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Three parts (2.), six parts (4.), one part (5.), although I would heavily qualify "superior" - its superiority largely depends on how it is used and what the goal is. One can do more and less useful mathematical economics.

I think the implications of (1.) does both job-seeking economists and hiring departments a disservice.

Here's another theory - when I took "Mathematical Economics", it was basically calculus for economists. The economist's way of doing constrained optimization, in other words. I imagine this is what "mathematical economics" means in most departments. It's really an integral, foundational class that needs to be well staffed. Clearly, though, the material isn't fancy and new. My professor was a grizzled old guy, and I imagine a lot of these professors are. "Calculus for economists" isn't something that you chase after fancy new PhDs to teach. Most anyone can teach it. Could this be more of a cohort thing than anything else - a lot of the old Mathematical Economics professors are starting to retire? Could your reading of "mathematical economics" as "fancy new methods" actually just be the pretty standard "calculus for economists" job posting? I would think "fancy methods" is assumed in a lot of these other categories (macro and finance, etc.).

It's all those things, I suppose, but I think 2 is the main thing. Item #2 is not much different than 5, btw. We are invested in our methods, which therefore have inertia. There's lots of inertia for math in part because economics is not only about science, but also technical expertise as reflected in your option #3.

I don't think smart has much to do with it in any direct way, although the math helps to limit competition by weeding those who are not "smart" in a mathy way. It is noteworthy, however, that economists tend to be the smartest guys in social science, just as the physicists tend to be the smartest overall. IMHO, some of those smarts come from our math training itself, rather than the filter such math imposes. I doubt "smart" does much to make economics a better *science*, but it is valued outside of academia and thus helps raise our salaries.

Bob Subrick just sent me this link to an interview Ronald Coase recently did (100 years of age and still sharp). http://english.unirule.org.cn/Html/Unirule-News/20110101130956819.html

Favorite lines ...

RC: The bad or wrong economics is what I called the "blackboard economics". It does not study the real world economy. Instead, its efforts are on an imaginary world that exists only in the mind of economists, for example, the zero-transaction cost world.

Ideas and imaginations are terribly important in economic research or any pursuit of science. But the subject of study has to be real.

These Coasean words of wisdom seem to be relevant to the topic.


P.S.: Daniel -- have you read any of the work on the returns to education and signaling theory? I don't think signaling theory is doing a disservice to either side of the market.

Governments will surely need tons of technocrats to manage the economy in the following decades.

Besides, this makes the vicious circle of big finance, uncle sam and large universities even more robust.

Peter -
Yes, we spent time covering signaling literature.

I should clarify - it's not the idea of signaling that's all that problematic. It's the idea that math would be assumed to be predominately a signal of intelligence. I think it is broadly recognized that there is a problem with economists who can do all kinds of math but can't communicate or perhaps even understand the real meaning of the math. Because that problem is very broadly understood, I don't think is an automatic ticket to a good job.

I was at an event with Richard Freeman in October, and I was talking with him afterwards about math in econ. One of the things he said was that if you ever see anything he writes with lots of complicated math in it, it's probably a relatively undeveloped idea of his, that as he develops his thoughts and arguments the math becomes more elegant, less messy, and less of a crutch. He said as a rule of thumb his least mathematical papers are his most thoroughly thought through. I don't think Freeman is alone in this, and I think a lot of hiring committees probably pay close attention to who can actually elucidate the meaning.

Once you get to that level, math whizzes are a dime a dozen. I imagine departments are looking for real insight.

What I probably should have said is that yes, being good at math is a pretty good signal that you're an intelligent person. But I'm guessing a lot of applicants are going to meet that intelligence-hurdle, and that other signals (publications in major journals, dissertation advisors, etc.) are going to be more valuable. There's simply too many economists out there that know a ton of math for me to think that this is really a driving signal.

Certainly, though, it is a signal of intelligence.

It seems to me that most people just consider mathematical analysis more precise. I think that mathematics has the same basic flaw as verbal logic, though — it is only as strong as the practicing economist.

Jonathan -
Surely, even if we assume competent verbal logicians and competent mathematical logicians, we can admit that math has real advantages in precision, internal consistency, and logical validity, while verbal logic has real advantages in accessibility and richness.

Karl Menger (the mathematician son) has a great essay pooh-poohing the idea the math is more precise than verbal reasoning. It may not even be more *mathematically* precise as he illustrates nicely. A says utility rises with consumption and B, instead, uses mathematical notation to say that the utility function has a positive first derivative. B's statement is less general because is smuggles in the assumption that utility is everywhere differentiable with no kinks. A's statement is no less precise; it is not even less *mathematically* precise.

My recent contribution to JEBO points out that the math is an uninterpreted calculus. You need "understanding" to interpret the math. Thus, you cannot have rigorous mathematical economics without rigorous verbal economics. Math can often be a way to *evade* rigor.


the problem is: what does A's 'utility' mean? further, you can endow mathematical objects with economic meaning (e.g. positive cones of riesz space is a choice set, functionals in topological dual is the price system, etc...) and build up precise systems, letting math doing the job of precise reasoning. what's wrong with that, given that this approach also allows us to give a precise expression of the limits of such an endevor (e.g. SMD; sorry for bringing it up again)?

correction: ... positive cone of riesz space is a choice set, functional in topological dual is a price system ...


I agree, and I think any serious student of math should agree. Mathematical logic relies heavily on premises established through verbal logic (and math is not a language of its own). Also, it's important to point out that math cannot accurately model relationships which are not mechanistic (including value).

Pete, I highly recommend Marion Fourcade's "Economists and Societies: Discipline and Profession in the United States, Britain, and France, 1890s to 1990s" on the subject. She would put most emphasis on 1,3, & 5.

Roger -
Definitely. Given a set of assumptions that defines the field that you're talking about, math is more precise ("mathematically precise" as you say), but of course those assumptions reduce the richness (to say nothing of the accuracy) of the other forms of communication.

