Ivy League presidential pay is looking more like the big leagues.

Columbia University paid President Lee Bollinger $4.6 million in 2013, a 36 percent increase from the year before, according to a tax filing released Tuesday. Yale University recently revealed it paid former President Richard Levin a bonus of $8.5 million when he retired in 2013 after 20 years.

Presidential pay at elite universities is increasingly resembling that of corporate America, with performance bonuses and exit packages. While colleges say the rewards reflect the complexity of running multi-billion-dollar organizations, professors, alumni and others have questioned whether it is appropriate for nonprofits.

“There is increased scrutiny of compensation in higher education from the media, donors, the IRS and others,” said Alexander Yaffe, a compensation consultant at Yaffe & Co. in Towson, Maryland.

Bollinger’s compensation included a base salary of $1.17 million, a bonus of $942,600, as well as benefits and perks such as campus housing and a car and driver for university business. Robert Hornsby, a spokesman for New York-based Columbia, had no immediate comment.

Levin’s exit bonus was in addition to his annual compensation of $1.14 million. In 2004, Yale agreed to pay Levin a retention bonus if he stayed another 10 years.

We “regarded it as vital to retain his leadership for Yale for the long term,” John Pepper, the former chief executive officer at Procter & Gamble Co. who helped lead Yale’s governing board at the time the bonus was awarded, said in an e-mail. “The transformation of Yale during his two decades shows we were right to do so.”

Yale wasn’t the only Ivy institution paying a former leader, according to tax filings. Brown paid $686,483 in 2013 to Ruth Simmons, the president emeritus who resigned in 2012 after more than a decade at the helm, while Dartmouth College gave James Wright $316,866. Wright left the president’s office in 2009 after more than 10 years.

Mark Nickel, a Brown spokesman, had no immediate comment. Dartmouth’s Justin Anderson didn’t immediately return a call seeking comment.

A handful of Ivy League schools changed leaders midyear in 2013: Princeton University’s Christopher Eisgruber, who took office July 2013, was paid $762,400; Yale’s Peter Salovey, who started at the same time, got $801,020. Dartmouth’s Philip Hanlon, installed June 2013, was paid $695,568.