An advanced doctoral student who wishes to do research in a field for which the department does not offer a regular field course may be able to take an independent study course with a faculty member who does research in that field. One way independent study courses differ from regular classes is that the topics covered can be tailored to the interests of the student and professor. Independent studies can consequently help students learn fields not otherwise offered in the department.
Faculty are not paid to conduct independent studies, and time spent conducting one is time away from research. Why, then, should any professor to agree to do one? The answer is that independent studies must be of mutual benefit. It is certainly not reasonable to expect that faculty will prepare a lecture course. Instead, in a typical independent study course, students read journal articles and working papers in a defined area, and meet regularly with the professor to discuss the readings. This can be of mutual benefit in many different ways. For example, the professor may be intimately familiar with some readings and can help the student master the details of these. At the same time, the student can present other papers with which the professor is not familiar. Even for these, the professor can provide context, relating the paper to the broader literature in the field. But at the same time the student teaches the professor something new.
An independent study is notoriously fertile ground for friction between professor and student. Common complaints from students are that the professor is not sufficiently familiar with a paper being discussed, and that he or she is not putting enough time into preparation for the meetings. Students often complain that the professor should be explaining and presenting the paper to them, and this is not happening. Common complaints from faculty are much the same. The student is not putting enough effort into understanding the paper and, if a part of the paper turns out to be technically difficult, the student all too often just skips it with the expectation that the professor will lecture on it in the meeting. Professors often complain that the student should be explaining and presenting the paper to them, and this is not happening.
Most complaints arise from a failure to agree on mutual expectations prior to beginning the course. These expectations may differ according to the papers being read each week. Student and professor must work out what is expected of each other ahead of time, and put this in writing.
Advice to young economists
You may not trust advice given by economists about the state of the world. But some of them have produced some very good advice about getting jobs, being a successful student, writing theses and dissertations, and getting the most out of your advisor. Save yourself a lot of heartache (or headache, depending on where you keep your economics) and read what they have to say.
Where to present research papers
There are hundreds of economics conferences around the world each year, providing opportunities to present all sorts of research. Extensive and current listings of conferences are available here and here. Remember that you may need to submit a paper for consideration anywhere between three and twelve months ahead of the conference date, so plan accordingly.
A (very) small fraction of conferences provide financial support to help graduate students attend and present. It's up to you to track these opportunities down. The economics department is often able to provide partial support for travel to conferences, as can the Collage of Arts and Sciences. Contact the department chair at least a month before your intended travel date. Additional support is available from the Graduate Student Association.
The job market
If you are on the market with a Ph.D. in hand or expected, the primary sources of information are Job Openings for Economists (JOE) and Econjobmarket. There are other sources of information you will need to monitor, and they are collected together here. Almost every year there is a session on the market for new PhDs at the January AEA meetings, and the key findings are published in the May issue of the AER. There is also a very detailed explanation of how the US academic job market works. But see also here for advice about the job market. If you are selling a product (yourself), you need to know what the competitions looks like. This page links to lists of the current year's job candidates. You will be able to look at CVs, job market papers, and student home pages, which will give you some idea of what the expectations are on the market.