That's what I meant when I distinguished between the precision of math and the richness of language.

I'm not sure if you thought that implied something else, but I definitely agree with this point.

And I would note there's no obvious answer as to what is ideal. We absolutely aren't dealing with corner solutions here. I don't take either extreme very seriously.

Surely the quality of work depeonds on the quality of the theories used and the problems addressed, so no amount of sophistication and rigor in methods can save work from defective theories and bad problem-selection.

Of course if you can be well paid for work that you like and you are good at and which you were trained to do at great expense of time and money then you will probably persist even if the work has little or no scientific or practical use.

As for selecting for "smarts", outside of some special fields like physics it is likely that genuine scientific achievement has no relationship to IQ above about 130 (Liam Hudson, circa 1968). In the same way, outside of running, sports folk are not selected for speed provided they reach a minimum that depends on the sport.

Getting back to the two-strand economics course, what about the low-hanging fruit that can be collected by people of with modest mathematical skills who can think like economists and work with other disciplines in the social sciences? Has anyone done a count of the great or very good economists who would have been cut from the squad on the current selection criteria. Start with Peter Bauer and W H Hutt. So how much talent are we losing at present, and where to those people end up?

On mathematics and modelling these papers are interesting.

On the dangers in maths

And on spending too much time on neat computer models instead of looking out the window. This comes from a rural researcher in the 1990s.

Steven R. Postrel (husband of former Reason magazine editor Virginia Postrel) chimed-in on these matters economics vs. mathematics back in 2007 over on the Organizations and Markets blog with "Physics Envy and All That":

He's clearly no Austrian, and I think he ultimately misses the point (viz., a time-equation for the ordering of human preferences cannot be derived), but as for myself, when I was a physics major forty years ago, my professors struck me as actually downplaying the importance of mathematics: One had to know it - but merely as a matter of course - and if one made a math error on a test, only a point or two was taken-off one's grade; rather, what repeatedly was stressed in classes and massively was reflected on test grades was whether one demonstrated a grasp of the ~physical significance~ behind the equations, which had to be expressed verbally/in writing. (Well, except for quantum mechanics, where the math ~was~ the physical significance - aaarrgghh! - but never mind that exception for now.) The point is, whether mathematics is used or not, I would think that if one doesn't get the economic significance of an economic theory, then one is tilting at windmills. Moreover, I also remember that, on the other hand, in the mathematics department, if a textbook was found to contain even an iota of practical application, then the text was summarily dismissed as "it stinks!" Sometimes econometricians' attitudes seem more like those of mathematicians than even of the physicists to which they seem to aspire!

@ Arash

You can have mathematical rigor with pure math. You can economic rigor with “literary economics” and no math. But for economic rigor with math, you need rigor in the “literary” methods that translate the uninterpreted calculus into statements about humans or human systems.

I’m basically just sayin’ that the facts of the social sciences are what the actors think they are. This point should not be controversial. The fact that serious and intelligent people elevate mathematical rigor and forget about economic rigor just goes to show that we overvalue math, that the Coase quote Pete gave above is right on. And look, if you read my work there’s plenty of math and stats in it. So I’m saying “math is bad” or something. Indeed, I am always saying how Austrians should be more into complexity theory. But respect for mathematical methods should not imply a neglect of “understanding.” Why is this point hard to grasp for so many otherwise smart and serious people?

I think you’re getting it backwards, Arash. You need the “interpretive” or “literary” economic to know what the utility function is. You can take the derivative or whatever without knowing what U(x) means. To go from math-world to social world you need “understanding,” aka “Verstehen.”

I'm NOT sayin' "math is bad." Hope that was clear from context.

If anyone doesn't think basic Ph.D. economics is extremely mathematical, go look through a copy of Mas-Collel et al.'s "Microeconomic Theory." This was my (and most other) intro textbook for the "micro" stream.

Economics does the streaming out in the first class. If you have a Ph.D. in Econ from most any (not all) schools, the hiring school isn't worried about 1. above.

Here's another reason:

If you're hiring a new professor, you want someone who can teach the really boring classes to undergrads such as mathematical economics and basic econometrics.

A hire who can't teach these classes isn't worth much to a department that wants to take that burden off its back.In a sense, their teaching repertoire is larger and hence more valuable.


@ Roger,

I didn't want to ascribe an anti-math stance to you (BTW, I totally agree with your initial response to Peter's post).

You say that "You can economic rigor with “literary economics” and no math". This is certainly correct. You CAN have such a thing. Yet, it isn't probable. Just think of all the nasty debates between economists in the pre-formalist era (usually generating more heat than light, to say it with Schumpeter). Mises is my favorite case in point (also because he was so impressed by his own tautologies). Yet, isn't it nice that we are beyond that stage?

J'accuse ...!: I think that many mathematical economists should invest themselves in some "logical narratives". But I think it is evident that most Austrians should invest much more in math, and not only for strategic reasons (I think Peter doesn't like math-econ, but wants young Austrians to learn it for strategic reasons).

Finally, you say: "You need the “interpretive” or “literary” economic to know what the utility function is. You can take the derivative or whatever without knowing what U(x) means."

No. In fact, mathematical economics has shown that utility functions are just representing preference relations, and thus add no new information to the system. A util is and should be a auxiliary or derivative concept. Utility functions are useful, because you can apply them in many frameworks, whereas preference relations on choice sets carry interpretation (!) but are somewhat intractable in applied analysis. But they have no live of their own. Now go back to the pre-formalist literature on utility functions. Just annoying!

arash, do you think that Peter Bauer and W H Hutt should have invested more in math? Can you explain how that would have improved their work? Would you like to nominate the fields where Austrians could work more effectively if they invested more in math?

And how much more? It is possible to do regression modelling without any maths beyond high school, you just need good advice and you need to be alert to the strengths and weaknesses of the method.


