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Re: Profile Evaluation Phd Econ or Finance
General response: You're in great shape, and will almost certainly be admitted to multiple top 15 econ/finance programs.
(1) No, I don't think tenure status is important; academic econ is a fast-moving discipline, and financial economics is especially fluid as a subfield. Assistant professors may often have more credibility w.r.t whether you're quantitatively equipped for current research. I think you should choose your 3 best letters, and avoid paying attention to any connections they might have (unless they explicitly offer to help you with their network).
Additionally, among elite applicants, you're actually often doing a favor to assistant professors who recommend you. For example, if an assistant professor at Kellogg sees you as a very strong talent, they may benefit from recommending you to Stanford GSB or HBS, and continuing to co-author projects with you. If you are accepted and do well, they can eventually take credit for your success - e.g. get invited back for seminars, visiting positions, perhaps even a tenure-track position. Even if you don't do well, they still incur benefits from the fact that you're a grad student at a top department (with the counterfactual being you're a grad student at a second-tier department). In this sense, an assistant professor has a much stronger incentive to get you into a top program, compared to a tenured professor with everything else equal.
(2) Yes, PhD courses matter. If you're a US undergrad, taking a PhD econ course is the best way to signal your ability to finish the first year. The undergrad economics major is taken by a very wide range of students in top U.S. universities - including athletes and legacy admits. As a result, most undergrad econ sequences are simply not sufficient as a prerequisite for PhD-level economic theory.
With your excellent grades in undergrad advanced math/econ, I don't think the lack of PhD econ courses will matter significantly. These signals are, in a sense, substitute goods (i.e. adcoms may perceive you have 95% chance of passing first-year prelims; if you took PhD econ they might perceive 99%). Also important to note that the top 10 programs do not necessarily have a stronger quantitative requirement than the #10-30 programs.
But make no mistake (I say this for other readers), OP is at a slight disadvantage compared to an otherwise identical candidate who took first-year PhD econ sequences, because that is an almost perfectly accurate signal that they will eventually pass first year prelims
(3) Easiest way to keep in touch is to have an actual reason to talk to each other - e.g. a research-related connection to each of the writers. You can (implicitly) promise to do a small amount of free work (such as lit review) for these professors, in return for being kept in the loop.
(4) No, generally, you shouldn't rely on an industry letter. Some non-zero subset of adcoms have a strong prejudice against industry as a career option, e.g. they believe only failed PhD students would continue going to the industry.
As a rule of thumb, an applicant should assume that an industry letter from a PhD in fiannce/econ in the industry has the same authority as a generic character reference from someone who knows you --- Among some adcoms it may be viewed more favorably; among some adcoms it will be more negative; but in most cases they will simply throw away the letter and focus on your two academic references. (Many econ/finance programs filter out non-academic letters during the initial screening phase, by secretaries).