Modern macroeconomics — obscurantist axiomatics

16 July, 2014 at 15:52 | Posted in Economics | 3 Comments

In discussing modern macroeconomics, I’ve often mentioned my discomfort with a narrow view of microfoundations, but I haven’t commented very much on another disturbing feature of modern macro: the requirement that theoretical models be spelled out fully in axiomatic form. The rhetoric of axiomatization has had sweeping success in economics, making axiomatization a pre-requisite for almost any theoretical paper to be taken seriously, and even considered for publication in a reputable economics journal.

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.

Before discussing the situation in economics, I would note that axiomatization did not become a major issue for mathematicians until late in the nineteenth century (though demands – luckily ignored for the most part — for logical precision followed immediately upon the invention of the calculus by Newton and Leibniz) and led ultimately to the publication of the great work of Russell and Whitehead, Principia Mathematica whose goal was to show that all of mathematics could be derived from the axioms of pure logic. This is yet another example of an unsuccessful reductionist attempt, though it seemed for a while that the Principia paved the way for the desired reduction. But 20 years after the Principia was published, Kurt Godel proved his famous incompleteness theorem, showing that, as a matter of pure logic, not even all the valid propositions of arithmetic, much less all of mathematics, could be derived from any system of axioms. 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, in which Debreu, building on his own work and that of Kenneth Arrow, presented a formal description of a decentralized competitive economy with both households and business firms, and proved that, under the standard assumptions of neoclassical theory (notably diminishing marginal rates of substitution in consumption and production and perfect competition) such an economy would have at least one, and possibly more than one, equilibrium.

A lot of effort subsequently went into gaining a better understanding of the necessary and sufficient conditions under which an equilibrium exists, and when that equilibrium would be unique and Pareto optimal. 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

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3 Comments

  1. Nice work. I am also of the same opinion that modern macro economics should not be reduced to logical representations but should be able to predict realities

  2. As a mathematician, I take the opposite view to Glasner. If Debreu had not attempted his axiomatization he may have given a more convincing account. As it is, he clearly states that his axiomatization is too strong to apply to real economies, and it seems to me that the insistence on explicit axioms / assumptions coupled to peer review makes such admissions difficult to avoid.

    Debreu’s uncertainty axiom is very informative. He explicitly assumes that all acts of nature are exogenous, and thus assumes away endogenous explanations for surprises, such as those of 2007-8. Clearly, therefore, no amount of reasoning based on Debreu’s theory of value can rule out the possibility of crashes, of even comment on their likelihood.

    The problem in the 2000’s, it seems to me, was not that the mainstream theories relied on axiomatization, but that the axioms were treated as dogma.

  3. THEORY OF VALUE- An Axiomatic Analysis of Economic Equilibrium.
    by. GERARD DEBREU. New Haven and London, Yale University Press 1959
    http://cowles.econ.yale.edu/P/cm/m17/m17-all.pdf


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