I just know Hutt's work, so my respond is restricted to him.

I like Hutt's analysis and I agree with him on many points. Math could have improved his work however. Instead of hundreds of pages beset with his habit to invent new terms, he could have make his point more concise and reach a broader audience. Further, Hutt is a clear exception. As some of you know, I'm a big Hayek fan but I have to admit that his work on utility analysis and capital theory, though very promising, heavily suffers from his lack of tools. Just look at the three dimensional monster-figures in Pure Theory of Capital, where he just attempted to introduce a new margin of choice (the impact of different investment periods on yield and thus on investment choice). I already mentioned Mises. So the two Austrians with the biggest impact suffered from mathematical aversion.

How much more math? This depends on what you want to say. Don't get me wrong: I'm in favor of a pluralistic approach. However, I think Austrians opt for a corner solution and don't believe that this is the best choice. I remember Peter calling math econ "mental masturbation" on this blog. I simply cannot think of Arrow or Lucas that way.

V and J Oxman - that was exactly my understanding. I think GMU is a cloistered world in some ways. I do not think "mathematical economics" is some fancy job description for someone with tools that have no practical application. I think it's very practical mathematics, and a call for a very non-fancy glorified calculus instructor.


We seem to be pushing beyond the limits of the blog medium. I mean, really: The distinction between cardinal and ordinal utility is just not connected to my comments. We have come to the point where more serious reading is required. Please go to sciencedirect and check out my paper, "Some epistemological implications of economic complexity," in JEBO 76(3), December 2010, Pages 859-872. There you will find the argument that mathematical economics in some sense needs literary economics.


my argument is not about the distinction between ordinal and cardinal utility. You suggested that utility functions itself carry some economic interpretation ("You need the “interpretive” or “literary” economic to know what the utility function is. You can take the derivative or whatever without knowing what U(x) means.") and I countered that economic interpretation is imposed on the binary relations on a choice set AFTER you build the apparatus. I also argued that the utility function is a derivative concept so that "utils" or U(x) provides no ADDITIONAL information and no ADDITIONAL "meaning" for your model. Preference relations and choice sets, in turn, do carry meaning and nobody denies that (e.g., upper-contour sets that are strongly convex is meaningful in the sense that agents prefer smooth consumption profiles or mixed bundles). But this meaning is independent of the axiomatic apparatus:

"Allegiance to rigor dictates the axiomatic form of analysis where the theory, in the strict sense, is logically entirely disconnected from its interpretations." (Debreu 1959:x)

But I'll read your paper and, as always, look forward to doing so.

Forgive me, Arash, but I literally do not understand your last post. You say, for example, "You suggested that utility functions itself carry some economic interpretation." Huh?

BTW: I think professor Bourbaki is ailing.

The statement that the top fields are "mathematical economics" and "quantitative methods" does not make any sense. The people who specialize in economic theory and econometric theory are VERY small in number. The expansive interpretation of these fields, however, is virtually everything: most people make mathematical models and a lot of people test or estimate them. These aforementioned "fields" are very specialized indeed.

I guess what the author means is that most students do "modern economics" -- mathematical/quantitative economics. Duh!

Where is the raw data?


how else would you interpret your two sentences?

"You need the “interpretive” or “literary” economic to know what the utility function is."

"You can take the derivative or whatever without knowing what U(x) means."

you say 'to know what IT is' and 'to know what IT means'. you mean utility function by IT. and you say that literary economic reasoning tells us 'what it is' and 'what it means'.

I just responded that utils are purely analytical tools free of any economic meaning beyond the underlying preference structure. Look Roger, THERE ARE NO SUCH THINGS LIKE 'UTILS' THAT CAN BE MEANINGFULLY DESCRIBED OR UNDERSTOOD. Utils are solely analytic tools and all literary economics attempting to tell me what they are produces nonsense! In other words, utils have no external representation; they are metaphysical; not empirical.

BTW, Bourbaki (the professorS) is problemtic, especially from a constructivist viewpoint (I guess this is what you refer to, right? e.g., axiom of choice as a substitue for a decidable routine and the like). But Bourbaki is what math econ is usually about. So when we talk about math econ, and how to handle utils in such a framework, the quote about might be helpful.

"Certainly, though, it is a signal of intelligence" In a certain sense Daniel is correct and many people would agree. However, I find it interesting that so many "intelligent" students use their mathematical abilities so unreflectively -- they simply follow the leader.

What does it mean to use intelligence in an unintelligent way? This is a very serious issue. In a sense, this ignorant or even mechanical use of intelligence is the essence of idiot savantism.

Perhaps I go too far. But something is seriously wrong when the "highly intelligent" become robots.

@ Mario,

just a question: do you think that students would use logical narratives or other approaches to economics in a more reflective way? Or do you think that young people on average just follow the most promising path to a career?

"In the same way, outside of running, sports folk are not selected for speed provided they reach a minimum that depends on the sport."

Definitely not true for American football.

Mario - definitely, which is why I doubted its value as a signal. If mathematical ability among economists were more rare than it is, perhaps it would be a good signal. But since it's so common I'm not sure that would distinguish anyone, at least in the job search (maybe in the journals).

I really think this "math and quantitative economics" point is a red herring anyway. I really think they're just advertising for people to teach calculus to undergrads, but what do I know - it's not like I've ever been on the econ phd job market. That just seems to make the most sense. If you want a math braniac micro theorist you're not going to advertise for "mathematical economist" you're going to advertise for a "microeconomist".

First, anyone who gets a PhD in economics in last 25 years has an aptitude in quantitative analysis. If they didn't they (1) would not have been admitted to a PhD program, and (2) could not have survived the required courses. That is true even for schools that are not math heavy like GMU. I tell all students applying, the GRE score expect on the quantitative section is 760, and on verbal 600. To be competitive this is what we are looking at. So all the talk about math aptitude among "Austrians" is stupid-talk not based on an understanding of the facts.

