Paul Romer has recently attracted attention by his criticism of what he terms ‘mathiness’ in economic growth theory. As a mathematician, I would have thought that economics could benefit from more mathiness, not less. But what he seems to be denigrating is not mathematics as I understand it, but what Keynes called ‘pseudomathematics’. In his main example the problem is not inappropriate mathematics as such, but a succession of symbols masquerading as mathematics, which Paul unmasks using – mathematics. Thus, it seems to me the paper that he is criticising would have benefited from more (genuine) mathiness and less pseudomathiness.
I do agree with Paul, in effect, that bad (pseudo) mathematics has been crowding out the good, and that this should be resisted and reversed. But, as a mathematician, I guess I would think that.
I also agree with Paul that:
We will make faster scientific progress if we can continue to rely on the clarity and precision that math brings to our shared vocabulary, and if, in our analysis of data and observations, we keep using and refining the powerful abstractions that mathematical theory highlights … .
But more broadly some of Paul’s remarks suggest to me that we should be much clearer about the general theoretical stance and the role of mathematics within it. Even if an economics paper makes proper use of some proper mathematics, this only ever goes so far in supporting economic conclusions, and I have the impression that Paul is expecting too much, such that any attempt to fill his requirement with mathematics would necessarily be pseudo-mathematics. It seems to me that economics can never be a science like the hard sciences, and as such it needs to develop an appropriate logical framework. This would be genuinely mathsy but not entirely mathematical. I have similar views about other disciplines, but the need is perhaps greatest for economics.
Bloomberg (and others) agree that (pseudo)-mathiness is rife in macro-economics and that (perhaps in consequence) there has been a shift away from theory to (naïve) empiricism.
Tim Harford, in the ft, discusses the related misuse of statistics.
… the antidote to mathiness isn’t to stop using mathematics. It is to use better maths. … Statistical claims should be robust, match everyday language as much as possible, and be transparent about methods.
… Mathematics offers precision that English cannot. But it also offers a cloak for the muddle-headed and the unscrupulous. There is a profound difference between good maths and bad maths, between careful statistics and junk statistics. Alas, on the surface, the good and the bad can look very much the same.
Thus, contrary to what is happening, we might look for a reform and reinvigoration of theory, particularly macroeconomic.
Romer adds an analogy between his mathiness, which has actual formulae and a description on the one hand, and computer code, which typically has both the actual code and some comments. Romer’s mathiness is like when the code is obscure and the comments are wrong, as when the code does a bubble sort but the comment says it does a prime number sieve. He gives the impression that in economics this may often be deliberate. But a similar phenomenon is when the coder made the comment in good faith, so that the code appears to do what it says in the comment, but that there is some subtle, technical, flaw. A form of pseudo-mathiness is when one is heedless to such a possibility. The cure is more genuine mathiness. Even in computer code, it is possible to write code that is more or less obscure, and the less obscure code is typically more reliable. Similarly in economics, it would be better for economists to use mathematics that is within their competence, and to strive to make it clear. Maybe the word Romer is looking for is obscurantism?