Offered with the recognition that I am often wrong. Please weight appropriately.
Economics is useful preparation for jobs in public policy, urban planning, education, environmental non-profit work, and other fields not commonly associated with the discipline. It need not be a pipeline to finance and consulting.
Thomas Carlyle named economics "the dismal science" in a pro-slavery essay. He disagreed with economists like John Stuart Mill, who argued that incentives and institutions, not racial differences, explained patterns of wealth and poverty.
This short article, "Economics After Neoliberalism," sketches several important critiques of market fundamentalism and gestures toward more rigorous and nuanced types of economic thinking. The linked responses by other authors are also instructive.
On learning & college/university course choices
My respect for a student is not contingent on ability.
Mathematical ability is malleable. You can improve with practice.
You need not be the best at something to contribute valuable work, or to enjoy it.
Inputs are important. Carefully plan your study and allocate enough time to execute your plan, rather than allowing others to dictate your course.
If you never volunteer an incorrect answer in class, you aren't taking enough risks.
It is not only normal, but good and useful to begin a problem with no idea how you will solve it. If you train yourself to respond to a tough problem with patient fascination, rather than fear of failure, that will serve you well.
If you get stuck on a problem, try to formulate a narrow, well-defined question that will help you make progress. Go slowly and write the question down. (You may need to review notes or books order to write it.) Then find someone to ask.
A long-ago children's program, Square One, offered this advice in song form: "Think about the problem / Then step back / Try a different plan of attack / Ask for help / Ask around / Another solution / Can be found / Change directions, reappraise / If you get stuck / There are other ways / Take your time / It'll come to you / Most problems have answers / If you think 'em through."
A challenging class in which you earn a B will be more valuable to you than an easy class in which you earn an A. In the long run skills are far more important to your career than GPA.
Economist Chris Blattman wrote a good college advice column. I agree with his recommendation to avoid foreign language classes. Provided you have the opportunity, it is much more efficient to learn languages abroad.
Consider the phenomenon of double majoring, which is common at Williams. By completing all n courses in the second major, a student receives two payoffs: 1) a signal to employers, e.g. the word "economics" on the diploma; and 2) human capital (skills). Such a student could instead complete n-1 courses, winding up with roughly the same human capital but no signal. She would benefit from unconstrained choice of her nth course. Should this student complete two majors? Naturally the answer depends on the student. I suspect students may overrate the signalling value of the second major, and underrate the losses from pursuing a major-prescribed set of courses, rather than the set they would prefer.
Williams-specific: Many students express interest in the Williams-Exeter Program at Oxford (WEPO) and the Junior Advisor (JA) program. There is nothing wrong with either program, and either might be a good fit for a given student. But their prestige and their impact on future prospects are greatly exaggerated, and the competitive dynamic around them strikes me as unhealthy. Beyond Williams, for the most part people do not care about these programs. Either program should be undertaken because of the experiences it offers, not because one wants to say one has completed it.
Williams-specific: The library archives past course syllabi here; only Williams affiliates have access. While the archive is not complete, its coverage is pretty good. A syllabus is generally more helpful than a catalog description for assessing a course.
One of my graduate school professors, a famous theorist, told us (paraphrasing): "I first think about how people are behaving. Then I figure out the math that describes my intuition." I prefer to approach theory in this way. Sometimes working through the math causes me to revise my initial intuition, but I like to start from the intuition.
Ideas from daily life and social systems tend to yield better papers than ideas from reading existing research.
If you're having trouble coming up with a good research question, I recommend evaluating a public policy in an area that interests you. With luck this will lead to questions beyond the narrow effectiveness of the policy you study.
You are unlikely to answer a novel empirical question using only the variables from a single public data set. The costs of working with such data are low and many researchers have looked at them already. Either non-public data or a combination of public data sets improves your chance at originality.
Don't assume others are right. If you investigate and make up your own mind, you will find examples of the following. Cited articles don't establish what citing authors claim they do. Figures in research articles, rather than strengthening a result, actually undermine it. Multiple authors repeat an idea derived from a bad study decades ago.
"When you have put a lot of ideas together to make an elaborate theory, you want to make sure, when explaining what it fits, that those things it fits are not just the things that gave you the idea for the theory; but that the finished theory makes something else come out right, in addition." --Richard Feynman, Surely You're Joking, Mr. Feynman
It is difficult to learn about the world without first building a model that makes testable predictions. One of my graduate school instructors put it this way: "At some point you have to take a stand on the data-generating process." Judea Pearl has made similar claims. Without theory, one is frequently left with statistical associations that cannot be interpreted causally.
The mathematician Claude Shannon offered some useful thoughts on problem solving in a lecture entitled "Creative Thinking." The earlier paragraphs on IQ are dated and unhelpful; consider starting with the paragraph that begins, "The first one that I might speak of is the idea of simplification."
"The best of science doesn't consist of mathematical models and experiments, as textbooks make it seem. Those come later. It springs fresh from a more primitive mode of thought, wherein the hunter's mind weaves ideas from old facts and fresh metaphors and the scrambled crazy images of things recently seen. To move forward is to concoct new patterns of thought, which in turn dictate the design of the models and experiments. Easy to say, difficult to achieve." -- Edward O. Wilson, The Diversity of Life