Second, aptitude does not mean acceptance, nor does it mean comparative advantage. Since I actually was around "theorists" both at NYU and at Stanford, and unfortunately I have also been around many pretenders to being theorists as lesser tier schools, I have a strong sense of comparative advantage in economic analysis. I am also very elitist about what it takes to be a top flight theorist. Very few people have a comparative advantage in doing formal theory, the vast majority of people who think they do are pretending. Better they actually did economic analysis of real world practices or real world policy options than pretend to work on fundamental theory which they make little to no progress. When Buchanan says the Emperor has no clothes, he is going after the big game in formal theory, but his argument is even more devastating for the poor slobs who are coming in last in the game they pretend to be playing at. A lot of bad economics gets bounced around because of the form the argument takes rather than an analysis of the substance of the claims being made. That is a major intellectual error --- and its source is sociological (thus related to my post).

Third, I have a strong Coasean sense about the nature of "theory". I actually don't think we should call blackboard economics "theory", I think it should be called either blackboard economics or economic fantasy land. Most modeling exercises are the equivalent of playing fantasy football or fantasy baseball. It is not the same as playing football or playing baseball. It talks about the same things, but is not the same thing. Just because so and so is a good fantasy player, doesn't mean he is good player. The translation is not perfect. Theory should be about the world of the economy, not the make believe world of the blackboard. What language you use to theorize about the world is irrelevant to whether or not you have made advances? I recommend to everyone to read Kenneth Boulding's JPE review of Samuelson's Foundations. He comes to the exact opposite conclusion to Arash about the relative merits of modern mathematical economics versus the literary economics of yesteryear. I agree with Boulding. But I also agree with Coodington --- see his review of Shackle's Epistemics and Economics, where he makes the distinction between syntactic clarity and semantic clarity. Mathematics as a tool of reasoning only aids us in syntactic clarity, but not semantic clarity --- I read Koppl as making this same fundamental point.

Arash suggests I refer to mathematical economics as "mental masturbation" and then says that Lucas and Arrow certainly didn't do that. First, let me be clear (as should be from my 2nd paragraph above) really good mathematicians have something of value to say. If you look at a very old piece of mine now "What is Wrong with Neoclassical Economics (and what is still wrong with Austrian economics)," I actually start the discussion with Marshall's "Burn the mathematics". The idea is that mathematics can be an extremely good tool for reasoning, but what it cannot be is a good master. In modern economics, we evolved in a direction where math became a master to the detriment of economic thought in my opinion. Second, even among the really good mathematical economists --- lets say Peter Diamond --- mathematical tractability often is more important than capturing reality. Thus, we get toy economies populated by puppets which we model. That is mental masturbation --- in fact, I would argue masturbation of a particularly kinky type rather than pedestrian and can often end up chocking the life out of the one masturbating, and self-gratification devolves into self-destruction.

Nope, better go back to the Coasean wisdom of what the subject is --- property, contract, consent, etc. and acted upon by capable but fallible human actors.

Now my post was not an invitation to methodological discourse, it was a sociological observation. Mario the raw data is the number of jobs listed in JOE and the fields requested for those openings.

Pete Leeson offers the following explanation --- the heyday of theory was those who entered the profession in the 1970s-1980s, and they are retiring. So their faculty line is being replaced. But Pete hypothesizes that if you look you will find that there are less jobs in theory than there are spots opening, so that reflects not an increase in the demand for theorists, but instead a retrenchment of positions in pure theory. What do you think of that? It seems plausible to me, though of course, we could only answer that with a closer examination of the data. Empirical questions require empirical answers, not philosophical one!

So let me repeat my question --- why would formal theory be a leading field among those school hiring in 2010-2011? What do you think that indicates?

Look to V and J Oxman (and Daniel) --- read the JOE. If they are asking for a field in mathematical economics and quantitative methods it is NOT to teach math econ and econometrics at the undergraduate level. It is that you are a THEORIST. The other fields listed as popular in JOE include microeconomics, macroeconomics.

As J Oxman points out, ANY PhD in economics can teach a course to undergraduates in mathematical economics and/or statistics and econometrics.

This is NOT the issue in the JOE listings.


Scoring a 760 on the math section of the GRE does not show aptitude in math. It shows that you found a high school geometry and a calculus book and reread it.

Second, a GMU graduate on the Austrian track could not and should not teach even a basic undergraduate mathematical economics or an econometrics course. That's just a fact. There's no way to smooth it over.

At GMU, you're required to only take one Math Econ course and one Econometrics course. Further, both courses are weakly taught compared to anything in a mainstream program.

You note,

"So all the talk about math aptitude among 'Austrians' is stupid-talk not based on an understanding of the facts."

You're really just not being honest here Pete.

Even using math GRE scores as an example of math aptitude should raise a stink with anyone who has taken the test.

Peter -
The long post is excellent - parts I disagree with, but all in all very good.

I'm not sure I understand the point you direct to me (and V and J Oxman). Of course they're theorists. What else would they be? Well, they're theorists and econometricians.

Math and quantitative methods is, as I understand it (1.) econometrics, (2.) modeling, and (3.) game theory. That sounds like a broad, catch-all "math guy" category. You raise the issue of Diamond. Would he be a "math and quant methods" guy? I imagine he'd be a macro/public economics guy primarily, right? You mention Lucas and Arrow. Would they be "math and quant methods" guys? I wouldn't think so.

"Math and quantitative methods" seems to me to say "we don't care exactly what you work on, but we want someone that can teach mathematical modeling".

Let me put it this way... how many phds COULDN'T respond to a "math and quantitative methods" listing? Very few I'm guessing. The category is an implicit part of almost all the other JOE categories.

Maybe that alone explains the prevalence.

And maybe that's another thing to emphasize - yes these are theorists, but not JUST theorists. They're econometricians too. This may be a reaction to the "we have too much fancy math in our theories" movement. Might be worth looking closer to see if all these math and quant methods listings are actually all econometrician listings.

