Recently many econobloggers have offered their thoughts on what is often called “mathematics in economics,” but I think is really more about formalistic model building in economics. Here’s a very interesting post that has links to some of the other people in this dispute. For my part, just some scattered observations with no necessarily overarching lesson:
==> When discussing my thoughts on the Misesian “pure time preference theory of interest,” it was very easy to communicate a key distinction–a preference for earlier goods versus a preference for earlier utility–in the language of mathematical economics; it was the discount on future utils (often denoted by beta) versus the marginal rate of substitution between a good available at time t versus t+1. In contrast, Austrians use the same phrase–”time preference”–for both concepts, which made it very difficult to get anywhere. (If you want to read more of my views on this, check out the links at this post.) So this is exactly the kind of thing that the proponents of mathematical formalism cite–there are ambiguities and imprecision with spoken language that can be alleviated with symbolic modeling.
==> But don’t take the above point to be an award of victory to the formal camp. At the crucial point–going from the formal model to the spoken-language interpretation of what the model means–the formal economists lapse into whatever they want the result to be. For example, when I was at NYU I spent a good deal of time trying to get the mainstream professors to appreciate Bohm-Bawerk’s critique of the “naive productivity theory” of interest, and to see the dangers in teaching (as they did) that “interest equals the marginal product of capital” in equilibrium. At their encouragement, I stopped saying it in words and built little models to illustrate the problem. One guy finally “saw” it and said, “Well, assume you can turn tractors into bananas one-for-one.” I am not joking; that’s how he dealt with my concerns. And then another guy told me, “Yes, I agree there is more to it than just taking the derivative of the production function…but somehow we know.”
==> Continuing in the above vein, go look at the appendix to my dissertation if you can handle it. In my mind, this was analogous to Einstein’s special relativity; I came up with a more general framework that had the mainstream “r = MPK” as a special
condition case. But, so far as I can tell, I’m still the only person on Earth who thinks I’m this much of a genius. The proponents of the formal approach don’t usually stress this aspect of things: You can come up with the most brilliant model ever, which shows in crystal clear fashion how your critique of the orthodox approach is valid, but if nobody cares, and just ignores your model, then there’s not much you can do about it except whine on your personal blog for years to come.
==> Let me give another example. When Bryan Caplan chimed in to this discussion, he proved his bona fides by linking to one of his theoretical papers. It’s titled, “Standing Tiebout on his head.” Here’s the abstract:
Much of the public ﬁnance literature argues that local governments behave competitively due to residents’ ease of exit and entry. The model presented here challenges this widespread conclusion. Though it is costless to relocate to another locality, the presence of tax capitalization makes it impossible for land-owners to avoid monopolistic pricing of public services by moving; land-owners can only choose between paying the tax directly, or paying it indirectly in the form of a lower sale value for their housing if they exit. In consequence, the only real check on local governments comes through imperfectly functioning electoral channels.
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.)
==> 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. 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.