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Re: Work for a professor or for the Fed?
It seems like you have a pretty good sense of the pros and cons, and the big jump from here is making what is really a personal decision based on your preferences. The best anyone here can do is provide information, but it will always be your decision at the end of the day.
That said, some thoughts that may be useful...
- You are not wrong to give due consideration to where you live and how you spend your time over the next couple years. If you already have a signal that your current situation won't make you happy, that's useful information and you shouldn't disregard it.
- It's likely that continuing with this professor will lead to better admissions outcomes than Fed. At the same time, remember that if you do choose Fed, I presume you'll still have a letter from this professor based on your current work. Also, note this is all probabilistic. You could well end up with the same placement from either, though it sounds like in expectation the Fed may place you a couple/few programs lower.
- Maybe worth thinking a little about courses you'd like to take over the next couple years, if any? Can your GPA stand to gain? Any courses you never got around to (real analysis etc)? Would you like to take grad courses while working? If any of these apply, does the Fed have a good university nearby and a policy of tuition reimbursement / would your university allow you to take further courses? (all rhetorical)
- Seeing the work at a policy institution firsthand does provide some benefit for thinking down the road whether you might prefer that career path over academia (or industry).
I think it will boil down to: how much happier might you be at the Fed versus how risk averse are you and how much do you care about possibly going to a program a few spots higher/lower in the rankings?
I feel this is a somewhat rambling reply, which maybe reflects that this is just a tough call you'll have to make. Maybe the more useful things I can say are these:
- These are both great options.
- Tough decisions inherently imply that you value both options similarly. As such, you have little reason to dwell over the road not taken. Once you decide, just look forward to what's ahead.