Alumni donate more to a college when their children are getting close to applying, and they give less if their children don’t get in, a new economic paper says.

The paper published this month by the National Bureau of Economic Research is written by a professor of economics at Princeton University, Harvey Rosen, and a graduate student in economics at Stanford University, Jonathan Meer, and offers a “child-cycle” theory of alumni giving. They found that parents appear to increase their donations when they have children close to college age and those children actually later apply to that university. Their children applying appear to be “one of the motivations” for giving, said Mr. Rosen.

Whether the donations help the children get into the schools is a “sexy question” that Mr. Rosen said the study does not address. The economists found that alumni with children in their early teens who eventually apply give more than alumni whose teenagers do not. The parents appear to be making a guess about whether their children are going to apply, Mr. Rosen said.

They examined data of over 30,000 alumni at an anonymous university labeled “Anon U” to come up with their results.

Mr. Rosen said the study showed that alumni with teens who later applied “both gave more and were more likely to give.”

Their research also showed that giving drops off after the admissions decision is made and that the decline is larger if their son or daughter is rejected.

Mr. Rosen cautioned that their research does not come close to explaining all donations. He said there were both altruistic and self-interested components to giving.