Caldwell, Hayek, and Math

Surely, the same thing that is used by journals now: Judgment.

Having served as a referee for many journals and as part of some editorial groups, I can assure you that all math does is ratchet up the minimum standards for acceptable publication. It does not eliminate the need for choice (not all sound models are published).

The problem is that good papers without the necessary modelling are not published. And useless models are tacked onto good papers just to get published. It is the latter cynicism that is wrong.

Further, as physicists understand, but many economists do not, rigor is not the same as mathematical formalism. Most formalism in econ is derived from math dept values not science. It has little substantive justification at any level.

Steve Keen puts it nicely in Debunking Economics...

"Many critics of economics have laid the blame for its manifest failures at the feet of mathematics. Mathematics, they claim, has led to an excessive formalism in economics, which has obscured the inherently social nature of the subject.

While it is undeniable that an inordinate love of mathematical formalism has contributed to some of the intellectual excesses in economics, generally this reaction is as erroneous as blaming the piano for the discordant notes of a bad piano player. If anything should be shot, it is the pianist, not the piano. Though mathematics has definite limitations, properly used, it is a logical tool that should illuminate, rather than obscure. Economists have obscured reality using mathematics because they have practised mathematics badly, and because they have not realised the limits of mathematics..."

What form would economics take if the current "formal" approach is cast aside? Tough to say, but hopefully it would take a form that stresses emperical validity and applicability.

The problem is that in order to validate something empirically we at least need some sort of minimal mathematical model. Even in order to get a regression to be useful we need to make a myriad of mathematical assumptions about disturbance terms. Waving hands is an unacceptable substitute.

Fixed point theorems do seem pretty uninteresting, I'll grant you that. But verbal philosophy with five-syllable German words isn't any more illuminating. My personal preference is for English spiced with math where it actually helps make a point.

Chris misses the point that the number of "fixed point" style papers has exploded in the journals, while good mathematics at the level of the JPE in 1964 are unpublishable in many top journals. English spiced with math is more and more considered the barest minimum at a weak journal.

The point is not to go to German philosophy. The point is that the increase in mathematical sophistication from 1964 to 2004 has not been accompanied by a requisite improvement in a) logic b) applicability c) empirical sophistication or d) useful predictions.

The fact is that neither of Coase's seminal articles would be accepted to the American Econ Review today. And as Tyler points out, Friedman and Schwarz might not even make it as a Chicago PhD thesis today.

I say that except for the J of Math Econ or Econometrica, no major journal should have math more formal than that typical of the AER and JPE of 1964.

Resort to parallelism, or the fancy verbal drawing of pictures; wait, is that not what We do now, simply inputting numbers every time We cannot think of a correct word. lgl

The purpose of mathematical formalism is to cause the writer to not only be logically tight, but also specific enough to avoid arguments over semantics. While this may seem unnecessarily abstract, it is crucial to the advancement of science (incl economics). Steering economics to some sort of non-quantitative basis will only lead to unanswerable questions and unfalsifiable conclusions. I think physics would be the best model for how to apply math to a subject. The fact that a physicist works with real objects allows him to cut away a lot of the more cumbersome parts of mathematical formalism, but in such a way that the predications still have the sharpness of mathematics.

I absolutely agree that physics is a good model for this. But given the lack of clear tests, math economists have taken to using pure math as the standard, hence the excessive formalism.

I can assure you, most physicists I know are astonished when they see the degree of formalism in many economics journals.

There should also be a place for verbal speculation that can only be partially mathematized. Given our lack of power laws and true dynamic equations of motion it is imperative that room be given for good ideas that might be properly formalized after people have had time to digest and discuss the ideas.

The argument Hayek made to differentiate physics with economics is the latter deals with complex phenomena. In an economy, there's too many feedback loops, chaotic attractors, and other elements to make accuarate predictions possible. The best we can hope for is to explain the economic process taking place and describe the direction it's headed.