The AEI authors note
The institutions covered in this report run the gamut from large, public research universities to small, private liberal arts colleges; from highly selective, world-famous institutions to regional, open admissions ones. America’s college graduation rate crisis is not happening at the handful of institutions that admit only a few of their applicants and graduate most—it is happening at a large swath of institutions that admit many but graduate few.Another crisis! Who knew?
The study does not look so bad. The authors recognize that transfers, which are not counted in the graduation rates they analyze, pose a major problem, and the discuss the available data on transfers. They seem less up on the idea that simply conditioning on the crude Barron's quality categories might not be enough to really hold "all else constant". These categories capture real variation but within-category variation in quality (which is more than just selectivity) remains large. For example, the top category includes both Tulane and Harvard, which are a bit different on a number of dimensions.
The authors also note, correctly, that you do not want to reward or punish schools based on these rates, as they are easy to manipulate. Harvard graduates 97 percent - does anyone really think that 97 percent of those they admit perform up to this level in their classes?
I think a more useful view is that parents and administrators should look at these rates but at the same time keep in mind that students play a much larger role in the completion decision than do college administrators and also that college itself, as well as particular colleges, are experience goods, which is to say that the only way to really find out if you like them is to do them and then, if you do not like what find, to change your mind and go elsewhere or avoid college altogether. Particularly at the low end of the distribution, colleges are playing this informational role, which means that their socially optimal completion rate is likely far from one.