A reason people are obsessed with department rankings is, for graduate students, faculty quality reflects the quality of their education, and for faculty, it determines the quality of the students they will attract. The presumption here is that there is a strong correlation between quality of faculty, as measured by citations or article placement, and quality of students, as measured by potential or job placement. This correlation is, however, not that close to one, I can think of several top programs whose students turn out not to be that great. The student placement ranking by Rabah Amir and Malgorzata Knauff unfortunately does not compute such a correlation.
This introduction is a little bit of a stretch to the paper by Fabian Waldinger that looks at a stark natural experiment: the massive exodus of top mathematics faculty during Nazi Germany. Some top departments, the best in the world at the time, lost over half of their faculty within a year, giving us very clear identification. Measuring the likelihood of doctoral students to publish in top journals before and after the exodus, he finds that a one standard deviation in faculty quality, as measured by citations per faculty, increases the probability of publishing the dissertation by 13%. It also has a similar impact on the probability to become full professor, and gives 6.3 more lifetime citations (for an average of 11). One conclusion that Waldinger reaches is that few top departments with top faculty should concentrate on conferring doctoral degrees.
What could be the implications for today? The United States is now the most vibrant arena for doctoral studies in most fields. But the success of US universities is possibly not sustainable, which could lead to an exodus of faculty, a watering down of top doctoral programs and thus an important reduction in the quality of graduate education. Under such circumstances, the only way to save the preeminence of the US is to close many doctoral programs and concentrate the top researchers in the remaining programs.