Some Brief Thoughts on Paul Romer and Mathiness

Catching up with work after grading. Posting will continue slow for a few weeks. Just a brief note on the brouhaha that the Romer (Paul) paper has led to. I mostly read it in Lars blog. Lars quotes Romer as saying:

"About math: I have an undergraduate degree in physics.* I’ve seen clear evidence that math can facilitate scientific progress toward the truth. If you think that math is worthless or dangerous, I’m sure that there are people who will be happy to discuss this with you. I’m not interested. I’m busy. 

About truth and science: My fundamental premise is that there is an objective notion of truth and that science can help us make progress toward truth. If you do not accept this premise, I’m sure that there are people who would be happy to debate it with you. I’m not interested. I’m busy."

I should say that I only looked cursorily at the paper, which seems poor at best. The notion that: "Joan Robinson (1956) was engaged in academic politics when she waged her campaign against capital and the aggregate production function," misses the quite important logical point of the capital debates, which were acknowledged by none other than Paul Samuelson in his 1966 "Summing Up" (subscription required).

It seems clear that the very concept of mathiness is murky at best.** Some mathematical concepts are fine, some aren't. The criteria seems to be Romer's personal preferences. Mind you, the quote above is one of the few things in that post that is clear and on the mark. Math is just an instrument. If Romer spent the time to read Sraffa's short monograph, he would have to conclude (mathematical logic requires it) that mainstream notions about relative prices associated to relative scarcity are not logically tenable. Progress would imply discarding illogical models. He is busy, though.

I should add that, in general, I'm in agreement with Lars critique of Romer. However, the problem to me seems to be less concerned with the use of mathematical models because "the real world is fuzzy, vague and indeterminate," which it clearly is, but with the logical inconsistencies of the neoclassical model per se. It is the kind of models that Romer uses (and the authors he criticizes too) that are problematic, not the fact that he formalizes his ideas in mathematical models. That's why it's a bit funny that he thinks that some RBC or New Classical authors are the problem, because presumably they fool you with math or, as one of the definitions of mathiness suggests, the words that these authors use to describe their mathematical results do not accurately convey what the math shows.

Sure enough, there are important elements in economic theory that cannot be easily formalized, and that does not mean that objective understanding is impossible. I haven't seen the formalization of the concept of mode of production, but that does not mean that the definition of capitalism is devoid of meaning. My two cents.

* This has been amended in the last version. Now reads: "I studied physics as an undergraduate." As it turns, some economists DO have physics envy. But you know what this means. He knows math people. He is an authority. Arguments of authority are so sciency, aren't they?

** At least two definitions are possible it seems. Logically incorrect mathematical arguments that are defended anyway (Romer would incur on this version of mathiness), or a discrepancy between the mathematical model and the underlying economic theory (the one Romer suggests some in the mainstream incur). They are not necessarily equivalent.