Harvard selects students with higher expected earnings.
Given the statistics, that's almost a tautology.
Harvard selects students from families who are already wealthy (more than other top schools: the wealthy alumni are not self-made). Students who aspire to make a lot of money choose Harvard (over other top schools). Going to Harvard increases students' earning power (more than other top schools), for example, through better networking opportunities.
All these things may work together: rich kids who value money a lot go to Harvard, which gladly accepts them, in order to network with other greedy rich kids.
What we need to do is convince Harvard to perform a double-blind test. Accept half their students as normal, and the other half at random from their applicants. We'll have an answer within a couple decades.
[Added: Solipsist made good comments that partially account for the phenomenon, and Douglas_Knight pointed out that the figure of $200m+ below should be $30m+]
This article reports that Harvard has 2,964 alumni worth $200+ million, with a total wealth of $622 billion. These figures are staggering:
Note that Bill Gates "only" has ~$75 billion and that Mark Zuckerberg "only" has ~$30 billion, so that they don't account for Harvard's decisive advantage over other universities.
What is going on here? Why would Harvard come out ahead by such a large margin? Its acceptance rate is smaller than those of Stanford, Yale and Princeton, but by no more than 25%. Moreover, this has been true historically
One can ask a similar question of University of Pennsylvania, which is significantly less selective than Yale and Princeton, but has a decisive advantage over them.
Some possible explanations for the discrepancy:
Regardless of which of these explanations hold, there remains a question of why they would hold.
Is Harvard a better choice than other universities for students who aspire to be wealthy than other top schools?