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I am a economics major student who will be applying for PhD programmes pretty soon. I am quite interested in economics, but I find myself even more interested things related to probability theory, such as stochastic processes. And if I ever get into a econ PhD programme, I'm pretty sure that I should be looking for co-advising from the math/statistics department if allowed.

So I am curious about what happens in academia if you ever find yourself more interested in a topic that you don't have a degree on. If you can write some good papers during your PhD, can you find good career opportunities in that field in academia even if you did not start out as a "professional" scholar in that field?

Any idea would be very much appreciated!!

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    Have you considered financial maths or econophysics? Both of those fields combine economics and stochastic processes. – James Apr 16 '12 at 10:54
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Yes, it is possible to cross over between different fields following the PhD-level studies. However, in general, this tends to be more applicable to "interdisciplinary" fields that can fall into multiple disciplines. For instance, the engineering department I studied at hired people with PhD's in applied mathematics and physics, because their research fields—in fluid mechanics and interfacial science, respectively—meshed well with the research interests of the department.

To give a counterexample, however, it will be much harder to make the case for a high-energy physics person to move into another discipline, just because it is so strongly identified with physics.

Thus, if you have a PhD in a field such as mathematical economics or econometrics, it will be a lot easier to make the lateral shift. However, if you're in a more "traditional" subfield, that move becomes much more challenging.

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Moving from an economics Ph.D. program to a job in a mainstream math department will be difficult. There will be the practical difficulties (are you able to teach as broad a range of courses?), the incentive issues ("If he's so great, why doesn't the economics department hire him instead? What's in it for us? If he's really a mathematician, why did he go to grad school in economics in the first place?"), culture clashes (mathematicians will have no idea what a working paper is, won't know whether the American Economic Review is any good, won't recognize the names of letter writers from economics or care as much about their opinions, etc.), and so on.

If you turn out to be a superstar, you'll have more flexibility, but anyone less gifted will have to work very hard to fit in. In particular, to have any real shot at this you'll have to:

(1) Demonstrate that you have a broad background in mathematics, in particular in the areas that are not used in economics. I.e., you'll need to study mathematics to the extent that nobody would guess you didn't go to math grad school.

(2) Publish papers primarily in mathematics journals. An economics paper, even a very mathematical one in an excellent journal, will count substantially less than a mathematics paper. if you have more economics papers than mathematics papers, then mathematicians who support other candidates will use this as an argument for why the economics department would be a better fit for you. (And they will convince many people by arguing that if the economics department wants you, then the math department would get the benefit of having you around for free, and if they don't want you, then maybe that's a bad sign.)

(3) Find leading mathematicians to write letters of recommendation for you. There's a widespread belief that recommenders lower their standards a little when recommending for other departments, or may not fully understand the standards or needs of these departments, so math departments will on average pay less attention to a letter from an economist than from a mathematician.

All this is unfair, but these issues are real. If you might want to work in a different department, then you should start preparing as early as possible.

P.S. You'll also run into other cultural issues. For example, economics candidates regularly get tenure-track jobs in top departments straight out of grad school, while mathematics candidates almost never do (i.e., the number of people who do this in a typical year is 0 or 1). This may work to your advantage, for example by giving you a chance to do a postdoc and improve your credentials, but it's something you'll have to deal with.

  • Thank you so much AM for the enlightening and detailed guidance! But I am still curious about what you refer to as a "mainstream math department". I guess it's very hard for economists to do meaningful work in pure math. But how does probability theory count here? I know in some schools probabilists are under the math department. But in most other schools (and some top ones like Berkeley) they are under the stat department. And econometricians are actually quite well-equipped with probability theory. I would very much appreciate it if I could hear more of your comments on this. – Vokram Apr 16 '12 at 5:36
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    By "mainstream" I just meant one that calls itself "Department of Mathematics" or a similar name, as opposed to statistics, operations research, etc. (or, occasionally, a particularly interdisciplinary applied math department, although this is unusual). A statistics department may be more open to this, although points (2) and (3) above could still be obstacles. Outside of economics departments, business schools are particularly likely to understand and value background in economics. The best case scenario would be a statistics group within a business school (for example, Wharton has one). – Anonymous Mathematician Apr 16 '12 at 12:52
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One additional difficulty of doing this, which may indeed be a hurdle, is that it will be difficult to teach undergraduate courses within the new department, because you may not have the background to do so. This will cause a course assignment problem for the head of department, one which could be avoided by not hiring you. On the other hand, you will be capable of teaching cross-disciplinary courses giving the education provided by the department a new angle, which may be appealing to the department.

Duncan Watts, of Six Degrees fame, switched from Physics to Sociology. It's hard to imagine a more extreme cross-over.

  • The issue of teaching undergraduate classes is a significant one. I know people who have tried to do something similar, and the main difficulty they've reported is convincing departments that they'll be able to contribute to teaching general undergraduate courses. (One way to address this is to make an extra effort as a PhD student to find opportunities to be involved with courses in the other department, but this can be difficult.) – Henry Apr 15 '12 at 18:30
  • People care about teaching undergrad courses? Although it surely isn't common, I know of two other (well known) sociologists who had higher education backgrounds in Physics, Hubert Blalock and David Greenberg. I would suspect the other way (from sociology to physics) would be much more difficult (and hence more extreme). – Andy W Apr 16 '12 at 0:31
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    The issue is not always concern for undergrads, but rather annoyance that if one department member is only able to teach a narrow range of courses, then they may always get to teach what they like, while other faculty may have to pick up the slack by teaching more frequently outside their own subfields. – Anonymous Mathematician Apr 16 '12 at 0:49
  • Thank you Dave for the important reminder. I see how the teaching issue might be an obstacle here now. – Vokram Apr 16 '12 at 5:12
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    Thank you Dave I won't :) I guess even if it turns out hard to get a tenure or teaching position, one can always do some research in that field whenever it he is interested, which should already be enough to satisfy me. – Vokram Apr 16 '12 at 8:55
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My father, a retired engineering professor, told me that some fields that are "feeder" fields into others, lend themselves more easily to the "crossover" process.

In your case, mathematics is a "feeder" field to mathematical economics. My father felt that it was relatively easy for a math (or engineering) PhD to cross over into economics (as he did in his later years), because most economists feel that their field does not have enough mathematics. In fact, many senior economics professors of his time recruited graduate students with strong "quant" backgrounds to work with them.

The reverse is not true. Most mathematicians would find it hard to take an Economics PhD "seriously" as a mathematician. It is said that mathematics is the "queen" of sciences, so its practitioners don't feel the need to cater to "lesser" fields.

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Definitely. Economists are routinely hired at finance departments, as well as public policy, public health, and even marketing departments. Sometimes they have appointments across different departments including statistics. For instance Francis X. Diebold has appointments in the Department of Economics at Penn, as well as the Finance Department and Statistics Department at Wharton.

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