So far I have not delved specifically into the PhD labor market in my work on S&E and high skill labor markets. As many of you are probably aware, it is a completely different world. Many of the same issues apply: lagged labor market adjustmet, prospects of a glut if demand shifts, specialized labor, likely externalities, etc. If you are interested in this labor market specifically, you'll want to read Ronald Ehrenberg, Paula Stephan, and Richard Freeman.
But there is an interesting series of blog posts on this labor market I wanted to bring attention to by Jordan Weissmann here and here. My co-author on a lot of this work, Hal Salzman, was talking with Weissmann in preparation for these posts and he told me he gets the impression more will be coming.