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I am a current graduate student at a research-oriented university. Nonetheless, for me, it is a big mystery why and how the professors are incentivised to recruit and train the graduate students.

In an experiment-oriented research group, graduate students are the work-force of the principal investigator, so the professors train the graduate students to conduct experiments and research so that they contribute to the research group. However, in theory-oriented research areas such as pure mathematics, theoretical computer science, and theoretical physics, in many situations, graduate students do not contribute to the professor's research. They receive training and guidance for their research career unilaterally.

It should depend on the system for each nation, but what are the designed incentives for the professors in such areas to hire and train graduate students other than volunteer service spirit? In addition, I have heard that there exists an incentive system to push the professor to let their graduate students graduate within a reasonable time. What is such a system?

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    Well, in applied topics the funder is often the government and the government threatens to revoke funding unless graduate students and undergraduate students are used in research. – FourierFlux Sep 10 at 6:00
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    Many professors simply enjoy working with graduate students and get satisfaction out of the work, and the feeling that they are helping advance research in their field and train the next generation of researchers. There’s more to why people do things than economic incentives. – Dan Romik Sep 10 at 6:12
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    @DanRomik that should be an answer! – astronat Sep 10 at 7:57
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    In some cases the university either forces them or strongly pressures them to do so. Professors and other academic staff will have an expectation to have X-Y graduate students on their roll at any one time. Have too few (or indeed too many) and you may be questioned about it by your superiors. – Crazymoomin Sep 10 at 15:26
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    @RodrigodeAzevedo Hahahahaha. Well, ok, in some countries they can. But in the UK at least it's pretty hard at times to even spend it on your own research. A colleague won a large grant, and was allowed by the uni to freely decide how to spend something like £50. – Jessica B Sep 10 at 16:49
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Since you mention economic incentives, one obvious answer might be for teaching, at least this was the way it was in Germany. Even the most theoretical professor is supposed to teach a certain number of classes each semester. Generally the work involved in this is too much for one person alone, that is why the professor is supposed to do the lectures and the PhD students handle exercise classes and organisation. So its either supervise a bit on a research level or spend twice the time dealing with undergrad students having missed the deadline for their homework again because their grandfather died for the fifth time in this semester. Personally I'd know what I'd choose...

To this end each professor has a number of positions available, which can only be used to hire PhD students or postdocs. In particular it is not possible to hire someone to just help with the teaching without supervising them scientifically (Not that many qualified people would be willing anyway), or use the money for something else. Also like with any budget item, not using positions for too long is a great way to have them reallocated to someone else.

Regarding incentives to have them graduate on time, that one is also simple, if a bit unrefined: There is a maximum amount of years one can be employed in such positions. So in order to supervise the next student, the old one should be finished.

But I have to say that homo economicus is a spectacularly bad model for professors in theoretical subjects. Most of the ones I know are primarily motivated by science and would gladly work with a gifted student even without receiving any compensation.

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    +1 for the last paragraph especially. – astronat Sep 10 at 7:58
  • I also would not restrict the last part to theoretical subjects. The other way around, there is a subset of applied sciences or rather sub-fields in some sciences that focus on applied branches with a particular notion of close industry collaboration and there the likelihood is larger to meet homo economicus in professor garb. There are lots of professors in applied sciences that kept their ivory tower intact and like it being built on non-monetary motivation just like your theoretical subject profs. Okay, and then there is law ;) – Frank Hopkins Sep 10 at 19:22
  • Most of the ones I know are primarily motivated by science and would gladly work with a gifted student even without receiving any compensation. Just means one needs to ascribe a monetary value to "science", no? – Allure Sep 10 at 21:53
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A few reasons:

  1. It might be required by the funding agency.
  2. Graduate students let the professor expand his/her research program. If one is interested in the results, but don't have the time to do it yourself, then graduate students are great.
  3. Successful graduate students produce papers which have their advisor's name on them, and if they go on to become successful, the advisor benefits professionally (since it indirectly shows they are a great mentor).
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    To expand on point 3: A history of successfully mentoring graduate students may increase the advisor's chances of getting funding and/or promotions in the future. (Also note that it is not universal for advisors' names to appear on their students' papers, particularly in the fields mentioned by the OP, as discussed in many places on this site.) – Mark Meckes Sep 10 at 8:46
  • point 1 seems answer my questions. Thanks ! – Guldam Kwak Sep 10 at 13:07
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    But point 1 is only an issue if you have a grant. What is the economic incentive for having a grant? – user151413 Sep 10 at 17:29
  • @user151413 "If you don’t get funding, you can’t do research. If you don’t get funding, you definitely won’t get promoted. In my university, if you don’t get funding you won’t pass your probationary period to get a lectureship, and at many places if you don’t keep getting funding, you are in danger of losing your job." source – Allure Sep 10 at 21:39
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    @user151413 While you might have meant the question rhetorically, it has been raised in all earnestness on this site before: academia.stackexchange.com/q/107227/101 – Mark Meckes Sep 11 at 13:40
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It's a requirement of their job.

