Graduate Coursework -- PhD Real Analysis vs PhD Micro

[gollin]

Hi all,

I am RA at a top university in the U.S. and have the chance to enroll in graduate courses in the coming fall. I am split between taking the graduate real analysis course (measure and integration) in the math department or taking Micro I (consumer and producer theory, choice under uncertainty MWG chap 1-6). As a prospective economics Ph.D student, the obvious choice would appear to be Micro, given that it is a direct signal for performance in the first year coursework. However, given the pervasiveness of measure theory in various fields -- from statistics and econometrics to the economics of information and Bayesian learning -- it seems like a solid real analysis course may be good for my own edification.

For context, I have been studying from Papa Rudin (RCA) for the past couple weeks, albeit progress is slow since I am doing all the problems by myself and have not really put all that much time into it given my other commitments as an RA. I suspect peer effects are important with respect to outcomes while engaging with material like this. I have no experience with MWG (only baby Varian).

People here tell me that getting the highest grade is crucial in Micro but to do so you need to be in the top 5% of the class. That does not seem realistic for me given I will be competing with a host of international students who have seen the material before. I do not know how the grading works in the Math department.

Does anyone have any advice for me? Did you take both the courses? If so, which one was more challenging and/or edifying?

Appreciate the help

[Double Jump]

I'd advise getting to know the professors styles for each class. We had a couple 2nd and 3rd years take a Real Analysis class similar to what you described and they said averages for exams were around 20-30%. I've had Russian math professors that were completely fine not giving out A's to an entire classes. There's a lot of idiosyncrasies in grading styles in math classes. Also, if you're in a Phd program there's nothing that would preclude you from taking such a math class.

[dogbones]

What are some alternatives to the 2 PhD classes you mentioned? Both seem rather daunting and maybe your application could be better served by a peripheral course that is related to your research interests?

[gollin]

Hi dogbones,

From what I have heard, doing a field course (in say development, which is what I work on as an RA) is not considered a positive signal since it is not very rigorous compared to the first-year core coursework.

[dogbones]

Hi gollin,

I would suggest taking whatever class you feel confident about getting an "A" in, whether it's development (it's not *that* bad right?), graduate math, or a first-year core econ class. Not getting an "A" in the courses as an RA is probably worse than taking an easier course and doing well. Others on this forum, please chime in because my advice is limited in the way of experience...

[tutonic]

Hi dogbones,

From what I have heard, doing a field course (in say development, which is what I work on as an RA) is not considered a positive signal since it is not very rigorous compared to the first-year core coursework.

This is true. Field courses are graded much more leniently since there's no need to separate students any further, after the first year.

[chateauheart]

Between your two choices, I'd absolutely take PhD micro over a course around Rudin's RCA. The fact that you're studying from RCA, by yourself, shows that you have sufficient math preparation for any econ PhD.

Dogbone's suggestion - a good field econ course - is worth considering. You're right that it may look less rigorous on your transcript, but it will also provide more opportunity for interaction with your professors - and potentially a good letter of recommendation. When I applied to grad school, my most important LOR came from participating in a grad field course.

Also:

People here tell me that getting the highest grade is crucial in Micro but to do so you need to be in the top 5% of the class. That does not seem realistic for me given I will be competing with a host of international students who have seen the material before.

At my department, statistically, grad econ students who had *not* previously been exposed to grad econ material end up with higher median grades at the end of the course. I don't know how valid this is across different institutions, but in any case, no need to worry about your competition too much.

I do not know how the grading works in the Math department.

AFAIK, grad math courses often have an A or A- median in most math departments, i.e. more generous than first-year grad econ courses.

You are probably correct in thinking that it'd be safer to get an A/A- in a grad math course. But (1) it probably won't be a better signal than getting an A in a grad econ course, because many econ adcoms will have the same information that you have; (2) in the long run, it's definitely more useful to take a grad econ course. Most of the material you'll learn in a grad real analysis course is useless in econ research.

[gollin]

Hi all,

Thanks for your advice, I think I'm going to take Micro. Most of the other predocs are not taking this class but I think should be able to figure out(?) a study group.

The professor teaching the second quarter of the class is someone I used to RA for at a different institution (we both moved here, coincidentally); hopefully I can get a letter out of this.

