Home > Employment, Graduate Schools, Mathematicians > How many graduate students do we need?

How many graduate students do we need?

In response to my previous post “Academia is nothing like a drug cartel“, a fellow blogger Adam Sheffer asks:

I was wondering what you think about a claim that I sometimes hear in this context – that one of the problems is that universities train too many Ph.D. students. That with a smaller number of math Ph.D. students the above will be less of a problem, and also that this way there will be a smaller number of people dealing with less “serious/important” topics (whatever this means exactly).

This question is certainly relevant to the “adjunct issue”.  I heard it before, but always found it somewhat confusing.  Specifically to the US, with its market based system, who exactly is supposed to decrease the number of Ph.D.’s?  The student themselves should realize how useless in the doctoral degree and stop applying?  The individual professors should refuse to accept graduate students?  The universities should do this together, in some kind of union?  The government?  All these questions are a bit different and need untangling.

I was going to write a brief reply, but after Adam asked this question I found a yet another example of lazy journalism by Slate’s “education columnist” Rebecca Schuman who argues:

It is, simply put,  irresponsible to accept so many Ph.D. students when you know graduate teaching may well be the only college teaching they ever do.

Of course, Dr. Schuman already has a Ph.D. (from our neighbor UC Irvine) — she just wants others not get one, perhaps to avoid her own fate of an adjunct at University of Missouri.  Needless to say, I cannot disagree more.  Let me explain.

Universities are not allowed to form a cartel

Let’s deal with the easy part.  If the American universities somehow conspired to limit or decrease the number of graduate students they accepts, this would be a classical example of anti-competitive behavior.  Simply put, the academia would form a cartel.  A textbook example of a cartel is OPEC which openly conspires to increase or decrease oil production in order to control world energy prices.  In the US, such activity is against the law due to to the Sherman Act of 1890, and the government/courts have been ruthless in its application (cf. European law to that effect).

One can argue that universities are non-profit institutions and by definition would not derive profit should they conspire, but the law makes no distinction on this, and this paper (co-authored by the celebrity jurist and economist Richard Posner) supports this approach.  And to those who think that only giants such as Standard Oil, AT&T or Microsoft have to worry about anti-trust, the government offers plenty of example of going after  small time cartels.  A notable recent case is Obama’s FTC going after Music Teachers National Association, who have a non-poaching of music students recommendation in their “code of ethics”.  Regardless what you think of that case, it is clear that the universities would never try to limit the number of graduate students in a similar manner.

Labor suppy and demand

As legions before her, Schuman laments that pospective grad students do not listen to “reason”:

Expecting wide-eyed, mind-loving intellectuals to embrace the eventual realities of their situations has not worked—yes, they should know better, but if they listened to reason, they wouldn’t be graduate students in the first place.  Institutions do know better, so current Ph.D. recruitment is dripping with disingenuousness.

But can you really be “wide-eyed” in the internet era?   There is certainly no shortage of articles by both journalists and academics on the “plight” of academic life – she herself links to sites which seem pretty helpful informing prospective graduate students (yes, even the link to Simpsons is helpful).   I have my own favorites: this, that, that and even that.  But all of these are misleading at best and ridiculous at worst.  When I mentioned them on MO, José Figueroa-O’Farrill called them a “parallel universe”, for a good reason.

You see, in this universe people make (mostly) rational decisions, wide-eyed or not.   The internet simply destroyed the information gap.  Faced with poor future income prospects, graduate students either choose to go elsewhere or demand better conditions at the universities.  Faced with a decreasing pool of candidates the universities make an effort to make their programs more attractive, and strive to expand the applicant pool by reaching out to underrepresented groups, foreign students, etc.  Eventually the equilibrium is reached and labor supply meets demand, as it always has.  Asking the universities (who “do know better”)  to have the equilibrium be reached at a lower point is equivalent to asking that Ph.D. programs become less attractive.  And I thought Schuman cares…

Impact of government actions

Now, when it comes to distorting of the labor market, the government is omnipotent and with a single bill can decrease the number of graduate students.  Let’s say, the Congress tomorrow enacts a law mandating a minimum wage of $60,000 a year for all graduate students.  Of course, large universities have small armies of lawyers and accountants who would probably figure out how to artificially hike up the tuition for graduate students and include it in their income, but let’s assume that the law is written to prevent any loopholes.  What would happen next?

