Bryan Caplan (here and here) and I (here) have both posted in Econlog on economics in math. You can read our posts and find links to much of the other discussion.
Now Robert Murphy has laid out some of his thoughts and they're, well, thoughtful. Murphy is one of the leading young Austrian economists and, for that reason, one would expect him to be particularly critical of math in economics--and he's not. His post is a judicious mixture of defenses of math in economics and criticisms of mathematicians in economics. Whatever his goal, his post has made me less critical of what Bryan calls economath while I'm still just as critical of mathematical economists who don't understand basic economics.
I could quote some highlights from his piece, but I fear that I would quote the whole piece.
Now my first reaction to the above is, "Huh? That sounds like it's standing Tiebout on his feet. It shows that workers can indeed escape the clutches of the taxman, whereas landowners can't, since-duh-you can't move land out of the jurisdiction of the taxing authority. By the same token, if workers were only allowed to sell their labor in their current jurisdiction, then they wouldn't have much scope to vote with their feet. Yet that insight hardly refutes Tiebout."
Now maybe Bryan is actually saying something more profound than what I think he's saying; the way to be sure would be to read his paper. The virtue of a formal model is that it would be crystal clear how he was achieving his result. However, we once again come back to the problem that the interpretation of the result is not something the model itself can give you: whether this is standing Tiebout on his head, or whether it's an obvious extension of Tiebout, is something that we have to discuss in words, not symbols. (It's also possible that the title is just to be provocative, and really Bryan's claim is an empirical one on whether the immobile land effect outweighs the mobile workers effect. Again, I would have to sit down and read the paper to be sure, but even here, the crucial step would be in interpreting what his model "means" in the grand scheme of things.)
On Austrians' critiques of unrealistic models:
Austrians need to be a little careful when they make sweeping condemnations of the "unrealistic models" of their opponents. After all, when "our side" teaches comparative advantage, we use the completely unrealistic 2-good 2-country model. [DRH note: As does everyone else who teaches comparative advantage.] When we explain Menger's theory of the origin of money, we tell simplistic stories that have no basis in history. When we explain Bohm-Bawerk's views on capital accumulation, we often start with ludicrous Robinson Crusoe tales. And even Mises himself pounds home the fact that his "evenly rotating economy" is not only false, but internally inconsistent.
Last point: Until I saw it with my own eyes, I would not have believed how much the people in top-ranked economics programs are great at math, but bad at basic economics of the kind that I learned by reading op eds from Walter Williams and Thomas Sowell growing up. For example, one of our professors went through the Solow growth model and then concluded that it was a great mystery why the return to investment had been so low in the former Soviet Union, since after all their engineers trained at Western universities so they had the same production functions. (!) Our game theory professor relayed an anecdote in which all but one person (Aumann) at a game theory conference said he or she would offer "0″ in the Ultimatum game, since this was the unique subgame perfect Nash equilibrium. (And just remember, these were the guys helping to design strategy during the Cold War.) I And my all-time favorite: I didn't witness it personally, but apparently at a meeting when the United Auto Workers were trying to unionize our grad students, a guy who was really good at math in our program piped up and told the provost that NYU owned some apartment buildings, and so it could offer to give them at zero price to the grad students since it wouldn't cost NYU anything. To repeat, this was a guy who would go on to get a PhD in economics from what was, at the time, probably ranked about 15th in the world.
In my opinion, this is one of Bob's best blog posts in the last few months. I was in a discussion with some people (including some other bloggers) the other day about other economics bloggers. I pointed out that one of the main things I appreciate about Murphy is how fair he is. He will criticize, say, Paul Krugman, for something, but then, if someone can point out how Krugman is right and Murphy is wrong, he will admit it. When I have criticized various economists, Murphy will write me when he thinks I am wrong or have misstated--and he's usually right.
Here's how Daniel Kuehn, himself a blogger and also a frequent commenter on this site, put it:
That having been said, I will still push the hopeless line that Keynesians ought to follow Bob's blog. Unfortunately, a lot of Austrian bloggers don't offer much interesting. It's complaining about vaguish methodological concerns. Bob, meanwhile, doesn't raise some kind of purist methodological objections - he jumps into mainstream modeling and keeps up with the best of them (Nick Rowe, for example). Bob also doesn't really have any sacred cows. He's happy to knock Mises and Hayek on substantial points and not only agree with Sraffa but claim that Sraffa didn't go far enough. And he's a clear writer. He's too obsessed with Krugman gotchas IMO, but nobody's perfect. I'm sure there are things about me that bug people too. So I enjoy following him.