If President Barack Obama nominates Janet Yellen, the second-ranking official at the Federal Reserve, to be the next chairman of the central bank, she would be the first woman to ever occupy the post.

This fact—and reports that Obama is considering former Treasury Secretary Lawrence Summers for the same post—has prompted editorials worrying that Yellen wouldn't be up to the job, as well as more subtle attacks on her lack of "gravitas."

Although Obama has spoken of the importance of diversity in his administration, his inner economic team is a boys club, says Sheila Bair, a former head of the Federal Deposit Insurance Corporation who has pushed publicly for Obama to pick Yellen to run the Fed.

The top administration jobs that most affect the financial industry, Bair explains, are the chair of the Fed, the secretary of the Treasury, the head of the New York Federal Reserve, and the comptroller of the currency. And although there have been a few women in other top economic policy positions in the Obama administration, none of these big four spots has ever been filled by a woman.

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