booksMy videos
Follow on:Twitter

How could ‘testing axioms’ be controversial?

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.

J. Barkley Rosser Jr

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?