What motivates alumni to get out their checkbooks and donate to their alma maters? Nostalgic attachment to the football team? Careful reflection on Russell Kirk’s arguments in Decadence and Renewal in the Higher Learning?

Those are both possibilities. Here’s another one, which donors might not be so willing to confess: a belief that their donations will increase their children’s odds of winning admission.

In a new working paper, two economists have examined the giving patterns of more than 32,000 people who graduated from an unnamed selective university between 1972 and 2005. The economists found that, among people whose children applied to the same university, donations increased significantly in both number and amount when the children were between the ages of 14 and 17. And when an alumnus’s child was rejected by the university, the alumnus’s odds of donating declined sharply.

It seems clear that “some donations are made in the hope of a reciprocal benefit,” write the authors, Jonathan Meer, a doctoral candidate in economics at Stanford University, and Harvey S. Rosen, a professor of economics at Princeton University.

In a column on Slate, Joel Waldfogel of the University of Pennsylvania suggests that selective universities subtly encourage the belief that donations will improve one’s children’s odds in the admissions lottery, “like a married woman who hides her wedding ring so that optimists will buy her drinks.” —David Glenn