(Longer version: in the UK at least, universities seem to be increasingly setting explicit requirements of academic positions, and at least some of those lists of requirements set out minimum rates of research students you must have graduate under your supervision.)

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  • If you are not tenured, one criterion for tenure will be how many (successfully completed, ideally) PhD theses you have supervised.

  • If you apply for a grant, showing that you successfully supervised X PhD students will help. In addition, having good students increases your publication output, which is again helpful when applying for grants.

  • You might argue that there is no reason to apply for grants in theoretical research, since all they buy you are PhD students/postdocs, so if you don't want to supervise PhD students, why apply for grants? However, even for tenured professors part of their salary might depend on dynamic factors such as grants acquired.

  • And finally, already mentioned by others - though this is not part of your question - most people really supervise students because they enjoy it, and not for economic reasons.

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At my university and several others I know of, our annual raises are based in part on a 'merit score'; all of our activity (publications, undergrad and grad teaching, grad mentoring, departmental and University service) is tabulated [by us] and judged [by a departmental committee or by the department chair]. Faculty with above-average merit scores get above-average raises, and below-averagers get below-average raises.

This makes a fairly small difference in the grand scheme of things, and I agree with the other answerers about the relatively low importance of economic incentives, but since that was your question ...

For an important non-economic incentive: faculty without graduate students often end up with a heavier course load, and many people would rather train graduate students one-on-one rather than lecture and mark exams ...

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I question your premise. For the theoretical groups I have encountered it would be extremely unusual for the graduate students to not contribute to the professor's research.

Yes, the professor may be more efficient at doing research. And the professor may have to heavily invest in the graduate students' training first. But overall over the course of an average graduate career the student will contribute much more to the professor's research than the professor would have achieved by themselves instead of supervising a student. (That is true even if the professor hypothetically could do the work that takes a grad student 8h in just 1h, to pick an extreme & somewhat unrealistic example).

I think that explains why theoretical research groups have graduate students. Any additional incentives are secondary (but exist, because society puts some value on training experts in itself independent of research output).

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    I think your answer is by far the closest for my field, but it goes even further. Professors have duties that prohibit them from spending enough time on research to be as productive as graduate student's can be, at least once a graduate student has been trained somewhat. In my field, professors manage graduate students and post-docs and hardly have any time to be doing the "grunt work" of research... – Davis Sep 11 at 22:56
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    ... The incentive to hire graduate students is to lead them into interesting topics that further advance the field, helping develop the professor's reputation not only as a solo researcher, but as a leader in the field who is pushing in multiple directions of work simultaneously, far more than could be done with just one person. – Davis Sep 11 at 22:57
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As a professor you typically like to do and/or teach science and have influence over what research is done in your field. You also like to stay employed. Your department will do well if it can teach and/or research well. The likelihood that you are perceived as being effective typically increases if you can increase your output in either field (with sufficient quality). To increase your output, it helps to have "employees". PhD students are employees. They might not always get paid (very much) with money, instead you pay them (also) with your time. You invest some time but get typically more of their time - to teach or research for you, do the menial tasks you as a professor are too busy to do yourself.

If your department does well, that increases the chances that your institute or your university does well. It also increases the chances that you stay employed if there are budget cuts or that you even get promoted. Therefore more graduate students help you do more teaching/research (with you influencing the research of your field by advising them) and it helps you to stay employed.

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It is economical for a professor when you look at the correct 'currency' that an academic strives to maximize: For those who have decided to stay long-term in academia, this currency is not money (if money beyond the getting-food-on-the-table level were of importance, they'd not have stayed in academia long enough to become tenured professors) but academic output (measured in papers, citations, conference contributions etc.) associated with that particular professor's chair.

They optimize for academic output given the funding available to them (in Germany, a full professor usually has funding for several postdoc-equivalent positions associated with their post), and advanced grad students - while time-consuming to train - can become almost postdoc-level resources at roughly half the price (since a PhD student in Germany gets about half a postdoc salary) or even for free if the grad student brings her own grant money.

Another criterion a professor might optimize for is 'legacy', i.e. having trained (and thus influenced) a large number of students, some of whom might go on to make research contributions in their own right, and thus each grad student they teach is another potential contribution to the academic legacy.

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At my Alma Mater, one particular tenured prof exclaimed the first lesson of grad students first class: "My lessons are aimed at the top 10% of you." He then proceeded to breeze through the curriculum and teach waaay above it

Not all profs are incentivized to teach grads.

This particular one did it to find future academics in his field.

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  • This seems a singularly inefficient way to find the future academics... – Denis Nardin Sep 13 at 9:28
  • @denis I am certain they do it primarily because they have to.... Then, having to do it, do it to teach the brilliant ones their field... – Stian Yttervik Sep 13 at 13:36

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