Oh dear. As I tried to suggest already, Arash, you're not getting my point in the slightest. I'm not willing to address the misconnect on a blog thread. I already said If you wish to continue the discussion -- and you are under no obligation to do so -- please read my "implications" paper first. I would apologize for being cryptic, but, honestly, I don't really don't get how you read something about "utils" out of my remarks. I get the distinct impression that you have some sort of wacky model of "literary economics" that is unrelated to anything I was referring to.

As for Bourbaki (I did raise the issue) my point was not really about constructive methods, though there is an issue there to be sure. Mostly I was hinting that economists are moving away from Bourbaki and toward more open and inductive tools, particularly those characteristic of modern complexity theory. You know: simulations instead of existence proofs. I gladly confess that my Bourbaki comment *was* cryptic. IMHO BTW, it is professor Bourbaki, not professors Bourbaki. Those fictive, he's still one guy.


I am being completely honest. David Skarbek is teaching statistics to undergraduates at Duke right now. I taught a calculus only micro course in the past, as has my friend Dave Prychitko. I am not saying it is our comparative advantage, but people who are identified as Austrian economists and who are products of the Austrian "track" as you call it, have taught very traditional courses. In fact, I'd say the vast majority of people who have had careers as academic economists have in fact done so.

GRE is an aptitude score, I don't put a lot of weight on it, but I am pointing out that it is aptitude. If you want to claim it is useless, then explain the required practice of submitting the scores and screening candidates based on those scores. There is also the additional screening of math pre-requisites for PhD programs in economics. I actually advice undergraduates who want to pursue a PhD, that they major in mathematics for undergraduate degree.

To clarify there is no Austrian track separate from the regular track at GMU for the 1st year --- you have to take math econ, micro, macro, and econometrics. Math course taught by Chicago guy, econometrics taught by U of Md trained guy. Is it at the same level as was taught at NYU when I was there, no? But are the basics covered in both classes --- yes.

Then in applied courses at GMU students need to learn how to do econometrics, etc.

I would like to point readers to recent GMU graduates Jon Klick (U of Penn) who does empirical public choice/law and economics; Peter Leeson (GMU) who does law and economics, institutional and Austrian economics, and public choice, and Ryan Oprea (UC-Santa Cruz) who does market process theory and experimental economics. Look at their CVs, look at their teaching records, etc.

I think any department would be happy to have such talented people of their staff. And they reflect extremely well on the education they received here at GMU. I think you can see that from GMU over the years --- Brian Goff (WKU) and Gary Anderson (CSUN) were contemporaries of mine that published in top tier journals such as J of Law and Economics and JPE and were great colleagues at their schools.

The record of GMU's graduates both research and teaching wise can stand of its own, but I do encourage you to familiarize yourself with the outstanding record of GMU's most successful graduates.

Another hypothesis provided by Will McBride is that in his reading of the JOE this year, many of the jobs were at Chinese universities and they specifically requested quantitative analysis.

I would need to have to go over the Inside Higher Ed article, but I interpreted the claim as being about the US market for economists. But perhaps that is the wrong way to read the article.

Prof. Boettke,

I largely agree with your assessments here and about your opinion regarding mathematical economics. Post of the papers I see in math econ capture intuition in several pages that I (or any succinct writer) could capture in a few written paragraphs.

I have a more practical question. Math econ and quantitative methods are different animals, it seems, in that they seek to answer different questions. Math econ is a technique that can be applied to many fields (like mine: finance). Quantitative methods, when grouped with math econ, makes me think QM really refers to econometric theory.

All the applied fields do their sinning in the basement (to use Peter Kennedy's line), but econometrics isn't taught by sinners. It's taught by the priests on the top floor - the theorists, where all assumptions are met.

In any case, these are the two groups who will provide the labor for the 1st year, non-field courses. But the math econ types could be applied (there's math macro and empirical macro, for example), whereas the econometricians are more likely to be pure theorists.


What I mean by "Austrian track" is students who are there to study Austrian economics. Students who are not likely to explore math classes beyond the required econometrics and math econ class.

Some GMU Austrian track students may be teaching these classes but they really shouldn't be.

Two graduate courses does not qualify you as knowledgeable enough to teach the subject, even if you were a very good student.

God forbid the students ask a question about something that isn't in the intro book.

V -

You are making assumptions about the education of the students that are interested in Austrian economics, etc. Yes, they trade off some of their formal courses, but others pursue additional courses in formal theory in order to prepare themselves. Charles Steele, a former student at NYU, actually passed the field exams at NYU in both game theory and econometric theory. Yet he did his dissertation in the field of Austrian economics, institutional economics and development economics.

Ryan Oprea teaches the first micro PhD course at UC Santa Cruz, he came to GMU well versed in Austrian economics having studied with Richard Ebeling, and besides his courses at GMU also supplemented his studies with formal theory courses at U of MD.

Students self-select how they want to supplement their education ... Prychitko and I supplemented our educations not only with courses on Marxism, but also with extra work on General Equilibrium theory.

GMU does give students the "space" to choose how to supplement their core education with the courses they want to pursue that enables them to pursue research as they want. They need to choose wisely. If they choose poorly, they find themselves poorly educated. A poorly educated economists will have a hard time publishing and getting ahead professionally.

So again, please do a little checking of your premises before making pronouncements. Not only can GMU students pursue formal course work through the consortium, but also there are technical courses offered in econ, public policy and computational science programs. Many of our students in fact do take advantage of these opportunities to expand their education. But our students also have the opportunity to expand their education with studies abroad (Adam Martin spent a term at Cambridge) or pursuing other disciplinary knowledge --- philosophy and history being the most prevalent, but others have pursued religious study, sociology, and political theory.

