orgtheory.net

the death of mathematical economics

Over at Econlog, Bryan Caplan notes the decline of mathematical economics, or “theory” as  it is called inside their profession. He asks (1) how can you measure that status decline? and (2) why the decline?

1. In the sociology of science, status of people, specialties or institutions is measured in a number of ways. For example, Burris (2005) used hires by elite departments. So once you identified math econ PhDs, you could measure status by comparing hires among, say top 20 depts, with hires in other specialties. You could even do a nice analysis of the speciality-department hiring network, like Burris did.

Other measures include: top journal placements (Caplan already notes this), citation counts, and prizes (Clark/Nobel awards). I’m not an insider, so I’ll take Bryan’s word that econ journals publish little math econ, which almost certainly means less citations because top journals get the most citations on average. Once again, I’m not an insider, but the list of Clark and Nobel medals show few purely mathematical economists in recent years. Hurwicz’ award a few cycles back is the only one that pops out at me, and he was *really* old.

2. In the study of scientific specialties, you get the following theories: (a) intrinsic – the status is based on the usefulness in building knowledge; (b) Abbott’s thesis – professional groups gain status by making a political/social argument that they should have a monopoly on some topic (e.g., doctors can only prescribe medicine); (c) life cycle – all specialties have a life course, people only get high rewards if they get in early; (d) supply and demand – for some exogenous reason, you get a shift in the number of competitors. Of course, more than one may have explanatory power.

Here’s the way I’d sift through the evidence. Around the 1940s or so, economics began a institution building project. They needed things to bolster scientific credibility. They chose mathematics as their strategy. At the time, there was little else they could do. Data was hard to obtain and difficult to process, and it wasn’t clear how to build experiments into the repertoir. But math was cheap – no extra funds needed and the tools already existed. Just translate everything into calculus, a la Samuelson. That leads to the drive from 1950 to about 1980 where all qualitative economics is ejected in favor of what you see today.

So the mathematical economists served a crucial professional function. They helped other economists feel better about themselves and increase their legitimacy. At the same time, math econ produced occasionally fantastic results (e.g., the Arrow impossibility theorem). So it wasn’t a bad deal for the profession as a whole. The initial status of math econ is probably something like 10% real success (via theory building) and 90% public good for the economics profession. Or a little (a) and a lot of (b), in my scheme.

Then, around 1990, you see other processes kick in. Desktop computing transformed all the social sciences. There was now another way to do high status activities, there’s real competition (d). There is also the life cycle issue (c), or “low hanging fruit.” A lot of easy problems are done, but now everything is very, very hard. Easier to just choose another specialty. People just get bored with the math and strive for something more concrete.

Finally, there’s a social psychological explanation. Economics is filled with cohorts who already know a bit of math. Econ programs require calculus + real analysis, which is the core math major at many colleges. So you probably don’t have much status anxiety and you can start focusing on the real world again. That likely translates into job hires and editorial decisions. You can unplug from the matrix and get back into the real world.

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Written by fabiorojas

March 6, 2011 at 12:56 am

20 Responses

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  1. I think there’s a lot to be said for the idea that “highest” sort of theory was in many ways a kind of foreign import that did not fit all that well with the characteristic style of American economics. The sort of French purity associated with Debreu had its postwar moment, but in recent decades American economics has returned to its pragmatic roots. Marion talks about this a bit in her book.

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    Kieran

    March 6, 2011 at 1:08 am

  2. I don’t think anything in terms of technology prohibited early experiments. Vernon Smith did some of the first trials in the ’50s. There are also Field Experiments, as with List, that don’t need any fancy technology.

    What’s also missing in this account is ideology. Samuelson and others liked that they could formalize a Keynsian economics. Friedman and others liked that they could formalize their own version of economics.

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    Thorfinn

    March 6, 2011 at 2:52 am

  3. The 2001, 2005 and 2007 Nobels all went to pretty pure theorists, and the 2003 prize to theoretical econometricians. In 05 and 07, the prize went to *really* theoretical economists. Three prizes a decade looks to be the norm back through the start of the prize, so I don’t see too much change.