Obviously, the universities wouldn’t be able to afford that many graduate graduate students.  The number of them will plunge.  The universities would have to cut back on the TA/recitation/discussion sessions  and probably hire more adjuncts to compensate for the loss.   In time, this would lower the quality of education or lead to huge tuition increases, or mostly likely a little bit of both.  The top private universities who would want to maintain small classes will become completely unaffordable for the middle class.  Meanwhile the poorer state universities will commodify their education by creating huge classes with multiple choice machine testing, SAT-style, and further diminishing student-faculty interaction.  In fact, to compensate for their increasing cost to universities, graduate students will be asked to do more teaching, thus extending their time-to-degree and decreasing the graduation rates.

Most importantly, this would probably have no positive effect on decreasing competition for tenure track jobs, since the academic market is international.  In other words, a decreasing american supply will be immediately compensated with an increasing european supply aided with inflow from emerging markets (ever increasing in quantity and quality production of Ph.D.’s in Asia).   In fact, there is plenty of evidence that this would have sharply negative effect on prospects of American students, as decreased competition would result in weaker research work (see below).

In summary, who exactly would be the winners of this government action?  I can think of only one group: lazy journalists who would have many new reasons to write columns complaining about the new status quo.

The out of control academics

Let’s go back to Schuman’s “it is [..] irresponsible to accept so many Ph.D. students” quote I mentioned above, and judge in on moral merits.  Irresponsible?  Really?  You are serious?  Is it also irresponsible to give so many football scholarships to college students if only a few of them can make it to the NFL?  Is it also irresponsible to have so many acting schools given that so few of the students become movie stars?  (see this list in my own little town).  In the previous post I already explain how graduate schools are apprenticeship programs.  Graduate schools give students a chance and an opportunity to succeed.  Some students do indeed, while others move to do something else, sometimes succeeding beyond expectations (see e.g. this humorous list).

What’s worse, Schuman implicitly assumes that the Ph.D. study can only be useful if directly applicable to obtain a professorship.  This is plainly false.  I notice from her CV that she teaches “The World of Kafka” and “Introduction to German Prose”.  Excellent classes I am sure, but how exactly the students are supposed to use this knowledge in real life?  Start writing in German or become a literary agent?   Please excuse me for being facetious – I hope my point is clear.

Does fewer students means better math?  (on average)

In effect, this is Adam’s speculation at the end of his question, as he suggested that perhaps fewer mathematics graduate students would decrease the number of  “less ‘serious/important’ topics”.  Unfortunately, the evidence suggests the opposite.  When there is less competition, this is a result of fewer rewards and consequently requires less effort to succeed.  As a result, the decrease in the number of math graduate students will lead to less research progress and increase in “less important” work, to use the above  language.

To see this clearly, think of sports.  Compare this list of Russian Major League baseball players with this list by that of Japanese.  What explains the disparity?  Are more Japanese men born with a gift to play baseball?  The answer is obvious.  Baseball is not very popular in Russia.  Even the best Russian players cannot compete in the american minor leagues.  Things are very different in Japan, where baseball is widely popular, so the talented players make every effort to succeed rather than opt for possibly more popular sport (soccer and hockey in Russian case).

So, what can be done, if anything?

To help graduate students, that is.  I feel there is a clear need to have more resources on non-academic options available for graduate student (like this talk or this article).   Institutionally, we should make it easier to cross register to other schools within the university and the nearby universities.  For example, USC graduate students can take UCLA classes, but I have never seen anyone actually doing that.  While at Harvard, I took half a dozen classes at MIT – it was easy to cross register and I got full credit.

I can’t think of anything major the universities can do.  Government can do miracles, of course…

P.S.  I realize that the wage increase argument has a “fighting straw men” feel.  However, other government actions interfering with the market are likely to bring similarly large economic distortions of the academic market, with easily predictable negative consequences.  I can think of a few more such unfortunate efforts, but the burden is not on me but on “reformers” to propose what exactly do they want the government to do.