My concern with this class (reflecting back on intermediate micro) was that while the material itself did not present to be particularly deep or challenging relative to the stuff in math courses, the exams were often deliberately tedious and time tight (lots of Lagrangians with unnecessarily complicated looking FOCs). I'd rather write proofs in a take home exam than sit through such an exam as I feel I am not a wizard calculator with calculus and algebra (unfortunately, my math professors drilled in me the notion that anything a computer could do better than me was not worth becoming particularly good at).

Another unfortunate facet of the course which I have gleaned is that some of the material uses "big guns" which they don't explain; Brouwer's fixed point theorem, for example, is used for general equilibrium stuff but is never usually proved in Micro classes (the intermediate value theorem corollary for the one dimensional case doesn't count). I find this disconcerting because if the point is to be "rigorous" then "lemmafying" some of the biggest steps without explanation (and no one expects you to have taken a course in algebraic topology where this would have been taught) is a bit of a hack. I wonder what is the point of this, pedagogically? In no "rigorous" math course that I have done have we ever discussed results that require substantial machinery outside the scope of the course (except, perhaps, Levy's continuity theorem as a lemma in the proof of the central limit theorem; that was in a non measure-theoretic probability class and it was primarily a non-proof based class.)

[laborsabre]

Addressing your concerns is difficult because while the material taught at most programs is similar, testing styles vary widely. Here is my input though, take it with the qualifier I just stated.

Re first concern: in my program clever FOC manipulation was mainly on homework assignments: professors generally did not expect you to correctly play with massive FOCs to get a neat equation in the span of a test and if they did it was understood to be something most people wouldn't finish. However, you should expect some minimum amount of algebra in many problems, but based on your math background it shouldn't be that much worse then stuff you have seen before. My experience has been that the macro sequence involved more terrible FOCs on tests.

Re second concern: in my program Kakutani's Fixed Point Theorem was the main one we used for stuff like equilibrium existence. We didn't prove it in the class, but supporting material and some of the proof details were provided. We also did go over all the main assumptions and how it fits into the main proof. If the Theorem was a tool, we read the instructions manual but didn't take it apart. This did bother some people, especially those with a more rigorous math background. I think part of this is because econ as a field has zoomed in on a few esoteric fixed point theorems that aren't widely used in many math departments. Anyway, the best advice I heard was "we are economists, not mathematicians." And to be fair I think this is good to keep in mind, otherwise you might drive yourself crazy. On the flip side you might grow too lazy, so I'm still learning to balance it myself.

To use an analogy, let's say you are a biologist trying to study microorganisms. You use an electron microscope for your research. You could spend a long time learning to build one from scratch, but then you could have spent that time actually studying what you intended to study. As long as you are sufficiently sure you know how to work it correctly, and you know enough to trust the tool, building complex electronics might be best left to engineers.

[gollin]

To use an analogy, let's say you are a biologist trying to study microorganisms. You use an electron microscope for your research. You could spend a long time learning to build one from scratch, but then you could have spent that time actually studying what you intended to study. As long as you are sufficiently sure you know how to work it correctly, and you know enough to trust the tool, building complex electronics might be best left to engineers.

laborsabre, you are exactly correct! We are (going to be) economists and not mathematicians (and most of us tend to understand the principle of comparative advantage). The majority of the matriculants at a PhD program would become applied empiricists who would perhaps be better off reading good empirical papers rather than reading proofs. It is just strange that we sort of go half-way and make things rigorous so that the applied guys feel like they are learning a lot of esoterica and the theorists are left dissatisfied, rather than making theory an elective which would present the material by building up all the tools necessary all the while getting the applied guys learn some of the same things but in a more applied research context, mostly omitting proofs completely unless they serve some pedagogical purpose. (By the way Brouwer is not esoteric at all and is fundamental to topology and characterizing the behavior of continuous functions on sets which are homeomorphic to a compact Euclidean ball and Kakutani is the set valued generalization)

I think I am maybe deviating into a whole new debate here, but I have frequently been perplexed by the way the Econ PhD is structured. My interests in math are pretty much orthogonal to Econ and the math I know hardly helps me better understand the work I do and the papers I read for my job. I don't see, therefore, the need for such a rigid core. People doing CS PhDs usually take courses as they need them for research; this is true at many math departments too. If something in my research would require some heavy theoretical machinery I would try to get a competent coauthor who understands it well rather than try to naively attempt to do everything myself.