California state Treasurer John Chiang has called for an independent investigation amid questions about the educational background of the head of the nation's largest public pension system.

California Public Employees' Retirement System CEO Marcie Frost is facing criticism after a blogger wrote that she implied in her application and in a statement announcing her hiring that she was working on obtaining a college degree from Evergreen State College. But she has not taken classes there since 2010.

Frost has performed well, but failing to investigate would leave a cloud over the $360 billion pension fund, Chiang said.

"Integrity and transparency matter. Ms. Frost's, as well as the pension system's long-term success depend on vigilantly maintaining the public's trust," Chiang, a Democrat who sits on the board, said in a statement.

CalPERS board members have told the Sacramento Bee Frost was forthcoming about lacking a degree when she was hired in 2016. Board members gave her a vote of confidence Tuesday when they approved a bonus of nearly $85,000 and a raise of 4 percent, boosting her salary to about $331,000. Chiang's representative on the board voted in favor of the raise and bonus, said John Wark, a spokesman for the treasurer's office.

Frost told the Bee earlier this month that she still intends to complete her degree.

Priya Mathur, the CalPERS board president, said Frost had distinguished herself leading CalPERS and an independent review is unnecessary.

"Marcie's leadership is exactly what we need, and the Board's review this week on all matters regarding her performance sends a clear and unequivocal message that she has delivered for California public sector workers and retirees," Mathur said in a statement. "She is the right person to lead CalPERS."

Chiang said Frost's supporters and critics have both rushed to judgment, and only an outside investigator without loyalty to Frost or the board can get to the bottom of the issue.

The CEO, who led Washington state's pension system before moving to California, is accused not of lying but of failing to correct a misperception.