P.P.S.  We sincerely wish Rebecca Schuman every success in her search for a tenure track appointment.  Perhaps, when she gets such a position, she can write another article with a slightly sunnier outlook.

  1. December 19, 2013 at 5:05 pm

    One action the government could take to reduce the number of Ph.D. students (if that were a desirable goal) would be to stop funding graduate fellowships (through the NSF, department of education, and others).

  2. December 19, 2013 at 6:12 pm

    Surely the best thing the government could do for current grad students (and all academics, in fact) is increase funding for research.

  3. December 19, 2013 at 6:14 pm

    @Ben Lund – Sure. This is indeed a way to do that. This would result in very small negative effects in some fields and enormous negative effects in others. In math, with its large army of roughly 1500 new grad students a year, the 30-60 NSF and DOD fellowships constitute a tiny portion. Support from the NSF grants maybe doubles the effect. In total, this would result in making math graduate programs maybe 15-25% more expensive with a minor version of negative effects I describe above. The big picture won’t change, maybe 10% decrease in students and their stipend, and 10% increase in graduate tuition, offset by raised college tuition. A noticeable side effect would be a decrease in the number of US students and increase in the number of foreign students, who are ineligible for the NSF fellowships.

    In humanities where there are very few such fellowships to begin with, so things would remain completely unchanged. However, in many areas of Chemistry, Experimental Physics, Computer Science, Biomedical Sciences, etc. – all sciences which require a lot of lab work, many grad students are supported by the research grants. There, such government action would have devastating effects similar to the one I described above.

  4. December 19, 2013 at 7:26 pm

    @Samuel Hopkins – Right. Except that would lead to increase in the quality and the number of math graduate students. Rebecca Schuman would be so disappointed…

  5. December 27, 2013 at 7:18 am

    Thanks for the great answer!

    You write “this is Adam’s speculation at the end of his question”. Just to clarify – this is not my personal speculation, but rather a claim that I sometimes hear from various friends. I don’t think that I can say anything against “dealing with less serious/important topics” since I bet that this is exactly what people used to say about combinatorics.

  6. February 1, 2014 at 12:58 am

    Hi Igor –

    Just a few thoughts.

    (a) The comparison with a drug cartel most likely comes from Freakonomics. If I remember correctly (I leaft through the book while waiting in an airport), the point there is not that a drug cartel is something terribly unique, but rather that a drug cartel operates much like a run-of-the-mill corporation, or, rather, like a large company with a particularly bad reputation for poor salaries and working conditions at the bottom of the scale (such as, er, McDonald’s). I think the book even draws the parallel with teenagers who devote a great deal of energy to sports or the performing arts, whether or not they know that only a tiny number can make it to the top, often for reasons having to do with luck or connections more than anything else.

    So, I don’t think you are making the case any weaker, and you may have unwittingly made it stronger 🙂 . What you have managed to support is the point that a comparison with a drug cartel is sensationalistic (rather than false): why not compare academia directly to McDonald’s or to sports, as you have done?

    (b) Personally, I agree that most service courses can and probably should be taught by non-researchers; researchers are not particularly good at them, and their time can be used more effectively in other ways (such as, er, doing research, and educating people who are likely to try to become researchers). Still, freshmen need some contact with researchers, or otherwise only those who are particularly well oriented (meaning, in part, those from academic families…) are likely to become researchers. Of course, one can say the same thing about high school students, but that doesn’t make it less true. There are plausible solutions to this: for example, an introductory seminar to contemporary mathematics can be taught side-by-side with service courses – and then, for that matter, a few researchers actually *want* to teach Calculus.

    (c) Further on (a): especially in times such as this, an argument of the form “this is how it is done elsewhere in the economy, hence it is fair” is going to weaken, rather than strengthen, any sort of case.

