Corporate chief executives have come under fire in recent years for their skyrocketing pay. But there's a place that puts those executives to shame: academia.

College presidents on average earn $377,261 annually, or more than twice the average pay for CEOs, who take home about $176,840 on average each year, according to new research from the Federal Reserve Bank of Cleveland.

At the same time, American students face ever-increasing tuition bills, with the growth in college costs for years dwarfing the rate of inflation. The question of why college now costs so much more than it did a few decades ago prompted the economists to ask if the cause could be the high pay taken home by college presidents.

Not every college president is pulling in the big bucks, however. Leaders at research universities -- considered the top of the academic heap -- earn much higher compensation than rivals at colleges that only offer bachelor's degrees. Presidents at research universities who are within the 75th percentile of pay are pulling in an average of $1.18 million, compared with $280,974 for presidents at four-year institutions focusing on the arts and sciences.

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That may seem like a tidy sum, but the researchers sat it's not college presidents' rich pay packages that are to blame for soaring tuition. If college presidents were to divide up their pay and write out checks to all their students, the per-person payout would be fairly low, amounting to no more than $300 per student.

"Because the president at a given college is only one person, whereas colleges generally enroll hundreds or even thousands of students, lowering the salaries of college presidents would not do much to contain per-student costs," the researchers note.

While the president is just one employee of a college, he or she represents the tip of the iceberg in terms of administrative pay. The bigger question, the researchers note, is whether reducing total administrative salaries would help to put a brake on rising college tuition.

Previous research indicates that there may be a link between a college president's high pay and a student's debt load. Graduates of state universities with the highest-paid presidents typically end up with higher debt loads than the average state university graduate, the Institute for Policy Studies found in 2014.

The study also found that schools with highly compensated administrators tend to reduce scholarships and rely on low-paid faculty labor such as adjuncts, rather than full-time professors.