One of the interesting things that’s come out of Krugman’s critique of macroeconomics is that it’s led to a lot of economists (and others) discussing how science should work and what science is. I found Robert Waldmann’s take on the role of mathematics in science and economics:
I’d say that economists have not accomplished much using the mathematical scientific approach, because economists almost never use an approach which is both mathematical and scientific.
The defining characteristic of science is that it is empirical and that hypotheses which are rejected by the data are abandoned (OK so the defining characteristic is that there are theories which bow to facts, just collecting facts is something else).
This is absolutely not true of mathematical economic theory. Rejected hypotheses are still maintained when we look at other subjects. Policy advice is guided by the assumption that rejected hypotheses are approximately true. The fact that a rejected hypothesis may still be a useful approximation is regularly interpreted as implying that famous hypotheses introduced by famous economists must be a useful approximation to the truth. Given that method of reasoning about the world, evidence is irrelevant….
In contrast there are economists who have committed science…. However, they all use quite little mathematics (in their science anyway). They do use theory — that is they attempt to determine causation from correlation by making identifying assumptions (that is assuming something is exogenous and is an uncaused cause). However the theory is theory which is immediately comprehensible to the man on the street and immediately convincing….
There is mathematical economics and there is scientific economics. The overlap is minimal.
When I first read this, I thought it sounded quite similar to my argument that “those stupid fucking natural history facts” are important to understanding economic phenomena. I chalked it up to mere coincidence, but, in putting this post together, I read through the comments, and found this by Waldmann (italics mine):
I am a failed biologist. I was a graduate student at MIT (then I dropped out). I know how much math some of the people who discovered oncogenes know — not much. I know how much math Salvatore Luria knew. It wasn’t much and he was not in the slightest embarrassed to say so. Now economists must recognise that biologists have achieved great things. However, I don’t think that economists who are not failed biologists have any clear sense of how it was done (I mean how much work was involved and how little math). When economists think of natural science, they think of physics. The hope is that if we do what physicists did maybe we’ll accomplish a tenth as much. It hasn’t worked out so far.
There are some economists who act like biologists. They work a lot. There [sic] expertise is knowledge of facts (often boring facts like what questions were asked in this survey and what was the response rate and stuff). I think they are making progress (note I have switched from “we” to “they,” I’m playing with math).
Now one might hope that the answer to a very narrow question (say what is the structure of DNA) will have all sorts of fascinating implications worthy of being called a central dogma. I sure wouldn’t bet on it. Other questions in biology have complicated answers that don’t lead to simple generalizations. That’s life (it’s complicated). I guess that’s what economists can hope for, and it’s a lot better that playing with math and calling it social science.
Too bad he didn’t remain a biologist. I think he nails it when he gets at the simple generalizations issue: theory can help us understand complex situations, but it’s usually not sufficient by itself. The details matter.