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Sunday, October 10, 2010

Elite universities and human capital mongering

In an earlier post I discussed the advantages of attending an elite university. A related question is: what fraction of the total population of top students in the US attend an elite university? The answer is a function of where we put the lower cutoff for top students.

One interesting population to consider is the subset of National Merit Semi-Finalists who are awarded scholarships directly funded by the National Merit Corporation. Semi-Finalists are themselves the top percent of PSAT/SAT takers, so this subset is an especially elite group. From my experience I would guess that only the top 10-20 percent (see *** below) of National Merit Semi-Finalists are offered these portable awards, as opposed to other "National Merit Scholarships" that are funded by individual colleges. (Almost all non-elite colleges use these self-funded NMS to increase the enrollment of talented students; any Semi-Finalist is eligible for such an award. The most elite universities do not need to offer self-funded scholarships of this type, as discussed below.)

About 2300 NMS scholarships funded by the corporation are awarded each year. It turns out that just 10 elite universities account for well over half of these awardees. The vast majority of universities in the US have zero students from this select population! Data from this report. (Thanks to a reader of the blog for sending it to me.)

Number of NMS in entering class / size of entering class.

Caltech       42 / 200
Harvard     266 / 1600
Yale         234 / 1300
Princeton     196 / 1300
Stanford     110 / 1600
MIT         110 / 1000
Brown       91 / 1500
Duke         105 / 1600
Penn         125 / 2000
Berkeley     91 / 6000

Total 1270

Note, large numbers of Semi-Finalists who are not in this top group (i.e., not among the top 10-20 percent or so) do not receive a National Merit Scholarship because they choose to attend an elite university that does not self-fund additional awards. Just by looking at average SAT scores one would guess that as many as half the students at some of the schools listed above were Semi-Finalists. Apparently, the marginal value to these schools of "just another Semi-Finalist" does not warrant the expenditure of a few thousand dollars in additional scholarship funds. ("If we wanted to, we could fill our entire freshman class with Semi-Finalists!" etc. etc.)

*** If Semi-Finalists are in the top .5 percent of the population (assuming some selection in PSAT takers relative to the general population), the threshold IQ is +2.5 SD (137 or so). The NMS population discussed above is perhaps another SD higher (IQ 150 or so). You can directly estimate the number of students at the Semi-Finalist level: if 4M students graduate from HS each year in the US, that means about 20K above the 99.5th percentile. If the 2.3K NMS are the elite of this population, they would constitute the top 12 percent or so.

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