    Two of the six Clark winners (Athey and Rabin) likely won for their theory work, though both certainly work in other areas. I see no Clark winners in theory in the 90s.

    The REStud tour, generally considered a fair estimate of the top few new PhD graduates every year, has seen no decline in invites from theorists. Demand at top schools for theorists doesn’t look to have changed recently.

    What is different is that demand for theorists at lower-ranked schools was particularly low the last couple years. But this isn’t surprising: we’re in the middle of a major recession! Hiring in general is down, and demand for applied work like explanations of the financial crisis is, unsurprisingly, up. This doesn’t strike me as a long-term issue.

    The only two long-run changes I see are that – outside of MIT and a handful of other places – applied work is *more* theoretical than it has been in the past. Also, computing power and funding for field experiments has increased, so empirical work in these areas is more common.

    Top econ journals certainly still publish a lot of pure theory. Econometrica is still almost wholly theory, and the other top journal in econ, the AER, published 3 articles that are *pure* theory in its last issue (I’m using December, b/c February is the 100th anniversary issue and a bit strange for that reason).

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    afinetheorem

    March 6, 2011 at 4:52 am

  4. @afinetheorem: I think there’s a bit of difference between what Caplan calls “theory” and what you might call theory. For example, you note econometricians. From the tenor of his post and others, he’d probably put “theory” and statistics in separate camps.

    But here’s the bigger issue for an outsider. When I first encountered economics in the early 1990s, I also found that mathematical economics ruled the roost. Debreu’s work was shown to me as a paragon of science.

    Now, the economics profession has taken a very sharp turn toward identification, experiments, behavioral and so forth. Mathematical? Sure, but not quite the high tech wizardy of past eras. That doesn’t mean that mathematical economics is banished, but you no longer have to prove equilibrium theorems in Banach spaces to impress people. A good instrument or experiment might do the trick.

    The more I think about this issue, the more I think it has to do with a recalibration of the field. As econ became more mathematical, the definition of “theory” changed a fair amount. If *everyone* has to know real analysis just to get through the first year of grad school, then the meaning of theory has changed. Now everything (in econ) has a lot of math in it, so there’s a lot of “theoretical” work being done. But that’s not quite the same as the brand of mathematical economics that Caplan is referring to.

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    fabiorojas

    March 6, 2011 at 7:19 am

  5. I agree: the econometrics isn’t what I would consider pure theory. But Athey won a Clark a couple years ago, for example, for work on monotone comparative statics in auctions. The 2005 Nobel went to Aumann and Schelling, and Aumann is the ur-theorist in economic history.

    I think experimental economics is a good example, actually. A huge portion of the econ profession still looks rather skeptically on lab experiments. Field experiments in the MIT Poverty Lab/John List style are pretty widely accepted now, but even there, a large portion of the profession thinks there is not much value in work with limited external validity. This is why RCTs and other experimental work is now quite common in, say, education and development, where internal validity is more or less all we need, but less common in other areas of econ.

    I agree that foundational work in theory – Debreu on equilibrium existence, or various refinements of Nash – are more or less played out. But all this means is that theorists are working in different areas. I think a good argument can be made that the three most significant areas of new research in econ over the past decade have been development RCTs, auctions, and market design (e.g., Roth on organ donations). The last two have involved a huge amount of pure mathematical theory. Further, as you note, in macro and in health and other non-theory fields, any good article published these days contains very strong microtheoretical foundations.

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    afinetheorem

    March 6, 2011 at 8:10 am

  6. Also, sociology could use more math.

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    Guillermo

    March 6, 2011 at 5:01 pm

  7. Most of what is contained in this is just flat-out incorrect. “Mathematical Economics” as a field is dead, but its influence now touches every other subfield of economics. That’s about it.

    The rest is largely speculation. “Oh economists do math just to feel good about themselves” lol what a crock.

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    An Economist

    March 6, 2011 at 6:12 pm

  8. “If *everyone* has to know real analysis just to get through the first year of grad school,”

    Just shut the fuck up already, you are so ignorant that it’s getting painful to read your words. NOBODY has to know Real Analysis to get through the first year of grad school. Real Analysis is normally the first course you can take as an undergraduate that teaches you how to prove things – that is the reason it’s so useful. Any advanced math needed for PhD econ is presented on a need-to-know basis in the core sequences.

