I think every self-titled economist should get a finance degree.
No, wait, here me out. Look, while "normal" economists do a great deal of econometric work, there's something to be said about the finance major who bolstered his degree with econ, and the econ major who supplanted her degree with finance. The two are strongly tied together, theoretically and in principle.
For example, introductory finance courses will have you look at the present value (PV) of a stream of cash flows. This exact same skill is presented to you in intermediate microeconomics, alongside such models as Stackleberg, Bertrand, and the Cobb-Douglas production function. Calculating beta values is a matter of understanding relative performances and supply-demand tensions that yield valuations. Essentially, it's an elasticity value. While the theoretical side of that explanation is all economic, the numbers and the math of it is all finance.
So why am I telling you that an econ major should pursue finance instead of, say, operations? Cobb-Douglas is, after all, a production function, and operations is all about Right Time, Right Place, Right Price. It seems like a match made in Nerd Heaven.
Well, it is. And that's something of the problem. Ops and econ guys will forever argue the finer points of each others' specialties. Ops people are all about the practicalities, while econ people can get too caught up in the beauty of their models. Finance is nice because it gives econ people the skills and tools to assign harder numbers to their assertions. It also aids in understanding valuation, understanding the logical extensions of economics, and to gain a more full understanding of the models in economics.
In turn, understanding economics gives finance majors a better theoretical basis for the hard numbers. It can, for some, provide the "why are these steps in this order" that finance students ask, especially early on. Finally, knowing econ models enriches a financier's understanding of her subject, as well. By being able to see the past, present, and future of a finance problem (relatively speaking: the past is the genesis of the theory, the present is the quandrary at hand, and the future is the application of numbers to the process) a finance major distinguishes herself from her colleagues by being able to speak intelligently and eloquently about the finer points of finance.
Finance and econ are like twin strands in a length of rope. As each lays over the other, the resulting cord is stronger. You are that cord. Knowing and understanding both well will give you greater strength than that of your colleagues.