    Incidentally, as you have yourself implied by a comparison with managers – large pay differentials often have to do much more with position in the hierarchy than with job performance. The former has *a little* to do with the latter, but it also depends on other kinds of ability, including the ability to be extremely unpleasant; to give an example that nearly all academics can relate to – we all know (very well-paid) deans who are poor researchers, and/or have left research altogether. About the only way to get paid substantially more for doing a much better job than your peers is to change institutions; again, one’s ability to do this certainly isn’t hurt by being a good researcher, but it also depends on personal factors and on many other things over which an individual has little control.

  7. February 1, 2014 at 5:57 pm

    Hi Valuevar! (I not sure if you want others to know who you are, so let’s go with that).

    Your comments are interesting, but I don’t think you are really arguing with me – more like reinterpreting what I wrote in a different value system. You seem to agree that we don’t need fewer graduate students, but disagree with my approach. Here is how I see it.

    a) You think comparisons to MacDonalds and sports present academia in a bad light. I disagree. Take sports. Everyone knows that some players make millions while others are less valuable and sit on the bench just in case somebody is injured. No one will seriously propose to pay top players less (or they will go play for another team), or ask to give more money and playing time to people on the bench (teams have fixed number of players and salary caps). Yet, in academia these are the type or requests we are hearing.

    Same with MacDonalds. No, not my favorite restaurant. But clearly highly successful as a business venture, pioneer in the field. No one seriously writes articles telling them how to conduct their business. Why do journos think it’s ok to tell us how we need to conduct our business is beyond me.

    b) Sure, maybe. In fact, I basically agree. But again, each university department can make their own decision on that. Since we all compete for best students, whoever has better approach will win and be an example to others. So why conduct a public hearing?

    c) Your market-forces-are-bad and many-managers-are-undeserving argument seems weak to me. In math like in life it takes many skills to succeed, that’s not a good argument against the system. You need to speak clearly, write carefully but fast, work well with others (aka “team work”), be organized enough to meet deadlines, etc. None of this is particularly fair to a very smart person lacking some of these qualities, but who cares? My claim is that academia the most meritocratic community I can think of. To those telling us how to be even fairer, I suggest they should look around take their zeal at worse offenders. Say, here is an drastic 200x salary gender gap for top players in major basketball leagues: http://tinyurl.com/lonedsh

  8. February 15, 2014 at 11:14 am

    I did not bother making a case (weak or otherwise) for the general point you isolate in (c); it has been made enough times elsewhere, and most people are fairly convinced by now. Also, I would call “market-forces-are-bad” a mischaracterization; rather, what we are talking about is a kind of distribution of wealth and power, supporting itself on “The Market” as part of its theology, but resulting from a very specific combination of preexistent conditions, laws, market forces, government input and corporate culture. (Any modern economy is the result of such a combination – just a different one in each case.)

    Why should academia be different? Because many of us in academia believe (o claim to believe) in a value system different from the one you support (with a straight face or not). Of course, the same is the case elsewhere, to a greater or lesser extent – and, yes, there is plenty of criticism of MacDonalds in the press!

  9. February 15, 2014 at 4:19 pm

    I think I understand where you are coming from, it’s a respectable opinion. I do however worry when I read quotes like “most people are fairly convinced by now” or “many of us in academia believe “. They always remind me of Brezhnev’s speeches during my childhood, full of quotes on what “Soviet people believe” (in all fairness, other politicians employed the same trick). I say, we can have an interesting discussion just about our own views. But a couple of easy points on this.

    1) Many people can be easily wrong. For example, people used to believe the Earth was flat. So what? This happens even in math: Aristotle and his numerous followers believed that R^3 can be tiled with regular tetrahedra. The mistake was eventually corrected in the Middle Ages.

    2) While many people believe there is a certain kind of inequality, a lot of them also sensibly believe that correcting this inequality will lead to another kind of inequality. This might seem counter intuitive, so let me give an example. Apparently, 35% of French people believe “Jews have too much power in the business world.” http://tinyurl.com/kfpqzy3 A time honored way to deal with a “Jewish problem” is to introduce Jewish quotas or Jewish taxes:
    But of course this would be contrary to “égalité” and I haven’t heard of serious proposals to enact this in France.

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