A lot of liberals have big ideological problems with Lawrence Summers. I really don't. Like anyone, I disagree with him about some stuff. But broadly speaking I subscribe to the same center-left/neoliberal/moderate Democrat/whatever ideological viewpoint as Summers and Robert Rubin and Jason Furman and Gene Sperling and Brian Deese. But all these quiet, off the record assurances from Summers' collaborators that despite a lack of clear public record on the issue he'd be a great Fed chair have been giving me the willies because I remember what happened when a similar set of reassurances got Summers the Harvard presidency. I think Summers should probably be a university professor at Harvard, make lots of money giving talks to various groups, write smart op-eds about a wide range of public policy issues, and serve as an informal mentor and adviser and all-around eminence grise to centrist Democrats. Nobody's entitled to the Fed chairmanship just as a capstone to their career.
Something I say in the piece but think it's worth elaborating on is that a great big country like the United States should probably put its central bank in the hands of people with central banking experience.
Ben Bernanke had a great reputation as an academic economist, and it was smart of George W. Bush to give him a spot on the Federal Reserve Board of Governors for several years of seasoning before making him Fed chair. Elevating Janet Yellen from the vice chairmanship to the chair's position would be good along those lines. Or if you want to pick someone who seems a bit more aggressively dovish (not a bad idea in my view) Chicago Federal Reserve Bank President Charles Evans seems like a sensible choice. The United States also has the ability to take advantage of people who live and work in America but who've gained valuable central banking experience abroad—people like Adam Posen and Stanley Fischer and Lars Svensson. In the abstract, I think Christina Romer is the person who has the best ideas about what the Fed needs to do, but for the sake of principle I'm willing to be consistent and say it might make more sense for her to spend some years on the Fed board rather than putting her in charge.
One issue here is just that it turns out to be hard to guess what someone's going to do based on outside writing. Bernanke is a great case in point where his conduct as Fed chair has been much more similar to his remarks in Fed meetings as a Fed governor than to his published writing as a Princeton professor. For better or for worse practical experience with the institution tempered his ideas.
But more broadly, I think the world needs to move past the idea of the central banker as some kind of svengali—or as they said in the Greenspan era, a "maestro"—and think of it as something a bit more banal. A very important job, yes. But not one that requires mystical powers or penetrating original insights into the operation of the economy. It's an important job so you should hire people who've done related work and done it well.