Choosing Ben S. Bernanke’s successor as chairman of the Federal Reserve is one of President Barack Obama’s most important remaining jobs. Nobody questions what’s at stake. Even so, the recent quarrel about the presumed front-runners, Lawrence Summers and Janet Yellen, verges on the ridiculous.

This is partly because both are exceptionally impressive candidates. But it’s frustrating for another reason, too. There’s more to setting the post-Bernanke Fed on the right course than choosing the best person for the top job. The fuss over Summers and Yellen is helping people to ignore this.

Obama is wise to take his time in deciding who ought to succeed Bernanke. Others should do the same, and here’s what they should be looking for.

Deep expertise in monetary economics goes without saying -- combined with the right ideas about what monetary policy can rightly be asked to do. The new boss should agree with Bernanke that the Fed’s dual mandate for price stability and full employment gives equal weight to both. (If you doubt the wisdom, take a look at Europe.)

The next leader will be more of a financial regulator than any previous chairman. This too calls for technical expertise plus sound ideology. Anybody who thinks financial markets can mostly be left to supervise themselves -- not an uncommon view before the crash, and not extinct even now -- is instantly disqualified.

Third, a harder thing to gauge, is ability to deal with the unforeseen. Bernanke never imagined the challenge he has faced. He has done well, considering. Sadly, the same might be asked of his successor. This isn’t one skill, by the way; it’s a bundle. Intellectual breadth, openness to unfamiliar ideas, steadiness in a crisis, a willingness to see that new facts may call for new thinking are all part of it.

Finally, individual excellence even of the highest order isn’t enough -- because the Fed is no longer a one-man (or one-woman) operation. The job demands leadership skills of two distinct kinds. In its areas of competence, the Fed should speak with conviction and authority both to Congress and to the country as a whole: Looking outward, in other words, the Fed itself has to lead, and its views must carry weight. But the Fed also needs to be led -- and that’s a harder job than it used to be.

This is the big thing that the quarrel over Summers and Yellen is missing: The central bank is more than its chairman. The other policy makers are more assertive than before, and financial markets pay much closer attention to their views. Aside from the top job, as many as four additional slots could open up on the Fed’s Board of Governors early next year. Getting those appointments right matters, too.

Elizabeth Duke has announced that she’ll resign at the end of this month. Sarah Bloom Raskin is set to become the next deputy Treasury secretary, creating another vacancy. Jerome Powell’s term ends in January, though he could be reappointed for another term. Yellen might leave if she’s passed over as Bernanke’s replacement. This gives Obama a rare opportunity to reshape the Fed. It’s a chance to widen the range of skills and experience its policy makers bring to bear.

And that’s needed. In the mid-2000s, economists and central bankers were too busy celebrating the “Great Moderation” to notice the dangerous rise in private borrowing that led to the crash. There were honorable exceptions, but the dissenting voices weren’t heard where it mattered. The Fed failed to think through the unintended consequences of the low interest rates it engineered in the early 2000s.

As a result, it didn’t use the tools at its disposal. It could have limited loan-to-value ratios in the mortgage market, for example, or told banks to fund a higher proportion of their assets with equity rather than debt. These and other measures could have made the financial system more resilient and let some air out of the house-price bubble.

The wisdom of hindsight is cheap, but it’s fair to ask whether these failures weren’t due to groupthink. Today, the dangers are better understood -- which is why the Dodd-Frank Act and other initiatives have broadened the Fed’s regulatory powers. Yet few of the people who’ve been suggested for the other top jobs at the Fed have hands-on experience in evaluating financial risks, much less managing or reducing them. The pool of candidates for the new board positions should be widened to include academics, financial engineers, market professionals and others with what central bankers might see as untraditional expertise in finance and systemic risk.

If the choice for the top spot does come down to Summers or Yellen, Obama can’t really go wrong. He and everybody else ought to worry a bit less about that and a lot more about the wider range of talents that the new Fed will need in all its governors but still lacks.

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