Axiomatics — the economics fetish

18 January, 2016 at 20:40 | Posted in Theory of Science & Methodology | 4 Comments

Mainstream — neoclassical — economics has become increasingly irrelevant to the understanding of the real world. The main reason for this irrelevance is the failure of economists to match their deductive-axiomatic methods with their subject.

The idea that a good scientific theory must be derived from a formal axiomatic system has little if any foundation in the methodology or history of science. Nevertheless, it has become almost an article of faith in modern economics. I am not aware, but would be interested to know, whether, and if so how widely, this misunderstanding has been propagated in other (purportedly) empirical disciplines. The requirement of the axiomatic method in economics betrays a kind of snobbishness and (I use this word advisedly, see below) pedantry, resulting, it seems, from a misunderstanding of good scientific practice …

This doesn’t mean that trying to achieve a reduction of a higher-level discipline to another, deeper discipline is not a worthy objective, but it certainly does mean that one cannot just dismiss, out of hand, a discipline simply because all of its propositions are not deducible from some set of fundamental propositions. Insisting on reduction as a prerequisite for scientific legitimacy is not a scientific attitude; it is merely a form of obscurantism …

theory of vlueThe fetish for axiomitization in economics can largely be traced to Gerard Debreu’s great work, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium … The subsequent work was then brilliantly summarized and extended in another great work, General Competitive Analysis by Arrow and Frank Hahn. Unfortunately, those two books, paragons of the axiomatic method, set a bad example for the future development of economic theory, which embarked on a needless and counterproductive quest for increasing logical rigor instead of empirical relevance …

I think that it is important to understand that there is simply no scientific justification for the highly formalistic manner in which much modern economics is now carried out. Of course, other far more authoritative critics than I, like Mark Blaug and Richard Lipsey have complained about the insistence of modern macroeconomics on microfounded, axiomatized models regardless of whether those models generate better predictions than competing models. Their complaints have regrettably been ignored for the most part. I simply want to point out that a recent, and in many ways admirable, introduction to modern macroeconomics failed to provide a coherent justification for insisting on axiomatized models. It really wasn’t the author’s fault; a coherent justification doesn’t exist.

David Glasner

 
It is — sad to say — a fact that within mainstream economics internal validity is everything and external validity nothing. Why anyone should be interested in that kind of theories and models — as long as mainstream economists do not come up with any export licenses for their theories and models to the real world in which we live — is beyond my imagination. Sure, the simplicity that axiomatics and analytical arguments bring to economics is attractive to many economists. But …

aSimplicity, however, has its perils. It is one thing to choose as one’s first object of theoretical study the type of arguments open to analysis in the simplest terms. But it is quite another to treat this type of argument as a paradigm and to demand that arguments in other fields should conform to its standards regardless, or build up from a study of the simplest forms of argument alone a set of categories intended for application to arguments of all sorts: one must at any rate begin by inquiring carefully how far the artificial simplicity of one’s chosen modal results in these logical categories also being artificially simple. The sorts of risks one runs otherwise are obvious enough. Distinctions which all happen to cut along the same line for the simplest arguments may need to be handled quite separately in the general case; if we forget this, and our new found logical categories yield paradoxical results when applied to more complex arguments, we may be tempted to put these rules down to defects in the arguments instead of in our categories; and we may end up by thinking that, for some regrettable reason hidden deep in the nature of things, only our original, peculiarly simple arguments are capable of attaining to the ideal of validity.

4 Comments »

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  1. It is not clear to me that the nearly exclusive reliance on a theoretical method of formal deductive reasoning from explicit axioms can be distinguished in practice from a stubborn refusal to allow facts to matter.

  2. Internal and external validity are usually thought of as a properties of a scientific study, or at least inferences from observations. An axiomatic system, with no necessary empirical content, does not even possess internal validity.

  3. At the blogpost linked to in the OP, David Glasner asserts:

    . . . there are very few scientific advances that can be ascribed to axiomatization. Axiomatization was vital in proving the existence of equilibrium, but substantive refutable propositions about real economies, e.g., the Heckscher-Ohlin Theorem, or the Factor-Price Equalization Theorem, or the law of comparative advantage, were not discovered or empirically tested by way of axiomatization.

    .
    Glasner talks about using math to solve problems and offers the anodyne, “the choice of tools to solve a problem should bear some reasonable relationship to the problem at hand” and the always popular (with economists) “A good economist will understand what tools are appropriate to the solution of a particular problem.” (if we could only find that good economist, he’ll know what to do . . . ) but is vague about what problem axiomatization might be thought to be useful in solving for economics. Which seems weird to me, because the traditional answer was that proving theorems from axioms was supposed to make the premises of the argument clear; economic arguments were being vetted for logical validity.
    .
    There’s one great and obvious example of discovery by axiomatization: Einstein’s Theories of Relativity — events, which triggered a revolution not just in physics, but in the theory and history of science. Thinking about the problem posed by experiments measuring the speed of light, Einstein came to realize that what high school students knew as Euclid’s fifth postulate — the parallel postulate — could not hold, and he would need a non-Euclidean geometry to describe a space-time continuum consistent with the observed “absolute” speed of light. Despite the challenge to the intuition of centuries, physics chose to let the fact motivate the revision of a fundamental theory about the nature of the universe.
    .
    I think the problem in economics is that economists never consider changing the theory in response to facts. They don’t consider changing the theory even when the analysis, itself, reveals deficiencies. The proliferation of models is about “proving” that the theory never needs to change, because all the facts can be accommodated by bolting on some friction or shock. But, they would never discard conceptions like the production function (output is a function of inputs) or the flow of investable funds, because nothing is ever wrong — it is just a matter of finding the right application. The notion that there is a singular reality, an actual economy the nature of which is the ultimate object of interest — that seems remote from consideration.
    .
    I don’t think it a bad thing that economists should do logical analysis. I think it a very bad thing that they do not seem to care to know anything about the actual economy or to revise their conceptions in light of such knowledge.

  4. Physics contains additional examples beyond Einstein and Euclidean geometry of how not being attached to particular axioms enables advances in understanding, although we do need to remember that the Riemannian geometry that he adopted was just as rigorous as Euclid’s, if not more so. 90% of today’s physics is covered by the “standard model” of quantum field theory (though that remaining 10% is scary challenging), and in its own territory it’s the most accurate theory ever seen. But concerted programs to axiomatize QFT from time to time have repeatedly run into insurmountable problems and been abandoned. Yet nobody is abandoning QFT because it can’t be axiomatized. Physics preferences workability over rigorous self-consistency.

    My training began in linguistics, where there is a long tradition of distinguishing between “descriptive adequacy” and “explanatory adequacy” of theories. Descriptive adequacy is always given precedence in preferability in most sciences; for them the slogan is that “many a beautiful theory has been slain by an ugly fact”. Only in economics do we hear people complain that facts don’t matter. Explanatory adequacy without a prerequisite of descriptive adequacy cannot be distinguished from just-so stories.


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