I'm a current grad student at Columbia.
Every department is different so I don't know how much of this applies to Economics, but here's what I've observed from helping professors screen applicants.
Targeting a specific professor: Undergrad admissions are handled entirely by an admissions office who look at all of the applicants and make a final decision to accept or deny. Grad school admissions are much different: the professors themselves play a large role in the process and have final control of who gets accepted. If a professor knows about a specific applicant and really wants to fund him as a student, that student is pretty much guaranteed to be admitted. If a student has a great application but doesn't target a specific professor, the admissions office will essentially send an email asking, "is anybody interested in this student"? If the answer is no, the student won't be accepted, no matter how brilliant.
As a consequence, instead of targeting specific schools, target professors. Figure out what kind of economics research you think you want to do and look up the top researchers in that field. Make it extremely clear on your application that you want to work for Mr. Whosit at Harvard, instead of that you want to work at Harvard. Even better, email the professor directly, introduce yourself as one of his prospective students, and tell him about how much you're interested in working with him to extend the brilliant ideas in his Paper X (being genuinely interested in Paper X, obviously). This will set you apart from other applicants. Of course, professors get tons of mail from underqualified applicants, so you will need to have the goods to back yourself up, specifically
GPA: The first thing they look at is your GPA, and the college where it was earned. Professors get hundreds of applicants a year and sorting the spreadsheet by GPA is the easiest way for them to narrow down likely good candidates. You didn't say where you went for undergrad, but assuming it's a decent US college your 3.91 is very helpful.
Letters of Recommendation: Obviously the ideal is for your letter writes to gush about how you're the most brilliant student they've taught in years, etc etc but the most important thing about letters is that the writers are recognizable as prestigious researchers in their field. A canned letter from senior faculty is much better than a glowing letter from a junior lecturer nobody has heard of; due to "letter of recommendation inflation" the actual contents of the letter are rarely taken seriously. Important exception: if you've done actual research for a professor, *definitely* ask him to write you a letter.
Evidence of research potential: It's too late to do much about this one if you're a senior in college, but if you've done extracurricular research work for a professor, published some papers, did a summer research internship, etc. you want to pimp that as much as possible on your application.
Everything else (GREs, essays, etc) is barely glanced at.