Speculation over the next Federal Reserve chair is running wild. Will it be Larry Summers? Or Janet Yellen?

Whenever a public debate gets so frothy, it's probably missing something -- a few things, maybe. This case is no exception.

First, the chair isn't the only appointment President Barack Obama will make to the Fed's Board of Governors next year. In fact, he may have to fill as many as five seats, counting the top one.

Ben Bernanke, Yellen, Elizabeth A. Duke and Jerome H. Powell will all complete their terms, and Obama is considering Sarah Bloom Raskin for the deputy position at the Treasury Department. The board's remaining two members, Jeremy Stein and Daniel Tarullo, were appointed in 2012 and 2009 respectively. For the first time in his presidency, every member of the board will be an Obama appointee (though the president doesn't pick regional Fed presidents, who also rotate through positions on the Federal Open Market Committee, which makes monetary policy).

That's about as clean a slate as one could have, and it suggests a different perspective on the race for Fed president: It won't be the Larry Summers Fed or the Janet Yellen Fed. It will be the Barack Obama Fed -- no matter who gets the top job.

Here's something else we've missed: Every woman now on the board may be leaving. What's the right way for Obama to approach the issue of gender balance at the central bank?

As I see it, none of these jobs should be designated for women only. We should be picking the best candidates regardless of gender. But here's the point: A good number of the best candidates are women -- yet monetary policy is still mostly a boys' club. Since the pool of eligible candidates, all of them elite economists, doesn't lack women, it's worth making sure the Fed's governors aren't only men.

Here are four worthy candidates: Christina Romer, Sarah Dahlgren, Carmen Reinhart and Anat Admati.

· Romer is an extraordinary macroeconomist at Berkeley, and she chaired Obama's Council of Economic Advisers.

· Dahlgren is the New York Fed's executive vice president; she leads their supervision of financial institutions and would bring the right knowledge to the Fed.

· Reinhart is a Harvard economist and an expert on banking, currencies and financial crises -- though admittedly the openings come at a bad time for her, after her and Kenneth Rogoff's paper on sovereign debt was widely criticized.

· Admati is a Stanford economist who is leading a crusade for smarter banking regulation, including a big hike of capital requirements.

Commentators have zeroed in on a Yellen-vs.-Summers personality contest. That's a big mistake. Obama has the chance to set U.S. monetary policy on a fresh course in the next decade. Seize the day.

(Evan Soltas is a contributor to the Ticker. Follow him on Twitter.)