unitroot

That's because every Ivy League wanna be treats schools like Brown, Rice, CMU, Rochester, and Emory as their "safety". In the end, some private schools get a ridiculous amount of apps because of this. I wouldn't be discouraged by that though. If you think they're a good fit, go for it. They're looking for people who would be a good fit for their program.

Jehle and Reny is a good book for self-teaching if you can teach yourself an advanced upper level math subject. I would say the mathematical maturity acquired through a good undergraduate real analysis course is sufficient to work through this book by yourself. However, if all you had is calculus, Nicholson is a much better book. It will teach you the essence of microeconomics without being bogged down in tons of math. In the end, I think the stuff taught in Nicholson is all that a typical non-microeconomist would care about in the long run.

I think real analysis is better, though, a lot of economics departments list an ODE course among the list of minimal math requirements (oddly). From my experience, RA will teach you math intuition that you need to work through more mathematical aspects of economic theory. Any ODE you see in a standard economics course can be taught within a half hour (Except for Black-Scholes PDE, which is hardly taught in an economics course anyways. You can solve it using straight calculus too, though it has a longer solution than basic ODEs. Several pages as opposed to half page in a text).

Someone with only a B.A. in Economics, can make 50-60K straight out of school (50K was the median for my undergrad school when I graduated). Given that, I think that the 100K salary for an A.P. is justified. Also note that A.P. make $100K only at the PhD granting departments (that is, may be the top 50 of them). In other words, the ones who get those jobs are the best of best. The A.P. that end up at primarily teaching or Masters granting institutions make a lot less. A state university with only MBA but no masters program would probably pay 60-80K to an AP.

I think it boils down to the fact that on average training in political science departments is less mathematically rigorous than in economics departments. This may have to do with the fact that today, either you do research that has to do with utility maximization theory one way or another or your work is not considered mainstream economics. The exceptions to this rule are empirical (purely data based, fact-finding) studies and econometrics. This is one of the reasons that traditional Keynesian approach to macroeconomics was kicked out of the mainstream. Other fields in the social sciences are more open minded, and so for example, many political science departments accept the idea that public choice theory or other utility based approaches to say voter behavior constitute a valid contribution to their field. Also, many social science fields started paying attention to econometrics, but generally they don't train their own graduate students in it as well as the economics departments.

I don't think Algebra is useful in Econometric at all. But there might be some applications in some areas of economic theory. I heard of some people using Abstract Algebra for some obscure research in Game Theory. But seriously, counting on this stuff being useful to you in particular is like counting on that the 30 year old data tape drive that should have been thrown away 20 years ago, but which you still keep just in case, somehow will be useful to you in future to read someone's obscure data set from an ancient tape. If you had been in a typical university sysadmin's office, you could have seen such artifacts; but at least it doesn't cost them anything other than shelf space to keep that junk.

I think the $30K loan is negligible on the grand scale if it buys you the dream of your life. E.g. it would probably worth it to take a loan to got to a top 15ish school vs a top 30 department. But if you're choosing among similarly ranked departments, which also stack up somewhat similarly for your interests, then going unfunded doesn't seem to make sense.

IUB is loaded with econometricians, both in time series and cross sectional, and Eric Leeper is a relatively prolific macro researcher with many students on the job market every year. This school IMHO stacks up well compared to the other two schools in these two subjects. Plus, it gave funding? I think the choice is obvious here.

I think dual major is generally a bad decision. It will fill up your schedule with many required courses just for the sake of major, and leave you little or no time for courses that truly interest you. Pick one major, then add only the best courses from other departments.

Taking additional econometrics or statistics courses will probably pay off in the long run more compared to non-essential math courses (anything beyond linear algebra and analysis) or economics topics courses beyond intermediate economics. In terms of term paper or thesis, no one expects you to use anything mode advanced for it than OLS, instrumental variables, fixed effects, or a simple discrete choice model (probit) in stata or some other package. Most undergraduate courses in econometrics should cover at least OLS inference. You can figure out fixed effects inference, probit, or IV as you write the thesis if you need those.

It sounds like you have already taken a lot math. It's a tough decision. It seems like there is relatively little "dynamics" in economics. There is a lot more emphasis on finding the equilibria. PDE are used in quantitative finance for pricing options, but relatively little otherwise. (never? I have seen it used just once in a finance seminar)

Nothing stops you from applying to better schools. But how likely will you be accepted in a better (higher ranked) program? Let's get real. Schools ranked below 30 may have many deficiencies compared to the top 30, but do not count that the program you're going to enrol in is going to be so easy that you're going to impress your processors and other schools to extent that they start thinking that you really deserve better if you have just the bare minimum math. There is a reason that math is so important in admissions. If you haven't done Calc3, I would assume you possess the bare minimum math knowledge to complete the coursework even at below top 30 place. I think it is fair to assume that your math prep is already below average even in the program where you had been accepted. Certainly, everything can happen. Perhaps you could transfer into a department that fits your interests better. Nonetheless, I would recommend to you right now to have a hard look at the departments where you have been accepted and choose the one where you think you will fit better for the long haul. Identify at least two faculty members with a proven track record of advising grad students and with interests similar to yours and see if you could stay there for 5 years working in those subjects. (Ignore any juniors or more senior people who haven't been primary advisers). Try to meet and talk to the graduate students. But avoid talking only to the "cheerleaders". I can guarantee you that for every cheerleader grad student, there is someone extremely bitter and disappointed locked somewhere in an office who could give you a valuable advice.

I think the two good specialties there are monetary economics and econometrics. The faculty includes several senior econometricians, and some good advanced juniors.

Not at all. You can make it through any finance course, unless it is taught by the math department, without prior knowledge of PDEs just fine too.

I think this depends on how badly you want to be an economist. Wisconsin is one of the top schools in statistics. Vanderbilt is not even a top 30 econ department. They did have good placements occasionally in the past. I think it's an exaggeration to say that getting a degree from any university will earn you a tenure automatically. An good degree, say from MIT and an influential adviser will help you get interviews and hopefully your initial placements. But tenure promotion happens 4-6 years after that, and when your considered for it, only your work after getting PhD will matter.