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Austrian Economics and Math

Austrian Economics and Math
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Several people have sent me this curious blog post by Brian Albrecht, who is a PhD econ student at Minnesota and (this academicequations year) an Adam Smith Fellow at GMU. The post is titled, “Study Math, My Austrian Friends” and is a plea for Austrian economists to put aside their alleged hatred for math, not because mathematical economics is better than the deductive verbal logic of standard Austrian theory, but simply for its own sake and the fact that studying math sharpens your mind.

My quick reaction is that Albrecht’s overall stance is fine, but that no serious Austrian would disagree with him. So in that sense, I dislike his blog post, only because it feeds the convenient caricature of Austrian economists that smug fellows like Noah Smith hold–and Smith tweeted out Albrecht’s post with glee.

Albrecht In His Own Words

Let me quote a bit from Albrecht’s post to convey his tone and the overall thesis:

Austrian economists hate math. That’s a broad brushstroke, but I stand by it.

And it’s a shame. I understand the Austrian concerns about math and agree with most. But the concerns call for hesitation when applying math to economic problems. Yet, justified hesitation wrongly became abstention. I want to fight that tide.

…[T]his [post] is an apology, in the religious sense, for math- pleading to young scholars interested in Austrian economics: Put away your concerns for a moment. Learn math. Math can be your friend. You will be a better (Austrian) economist for it.

Mathematical proofs have aesthetic beauty, in the way music and art does…

Math helped my thinking about the Austrian theory of utility, time-preference, and capital theory.

For example, I was discussing continuous preferences with a classmate. I was going through my basic Rothbardian explanation of the problems with continuous utility functions. Goods are never infinitesimally small, so a consumption set is discontinuous. Consumers either buy 1 apples or 2 apples, not pi apples. Boom, win for the Austrians.

Not quite. My classmate was able to explain to me that I also required an extra assumption: I need to assume the goods are finite. If there were infinite goods, continuous preferences is still workable.

It’s an obscure point, but I was simply wrong in my defense of Austrian economics. Knowing math helped me clarify my thoughts and communicate with a non-Austrian economist. Knowing a little about power sets, infinity, countability, and more was the only way that I could understand his (100% correct) point.

I think the above is a good summary of Albrecht’s post, which allows me now to go on to challenge his premise but agree with his conclusion.

Which Austrians Hate Math?

I can’t think of a single prominent Austrian who ever said anything remotely like, “I hate math.” In fact, even among the students I had at Hillsdale College, I can only remember one who made such a statement. And even there, her point wasn’t that “Math is stupid and irrelevant,” but rather that she personally was not good at, and did not enjoy, doing anything mathematical. Furthermore, the reason she brought this up is that she thought I was spending too much classroom time forcing my Austrian students to study math! So you can see why Albrecht’s whole premise seems foreign to me, and serves only to reassure outside critics that Austrians are a bunch of Know Nothing rubes.

To be sure, in Internet discussions you can often see rank-and-file fans of the Austrian School blasting the “mathturbation” of mainstream economists. But their point isn’t, “Math is stupid and a waste of time.” No, their point is that the elegance and majesty of mathematical truth is being illegitimately smuggled over to endorse the conclusions of the economic models in question, when such moves (they claim) are unwarranted. Since Albrecht doesn’t challenge that notion–and actually seems to agree with it–it really makes me wonder who his target audience is for his blog post.

Indeed, we really have no idea who Albrecht is tut-tutting in his post, since he provides not a single link to anyone guilty of the error he is chiding. I would encourage Albrecht to go find, say, three good examples of what he means, so we can be clear on whether there is really a problem in the School.

Austrian Giants on Math & Economics

Here’s a good example of a passage from Human Action (p. 351 of the Scholar’s Edition) where Mises talks about this issue. Referring to a “third group” of mathematical economists, Mises writes:

Their ideal is to construct an economic theory according to the pattern of mechanics. They again and again resort to analogies with classical mechanics which in their opinion is the unique and absolute model of scientific inquiry….

The deliberations which result in the formulation of an equation are necessarily of a nonmathematical character. The formulation of the equation is the consummation of our knowledge; it does not directly enlarge our knowledge. Yet, in mechanics the equation can render very important practical services. As there exist constant relations between various mechanical elements and as these relations can be ascertained by experiments, it becomes possible to use equations for the solution of definite technological problems. Our modern industrial civilization is mainly an accomplishment of this utilization of the differential equations of physics. No such constant relations exist, however, between economic elements. The equations formulated by mathematical economics remain a useless piece of mental gymnastics and would remain so even if they were to express much more than they really do.

Does that sound like Ludwig von Mises “hates math”? Does he deny that math can be quite useful? Of course not–he actually attributes “modern industrial civilization” to the use of differential equations.

It is clear from reading Human Action that not only did Mises have a general familiarity with classical mechanics, but he also understood the basics of relativity theory and quantum mechanics.

Furthermore, Ludwig actually had a dispute with his mathematician brother Richard von Mises over the foundations of probability theory–you can see Ludwig’s position in Human Action itself (just search for the discussion of “Case Probability”). So if indeed Austrian economists in the field today “hate math,” it’s not because they’re taking cues from their leader.

Or what about Rothbard? He wrote a short essay called, “Chaos Theory: Destroying Mathematical Economics From Within?” That is a good summary of Rothbard’s overall take: He was very intelligent and well-read in numerous fields, including math. And it was precisely because of his understanding of the differences between math and economics that Rothbard was so skeptical of the efforts of the mathematical economists.

Conclusion

I’m actually far more of a moderate on this particular issue than Mises or Rothbard. For example, I think one of my biggest contributions to advancing Austrian capital theory was to translate the insights of Bohm-Bawerk into a formal neoclassical model with all of the bells and whistles, so that mainstream economists couldn’t duck the challenge by saying, “Oh that’s just words, put it into math.” (If you’re curious, see the Appendix to my dissertation.)

Even so, Albrecht’s post seems to fall flat. His entire premise is that “Austrian economists hate math,” and yet the giants clearly don’t. Furthermore, I can’t think of more than one person who ever said anything like that in my experience. Lacking a single example, Albrecht should bolster his case.

  • Brian C Albrecht

    Bob,

    Sorry for the late response. Thanks for your comments and especially the Rothbard link on complexity. It's a nice read, especially since I've been looking into agent-based modeling lately.

    I was simply trying to encourage people like myself to give math a try, learn graduate math. Do you know of any article/post/video where anyone remotely connected with Austrian economics says something like this? I hadn't so felt like I should say it. I wasn't trying to tut-tut anyone.

    I am writing a longer response for my blog that I hope you will read.

    Thanks,
    Brian

  • hashthenazi

    I can math, What now Brian?

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Profile photo of Robert P. Murphy

Robert P. Murphy is the Senior Economist at the Institute for Energy Research, and a Senior Fellow with the Fraser Institute. He holds a PhD in economics from New York University. Murphy is the author of Choice: Cooperation, Enterprise, and Human Action (Independent Institute, 2015) as well as numerous other books and hundreds of articles.

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