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Economist Paul Krugman recently wrote that the multibillion-dollar salaries of top hedge fund managers proved that education plays little role in the growing wealth gap. The rich get rich, he said, because of the "runaway financial system" and investors making money from money.
"Modern inequality isn't about graduates," Krugman wrote. "It's about oligarchs."
But a new study offers a different view. Jonathan Wai, a research scientist at Duke University and part of the school's Talent Identification Program, looked at the world's billionaires and global elite. He found that billionaires are, as a group, very highly educated and have high cognitive abilities. About a third of the world's billionaires attended elite schools worldwide.
Even among billionaires, the billionaires with higher wealth were more likely to have gone to a top college.
"The average net worth of those that attended an elite school was significantly higher than those who did not," the report said.
The global elite—defined by media lists and culled from the attendees of the annual World Economic Forum gathering at Davos, Switzerland—are also highly educated. More than half of Davos attendees went to elite colleges, Wai found.
An outsized number of billionaires and Davos attendees also majored in science, technology, engineering or math—also known as the STEM fields.
Harvard, the study suggested, is the top billionaire-making machine. Among U.S. billionaires, more than 1 in 10 went to the school, and globally about 1 in 20 billionaires went there.
Read MoreWhere the billionaires are....
As Wai told me: "I was surprised by the extent to which elite schools within each country tend to serve as influential filters for who ends up as a member of these groups of the global elite, specifically the overrepresentation of people who had attended Harvard University."
Granted, the study makes some assumptions that could be challenged. It doesn't have IQ stats on billionaires. Instead, it equates cognitive ability with attendance of top universities as defined by U.S. News and World Report.
But wealthy children can also get into top universities in part because their parents attended or gave the school large gifts.
Wai acknowledged that "some students attend an elite school with lower-than-typical test scores due to athletics, legacy status or political connections." He said that because some high-scoring kids don't attend elite universities "factors in both directions likely counterbalance one another."
The report also said billionaires who inherited their fortunes were more likely to attend elite institutions than self-made billionaires—suggesting that privilege is often passed down by parents rather than earned through brainpower.
While billionaires are much better educated in most countries around the world, especially the U.S., education is not as correlated with billionaires in China and Russia.
In those countries, "those with greater wealth were not more likely to have attended an elite school." (That's likely because getting rich in China and Russia depends more on political connections than degrees.)
Overall, Wai concluded that the wealth gap goes hand in hand with the education gap. The world's super rich, he said, are also "scary smart."
"I think we should deeply consider the implications when a select group of scary smart people also tend to hold a disproportionate share of global wealth and power," he said. "We depend on these people to make wise decisions for all of us. "
—By CNBC's Robert Frank.