Damn, I can't help but regret waiving my right to read my LoRs now.
From what I can tell letters are about the only thing that distinguishes a candidate. We all have ample mathematics, perfect or close-to-perfect grades and scores, some research experience. Being that adcoms barely read SOPs in economics, it's up to letter writers to convey exceptional promise, drive, creativity, etc.
That said, I think the first letter is good and solid, though not stand-out. I would chalk it up to a lack of writing skills and personality on the part of the writer (which is not uncommon in the discipline). The second letter is very personal, which is good. I assume (for my sake, at least hopefully) that conveying a personal relationship with a student raises the credibility of everything said and also signals dedication of the student (i.e. did more in college than fulfill a list of minimum requirements for graduate school and write a couple sufficient papers).
I'm banking almost completely on my letters, being that I don't have measure theory etc. Judging from the vitriol and bitterness from posters whom had extraordinary math and didn't get into dream schools, letters seem to be the ticket.
I also waived my right to see them, which I think was the right thing to do. A gift dropped into my lap the other day, though. I'm really good friends with the dept. secretary and one of my LOR writers had the secretary help him send the letter out to the schools I'm applying to so the secretary was able to assure me I had a great letter from that prof. It always pays off to be on the good side of the dept. secretary.
Your right to read your letters is an anti-discrimination law imposed by the government and not welcomed by the academy, whose mission in this process is precisely to discriminate among candidates.
Schools give you that form 1) because they have to disclose the law. They 2) ask you to waive your rights at the bottom because otherwise they have to severely discount everything your writer says about you while trying to avoid hurting your feelings.
I think 08Applicant's letter is weak because it adds little to what the committee can already see. It describes your work in one econometrics course as "stellar", but rather than discussing your stellar analytical mind, it goes on to say you attended every class and are an earnest young man. Damning with faint praise. They want people who could skip half the classes out of arrogance and still get an A. As you might have seen in studying information theory, the agent tries to show the principal that his performance is due to ability rather than effort.
I think you should get some credit for the academic related work experience. Perhaps you didn't have a chance to contribute in a more meaningful way, but a committee might have been looking for a statement that you had incisive analytical insights.
The summary "better preparation than most graduate school applicants" is far from "than most top school admittees" and yet farther from "than most top school PhD graduates".
The overall impression is of someone who is maximizing his performance with hard diligent work, thus producing the numbers you have (whatever they are.) That's the problem I think. He never says you're brilliant, and if you're not coming from a top undergrad program, the prior is that you're not. They might be especially concerned if you're such a diligent student that you pass the qualification process for candidacy even without the ability to write a clever dissertation. (The qualification process is designed to weed out such people, if their interest is in theory.) But a lower tier program which flunks out a lot of students might be interested in admitting you to their obstacle course and using you for research assistance for two years, or longer if you make it.
Teardrop's letter is strong. Analytical skills demonstrated stronger than some PhD students -- who are presumably doing OK themselves, and with benefit of more experience and coursework. Demonstrated success in writing, not just assisting, in research related to her application area. Massive determination, required to persist and make progress in a world where hardly anyone is your friend, some are your very devious enemies. These are clues for success. One can see these qualities resulting in a good job offer and eventual tenure at that institution.
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