The "rich get richer" phenomenon doesn't apply only to people.

Colleges and universities across the U.S. are also being helped -- and hurt -- by the snowball effect as the country's elite institutions increasingly grab a larger share of donations.

Witness last year's record $40.3 billion in charitable contributions to colleges and universities: The top 20 institutions raised almost $12 billion of that total, or almost 29 percent of the whole basket. Stanford and Harvard alone brought in $1.63 billion and $1.05 billion, respectively, according to a new report from the Council for Aid to Education.

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The issue is a demonstration of the "Matthew effect" in action, a term coined after the Bible verse that describes how the rich cultivate greater riches while the poor lose out. In the case of higher education, graduates of top colleges like Harvard are more likely to score high-paying jobs, and that feeds back into the college when graduates write their charitable contributions each year.

The downside to the phenomenon, at least when applied to higher education, is that the schools that need the money the most -- whether to help support scholarship students or rebuild infrastructure -- are the least likely to receive generous donations because their graduates often don't go on to high-paying corporate jobs.

While the generous endowments have helped top schools like Harvard offer generous scholarships to low- and middle-income students, their enrollments remain overrepresented by the children of the rich. Only 3 percent of the students at the country's most competitive schools are from the bottom economic quartile, according to a study released earlier this month by the Jack Kent Cooke Foundation.

The vast riches of schools like Stanford and Harvard have created dilemmas about how their endowments should be directed. One slate of candidates for Harvard's board of overseers is calling for the school to spend some of its $37.6 billion endowment to cover tuition for all students. Lawmakers have also mulled requiring colleges with at least $1 billion in their endowments to spend at least one-quarter of the endowment's income on financial aid.

That might provide some relief to some students aiming to climb the economic ladder, but the bigger issue may be the fact that many less competitive colleges -- which enroll a greater share of low- and middle-income students -- are boosting tuition to offset cuts in state spending. More than three-quarters of tuition hikes at public universities from 2001 to 2011 were due to declining state appropriations, the think tank Demos found last year.

Increased investment in community colleges and public universities might help level the playing field. Whether graduates of Stanford or Harvard might be persuaded to open their wallets to help the little guys, however, may be a less likely proposition. About $11 billion of the total $40.3 billion given last year stemmed from alumni; gifts from corporations and foundations represented another $15.4 billion. The remainder came from non-alumni individuals and other organizations.

Below are the colleges that received the largest charitable gifts in 2015:

1. Stanford University ($1.63 billion)

2. Harvard University ($1.05 billion)

3. University of Southern California ($653 million)

4. University of California-San Francisco ($609 million)

5. Cornell University ($591 million)

6. Johns Hopkins University ($583 million)

7. Columbia University ($553 million)

8. Princeton University ($550 million)

9. Northwestern University ($537 million)

10. University of Pennsylvania ($517 million)