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    An Economist

    March 6, 2011 at 6:18 pm

  9. Caplan is really out of touch with the profession as a whole, as are most of the GMU faculty. He has no idea how the profession values pure theory, because he has never seen any. Analysis has always been required at decent schools (read: not GMU) because without one cannot even prove simple properties of models.

    Caplan and the rest can keep wishing, but it isn’t coming true — theory will always have a primary place in economics, and the crap they peddle at GMU will not.

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    Jabbadoo

    March 6, 2011 at 8:01 pm

  10. @ Economist: Real analysis is absolutely a requirement for PHD economics at any of the schools that put out academic researchers. If you haven’t already taken it, it’s part of the required first year sequences, and you won’t get into a good school without it.

    @ Fabio: I think another thing that mathematics does for economists is to restrict the supply of economists, thus putting on a premium on those that can make it. The emphasis on real analysis surely keeps a lot of would-be economists out, as does the *minimum* requirement of an 800 on the quantitative section of the GRE.

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    Charles Seguin

    March 6, 2011 at 8:28 pm

  11. @CharlesSeguin: Our anonymous friend seems to be implying that analysis is prerequisite to participation in an economic graduate program. I think you two are in agreement on that particular point.

    Pro-tip: I personally tend to not try to engage with people who begin their replies with long insults introduced with “just shut the fuck up.” They’ve made it clear they not here to engage in anything resembling meaningful or civil discourse. DFTT.

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    Benjamin Mako Hill

    March 7, 2011 at 1:28 am

  12. @Benjamin

    Good call on the pro-tip.

    Perhaps the economist and I are in disagreement about what to actually call “real analysis”. I took what was called real analysis with a number of econ PHD students at a fairly high ranking school (U of Minnesota). It was part of their first year sequence, and definitely wasn’t a first course on proofs.

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    Charles Seguin

    March 7, 2011 at 2:13 am

  13. In my country we had two recent presidents from “decent schools” (Harvard and Yale). They plunged the country in its worst economic crisis ever.

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    Guillermo

    March 7, 2011 at 4:46 pm

  14. It was a statement of fact. You do not need Real Analysis (or “Advanced Calculus”, or whatever it’s called at a particular institution) on your transcript to get into a good school, period. A couple of years back someone posted that a significant number of students at UCLA did not have Real Analysis, about half if I remember correctly. UCLA is a top 20 school at worst.

    Funny you call out people in the responses for their “insults”, yet when the OP says that Economists picked up math to “feel better about themselves” you sit silently. Seriously, fuck you.

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    An Economist

    March 8, 2011 at 2:35 am

  15. Geez, how can you write formal models without having studied real analysis? It’s pretty basic basic math really.

    I guess believing Caplan’s view of the state of modern economics is like believing a social philosopher’s take on the state of empirical sociology. A bit ridiculous.

    And churning out math models isn’t quite as easy as mining some longitudinal dataset for statistically significant effects; and its paucity is no indicator of formal models going out of favor (Fabio does hint at that, to be fair)

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    sd

    March 8, 2011 at 3:50 am

  16. I don’t know of any large-n study on this, but based on this thread, the stereotype of economists not being very nice or sociable or un-arrogant people is being confirmed.

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    Talleyrand

    March 8, 2011 at 2:22 pm

  17. @ Talleyrand,
    I agree that there is no call for rudeness and and vulgarity in this type of discourse. I shan’t defend their use. But I would offer a caution against painting economists who have, and have not, engaged in this thread as arrogant. After all, is it not arrogant for a sociologist to declare a part of economics (or any other field in which she/he has not published) as “dead”, particularly when the justification is, er…, breezy?

    The contributors to this blog provoke; the discourse is provocative. Occasionally, orgtheory.net provokes laughter, pique, snarkiness (guilty), scolding, and ire, in addition to scientific conversation. One hopes that rudeness would be held in abeyance when the conversation gets heated.

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    Randy

    March 8, 2011 at 4:25 pm

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