Bottom line: not only are the students here to study Austrian economics _not_ allergic to formal training, they are encouraged to excel in their educational background training in economics so that they can become not just good economists, but great economists. Not everyone meets those standards, but some do.

I remember Ryan from the summer undergrad experimental economics workshop!


are you talking about highbrow math or intro math in grad schools? I for one refer to the former. It's somewhat funny that you defend Austrian math-skills by grad courses and that some of Austrians actually teach them (here, I side with V). This only shows that you don't read a lot of pure theory stuff, sorry. When was the last time you actually worked through theorems, lemmas, and their proofs? BTW, math econ is not just calculus. Differential analysis after the axiomatic turn is more than the calculus you teach in high school. Behind derivatives there are topological choices to make, manifolds to define, etc. Do you guys teach this? Do you teach Ito's lemma and the like? But this is what mathematical economics is about!

It really seems that you build up a protective belt: you critize math econ and when someone turns your critique against you, you come up with your standard slogans (the 'math is a bad master' stuff). Thereby you drop some names (Coase, Buchanan) and hide behind these guys. Can you actually name three results that are somehow important to you, for whatever reason?


BTW: I'm not claiming that I'm a math-hero, but I know enough to realize that the Austrian perspective on math econ is just uninformed (I don't mean Roger btw)! So please don't come up with your usual slogans (like the 'you have to publish, before I take you seriously' stuff). This is not about me, it is about you and the Austrian believers.

@ Roger,


FWIW, GMU PhD ABD Petrik Runst is teaching our quantitative methods course at SLU this year and is doing an excellent job.

As someone who has actually taught at an undergraduate institution for over 20 years, I'm happy to say that a good PhD math-econ and econometrics course are sufficient to teach standard undergraduate quant methods/stats for econ majors courses at all but perhaps the very best universities.

Arash mentioned "pure theory." What Arash means to say is "abstract math."

I just read Ikeda's "Dynamics of the Mixed Economy." That book is pure theory. I defy anyone to mathematize the complexities of Ikeda's theory. The same statement goes for most of the Austrian work I've read - if not all. I don't say all because I'm against absolutes. Without a doubt.

Roger's first point is incomplete because he failed to mention that philosophers are the smartest in the humanities. So we end up with physics, economics, and philosophy. What are the commonalities of all three? Quantum physics in particular comes closest to being "philosophical" of any of the physical sciences -- physics, chemistry, biology, psychology. Economics is the most philosophical of the social sciences -- psychology, sociology, economics, etc. And philosophy is, well . . . So one could argue that it isn't necessarily the math, but the level of philosophical involvement.

#1 and #5 are sides of one coin -- the economics profession demands a formal metric for demonstrating understanding, because the material is otherwise very very hard and "good science" and "good economics" would otherwise be essentially contested and open to contention at every point in the guild process of "scientific" accreditation of journey-men economic "scientists".


I don't hide behide anyone. And I certainly do know the difference between undergraduate math and proofs. I taught at NYU and attended the Roy Radner seminar, and I spent a year at Stanford and attended both Milgrom's Comparative Institutional Analysis seminar and also the Social Choice Seminar.

There is a difference between reading and working with proofs, and actually being someone who can produce proofs. I never claimed to produce proofs.

In my own reading of economics theorems, I would say that Arrow's impossibility theorem, and Lucas's policy invariance. I think the work on mechanism design theory is important, but ultimately flawed (note the WSJ asked me to write the op-ed to honor Hurwicz, et.al. when they won the Nobel). But all of those results are flawed due to the tie to General Competitive Equilibrium theory; which I respect for its elegance but don't think it actually captures the invisible hand idea.

I don't really understand your rhetorical stance. I am not hiding behind anyone, my opinions are out in the open and also very visible in my publications, etc. I read economics all the time, I talk economics all the time, and I strive to continually learn from other economists all the time. I get accused by some of being so willing to learn from others that I sell out my Austrianism, while from you I am being accused (if I understand what you are saying) of being so stupid I cannot read papers in the journals and to know the difference between intermediate micro and pure theory and completely out of touch with the economics profession. So I get it from both ends.

My response.

1. A lot of what gets said about GMU is nonsense not based on any real knowledge;

2. A lot of what gets said about me, I don't agree with but I don't own a property right in my reputation so I cannot control what others think;

3. With regard to me, you get what you see --- my publications are public and easily available, my courses are public and easily downloaded, and my attitudes about economics are easily gleaned from my classes, my publications, and of course from the blog;

4. I think most people who think they can do theory, really cannot do theory and therefore should have a reality check about what they can and cannot do --- this is especially true of those not teaching at the very top graduate programs. It would be better if economists focused their energies on real problems rather than thinking they will develop new theories.


Other formal work I have learned from --- Dixit on irreversible investment; the Shleifer paper on shortages in the socialist economy; Fisher paper on disequilibrium foundations; Axtel paper on exchange; etc.

Most of the formal papers I read --- e.g., Stiglitz on asymmetric information and imperfect markets --- I find negative value in. They show what it is that is wrong with many mainstream results. And how far we have to go to reoriented economics along the Mises-Hayek lines I think is more productive research wise.

Bottom line: reading economics is not only fun for economists (that is why we become economists) it teaches us even when we disagree. We all need to learn to read formal papers otherwise you really cannot be a critic of economics. This doesn't mean we can produce formal papers -- especially one that is elegantly reasoned.

Arash -- I recommend that you look at 2 volume reference work that Prychikto and I edited on Market Process Theories. Formal theory circa 1960-1990 is well represented.


Professor Boettke,

Thank you for your insight. Here are my two cents.

I think the signalling aspect of math courses is most important going from the transition from undergrad to graduate school. An MIT econ grad student doesn't exactly need another honors analysis course to show his quantitative prowess. Rather, whether they are wrong or not, I think most top theorists (and those who hire them) genuinely believe that mathematical sophistication is the road to understanding economic phenomena.


