Tyler Cowen has a good thought on the Fed chair question. The next chair has to be a good politician, in all the positive senses of that word, more than a good technocrat:
The Fed has functioned as a technocracy for a long time, but might the future bring a Fed that is irrevocably split between competing factions? ...the future could bring a Fed divided over how much it should assert its political independence, how much it should assume responsibility for possible asset bubbles, how it should respond to an international financial crisis, or how much it should align with an “America First” mindset. ....
The backdrop is this: Ben Bernanke’s Fed, with its bailouts during the financial crisis, ate up a lot of the Fed’s political capital, though arguably for the worthwhile cause of saving the financial system. As a result, the Fed no longer has its pre-crisis credibility. As long as the American economy is on the path of a slow and steady recovery, with relatively high asset prices, that’s bearable.
But the next time major economic volatility comes around, Fed decisions will be scrutinized and politicized like never before. This will happen in the mainstream media, on social media, and perhaps by our very own president in his tweets or offhand remarks. The key factor for any Fed leader will be the ability to maintain and project a coherent, unified voice at the Fed, so that the Fed remains an island of relative sanity in the polarized nation. This will be a problem of crisis management, but unlike Bernanke’s crisis management it will be fought first and foremost in the trenches of public opinion.(The open vice chair positions are good ones for technocrats, who need to be able to translate the abstruse language of the staff.)
My related thought: We focus a lot on interest rate policy, but most of what the Fed does these days is financial regulation and supervision, and those decisions are likely much more important going forward. The challenging question there is "macro-prudential." Is it the Fed's job to worry about "asset bubbles," and to micromanage "credit booms" and their eventual busts? Or is it better for the Fed to limit its authority, to preserve independence, credibility, and insulation from political demands for action and political criticism of its actions, by pronouncing there are economic events beyond its scope?
Moreover, if the Fed is to limit the scope of its financial dirigisme, it had better do so beforehand not afterwards. If everyone expects the Fed to set prices and bail out hither and yon, and then the Fed gets religion (perhaps under relentless political pressure), the crisis will be so much worse. Bernanke also benefitted from acting far beyond expectations of what he would or could do. The next chair will be in the opposite situation, have to set limits of crisis reaction, and disappoint expectations. It's much better to do that ahead of time -- and much harder for an institution like the Fed to scale back people's expectations, and to renounce and pre-commit against attractive-sounding powers.
Narayana Kocherlakota predicts Jerome Powell. In line with some of the above thoughts, Narayana's view basically is that monetary policy is doing fine. Low unemployment, low inflation, low interest rates, low macro and financial volatility. Mission accomplished. Moreover, if there is a hawk vs. dove question, President Trump looks likely to be on the dove side of it. (Sadly, I doubt that rules and precommitment vs. discretion is ringing in the appointment decision.) However, supervision and regulation is the key issue going forward, and Narayana views Powell as Yellen monetary policy plus a regulatory/supervisory reform.
(I learned to use both words from Ms. Yellen's Jackson hole speech. Regulation is rules, supervision is sending Fed people to look over banks' shoulders. It's a good distinction.)