There is a growing literature measuring research excellence in economics. The h-index is noteworthy in combining quantity
and research quality in a single measure of researcher excellence, and its ability to be extended to measure the quantity
and quality of the researchers in a department. We extend the use of the first successive h-index further to measure the quality
of graduate education, specifically excellence in research supervision, based on publication and citation data for individual
researchers ascribed to their graduate supervisors.
We rank economics departments in the Republic of Ireland according to the number of publications, number of citations, and
successive h-index of research-active staff. We increase the discriminatory power of the h1-index by introducing three generalizations, each of which is a rational number. The first (h1+) measures the excess over the actual h-index, while the other two (h1*, h1Δ) measures the distance to the next h-index. At the individual level, h* and hΔ coincide while h+ is undefined.