Touché! My comment was way over the top. Excuse me. Your tempered response makes ME look stupid. Let me just say that 'stupid' is not a notion I think of when it comes to you or GMU. I still think that you are too negative when it comes to math econ, but perhaps this is because I'm so impressed by the negative results you mentioned. Without the formulist turn, there are no such results that can be turned against statist thinking. I also believe that in understanding why general equilibrium reasoning (including groping and the like) is not a good description of real market processes, we gain some hints at some properties of the system. The 'anything goes' implication of SMD, for instance, indicates that the system is more than the some of its components. So please excuse my harsh language. Certainly, it was not the best of my moments.

The problem with math in economics is that what is being studied -- both the humans in the system, and the system itself -- are far more complex than any math currently developed. That is, there is no such thing as a mathematics of economics. One can model a few incredibly simple sub-sub-sub-sub-sub-processes, but that's all. Statistical analyses are also of extremely limited value, because too often it hides what is really happening under the broad statistical umbrella.

Can one mathematically model any human being's behavior? Can you use math to accurately predict any individual's behavior? If the elements of economic study are mathematically incalculable, then can the economy be mathematically modeled in such a way that predictions are possible?

It's not even possible in biology, which is two magnitudes less complex than an economy. But the methods increasingly used in biological research are far more appropriate than are the mathematical methods of physics and physical chemistry. For the typical biochemist, molecular biologist, cellular biologist, etc. on up in complexity, the only math needed are Calculus I and biostatistics in grad school. Why? What is being studied is too complex to be understood using math.

Economics will remain backwards as a science until it gets over its math fetish -- or until the math finally catches up with the thing being studied. Which has happened to some degree with complexity math, catastrophe theory, self-organization, bios, etc. But each of these do not allow you to predict anything; they only allow you to make models to see if what you are getting resembles reality as it was at some point. For complex sciences, that is all that can ever happen.

"Austrians" write as if Kuhn and Wittgenstein and Hayek never happened.

Bourbakism / the formaist mistake just is the false idea that meaning and significance and causal explanation can be separated into formal structures of syntax and "given" interpretive semantics.

This is pre-Kuhn, pre-Wittgenstein, pre-Hayek thinking.

The proof against the "math" pictue of economic explanation is simple.

The central explanatory causal elements of economic explanation cannot be put into math constructs -- i.e. entrepreneurial learning and rule following (e.g. behaving according to the patterned rules of property)..

And the empirical pattern that gives rise to the demand for explanation is itself not a mathematical construct -- the pattern of the global economic coordination of plans exhibiting the tendency within it were prices tend toward costs.

And this stuff isn't about given "meanings" in the head or about the interpretation of syntatical structures.

It's about causal mechanisms and emperical patterns that don't take the form of math formulas or math rpoofs or tractable math constructs.

Hence the math as syntax with semantical interpretive narration picture is WRONG.


"Mathematical economics and quantitative methods are in high demand by those hiring economists outside of academia, and thus professors who can teach mathematical and quantitative methods are valued by universities and colleges"

I think this is by far the most important. Quantitative methods especially are useful outside of academia in the private sector, for market research and such.

I really don't care for these global, timeless assessments of what math can and cannot do. " Math is rigor!" "Math cannot capture learning!" Math is not one unchanging thing. "Geometry is about simple shapes and cannot capture the infinite complexity of English coastline." Right. Until, that is, Benoit Mandelbrot figures out how to model the English coast as a fractal. It makes sense to make judgments about current tools and literature. Sure, you absolutely can do that. But some of these grand judgments about what math as such can or cannot do go too far IMHO, because they literally pre-judge tomorrow's knowledge. I had better throw in a qualifier for computability results as in the JEBO paper I keep touting on this thread. In that case, however, you have a mathematical argument for the limits of math, which seems to be logically fine. I am objecting to grand statements based on somewhat vague general principles that would pretend to either permanently close the door to mathematics in some area or, on the other side, equate mathematics with sound reasoning.

Roger -- It begs the question to assert that Wittgenstein's results lie outside of "math" or outside of "logic" or outside of "formal logic", etc, just as it would would beg the question to assert that Mises's (parallel) Socialist Calculation Argument lies outside of economics.

Equally, it begs the question to assert that Hayeks's results about the limits to the prediction of the advance of science and limits to the knowledge of economic phenomena or limits to the knowledge our knowledge of the knowledge achieved by an individual mind/brain lie outside of "science" or outside of "economics" or outside of "cognitive science" or outside of "social science" or whatever.

After Kuhn and Wittgenstein and Hayek we have achieved an important understanding -- an understanding that formal systems are achieved and embedded within ourselves and our social systems, and no formal result can undo this achieved understanding

And this embedding has implications for our understanding of math and logic and other formal systems -- as well as for our understanding of such social structures as language, law, and economic order, all of which are at once social and individually embedded.

Roger writes,

"In that case, however, you have a mathematical argument for the limits of math, which seems to be logically fine."

The problem is with the LOGICAL and MATHEMATICAL incoherence of the formalist conception of logic and mathematics -- something exposed by Wittgenstein and by 130 years of intractable pathology in the philosophy of language, the philosophy of the foundations of mathematics, and in the philosophy of mind, etc., which is also revealed via direct paradox in the pure mathematics and logic of Godel and Russell, etc. as well as in the endless cul de sacs and muddles of all the other big names in the philosophy of math and logic and language and mind.

Look. Learning and discovery takes us into the realm of novelty and the previously unknown -- into the realm of previously unimagined conceptions.

Math and deduction isn't going to tell us much about that, other than as a exemplar, and a very limited and misleading one at that.

Roger writes.

"I really don't care for these global, timeless assessments of what math can and cannot do. " Math is rigor!" "Math cannot capture learning!""

Roger also writes,

"Math is not one unchanging thing."

OK. In this sentence you are sounding like Wittgenstein, to the point were you are all but conceding my argument ...

