As India's top institutions are being asked to admit, train, and graduate ever larger numbers of PhD scholars, the "overproduction" issue will come back to haunt us quite soon. Neuroskeptic presents a summary of a recent study of this question: Too Many PhD Graduates or Too Few Academic Job Openings: The Basic Reproductive Number R0 in Academia by MIT's R.C. Larson, N. Ghaffarzadegan, and Y. Xue.
The main conclusion is that academics are overbreeding PhDs. Here's the relevant plot from the (open access) paper by Larson et al:
Larson et al. approach this question by borrowing a concept from epidemiology: R0 (R nought), known as the basic reproduction number. In the context of an infectious disease, R0 is the average number of people who are newly infected by the disease by each existing patient. Influenza, for example, has an R0 of about 1.2 – 1.6. If R0 is greater than 1, the disease will spread exponentially.
Larson et al. define the academic R0 as the total number of PhD graduates created by (supervised by) the average tenure-track academic (i.e professor) over the course of the professor’s career. If this number is greater than 1, more PhDs will be created than there are tenured posts for them all to occupy – assuming that the number of tenured professors is roughly constant.
It turns out that the R0 at MIT is approximately 10. MIT produces some 500 PhDs per year, and it has 1000 faculty. So each faculty member produces 0.5 students per year. Since the average faculty member’s career at MIT spans 20 years, each faculty member produces 10 PhDs in total.
Though Neuroskeptic refers to the use of R0 in studies of disease propagation (an interesting parallel, isn't it?), a more relevant analogy is in demographics (see total fertility rate in Wikipedia). And analogy is what Bill Condie runs with in his post at Cosmos Blog:
"We show that the reproduction rate in academia is very high," they write. "For example, in engineering, a professor in the US graduates 7.8 new PhDs during his/her whole career on average, and only one of these graduates can replace the professor’s position.
"This implies that in a steady state, only 12.8% of PhD graduates can attain academic positions in the USA."
One quick critique of this research, which Neuroskeptic points out, is its focus on academic jobs as the relevant criterion for assessing whether the US is producing too many PhDs. Doctoral degrees in many applied fields open up many opportunities outside academia, and therefore, "overproduction" may not be an issue at all. However, there certainly are fields (humanities) and subfields (theoretical astrophysics and cosmology come to mind immediately) where academic jobs are the primary -- if not the only -- motivation for the incoming graduate students.