"grand statements based on somewhat vague general principles"

This sort of sentiment explains why economists reject good economics and insist on the formalist project.

It also is part of the explanation of why "top" philosophers embrace the endless publication opportunities provided by the degenerate research programs of the formalist projects in philosophy -- the profession as a profession needs a mechanical formal metric for demonstrating and evaluating understanding, and Wittgenstein's and Kuhn's and Hayek's deep and true understanding of the phenomena at hand does not give you that -- it doesn't give you a "mark-sense form" mechanical procedure for determining "who is smart" and "who is competent" that a professional organization needs and demands.

Call it "Seeing Like an Academic Profession".

Here's a simple question for Pete and everyone.

Has James Scott told us something important about needs and structure of a modern state in his book _Seeing Like a State_?

Is so, how do the needs and structure of a state differ from those of the professional academic guilds or the bureaucratic structures of the modern university?

When physicists confront phenomenon that defies tractable mathematics they say so it and mark down understanding of this fact as a scientific achievement.

Are economists better scientists than physicists because they refuse to do so?

There are all sorts of limits to the application of mathematics to physical systems (e.g. see the work of Nancy Cartwright).

Roger, is that a limit to math, or a limit to science, or a limit about the world? -- or is this result one you have compelling reasons to say will certainly be overcome by math in the future?

And do the same arguments apply to Mises' and Hayek's arguments about socialist calculation and the knowledge problem?


Yes, Goedel blew up Hilbert's program and Wittgenstein was great. I have a whole chapter in my Big Players book about language games. And even in the short comment you are responding to I throw in "a qualifier for computability results." And I certainly never said and do not feel that math has magic powers to neutralize verbal arguments or something like that. Even in the brief comment to which you are responding, I reject the view that somehow math is uniquely rigorous or something. So I most certainly do not "insist on the formalist project."

What I objected to was grand statements to the effect "here mathematicians may not go." (I also objected to sweeping statements on the other side, but let that go for now.) Let's take up Wittgensteinian language games as an example. In my Big Players book I was driven to construct a set theory model of language games to clarify an important point. In some sense, it is the actor(s) and not the scientific observer who picks the language game being played. And yet the social scientist is in some sense free to pick a description of the relevant language game that might be unrecognizable to the agents(s). That's kind of weird, and it looks like it might be a contradiction. I think (I hope!) my set theoretic exercise helps to show that there is no contradiction or even much of a paradox in asserting the "freedom" of both actor and scientist. The sort of sweeping statements I object to would rule out such a mathematical exercise ahead of time.

There is a common formal result in Wittgenstein and Hayek -- the many-many problem which blocks reduction. (See Hintikka on Wittgenstein's many-many problem, and Kuhn's most basic explication of the Hayekian many-many problem of perception and classification [which fails to credit Hayek]. Hull's phenotype / geneotype many-many problem is a paradigm of the form.)

"Language games" are linked across endless structures with "many-many" problem linkages.

But this is compounded by something more profound -- the fact that these games are embedded not in "givens" of meaning, but in common ways of going on together. The same point is implicit in Hayek's work on the "motor" foundations of categorization and the "imitated ways of acquiring traditions" found in Hayek's work on "unarticulated rules for applying articulated rules" -- a common issue shared by Hayek and Wittgenstein.

I'm not sure how anything I've said would rule out your own work.

But certainly, I don't think David Lewis has capture the fundamental nature of rule following and collective rule structures well in his own formal framework -- but in no way do I rule out the fact that these formal efforts do help us achieve understanding.

Very often, as Pete suggest (and Mises shows) by showing what the formalism as a matter of logic necessarily fails to capture.

Greg I think we had a consensus, at least some of us agreed that you need to understand the details of the problem, the rival theories and maths to decide whether maths (and which kind of maths) is useful in a particular situation.

On Wittgenstein, there is an alternative explanation of his influence, along the lines that he promoted or at least added impetus to two dead ends in academic philosophy. One was positivism and its offshot, logical empiricism. The other relates to the analysis of language and language games.

The "forms of life" and "games" approach could have been useful if only the followers had applied themmselves in a critical and informed manner to real games, and to institutional analysis of social, political and economic systems. Real scientists like Roger have picked up that ball and run with it, but how many others?

Karl Popper could have done the same thing but he wasted his opportunity in New Zealand to learn about cricket and football because his close friend, the economist Colin Simkin, hated manly outdoor games, being a lover of classical music, so he turned his back on them. Instead of introducing him to cricket, which would have helped Popper to develop his model of situational analysis and the rationality principle, he filled young Karl's head with stuff about demand analysis and Scandanavian welfare policy. For his part, Karl encouraged Colin to press on with mathematical economics.

Bill Bartley explored the early careers of Wittgenstein and Popper and found they were both shaped by the non-reductive psychology of the Wurzberg School (Selz, Kulpe,Buhler) and the Gestaltists. So their basic perception of the fundamental problems was similar but their responses were very different. Bartley wrote several papers to explain how the Wittgenstieniann problematic took root in the philosophical community and turned it into a machine for producing publications and professional advancement, but not insight, integration with other fields, or illumination of basic problems.

Bartley wrote a lot so I have abbreviated some of the papers.




This is the short form of the 10,000 word paper on Wittgenstein and Popper as Austrian schoolteachers.


Rafe, I disagree with Bartley on Wittgenstein -- I see evidence that Bartley gets Wittgenstein.

Certainly there is no evidence that Popper read or offered arguments against Wittgenstein's later work -- it's all an attack on the Tractatus passed off as something more.


I see no evidence that Bartley gets Wittgenstein.

Rafe, I see Bartley's non-justificationist / critical position as compatible wih Wittgenstein -- and Kuhn.

These writers are best viewed as supporting a common larger project -- a project also advanced by Hayek.

Thanks Greg, we will have to agree to disagree for the moment, this is not the place to continue this debate:)

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