Warsh, long seen as a candidate for Fed chair, has been gaining momentum in the betting markets, and in the minds of Fed watchers, after White House top economist Gary Cohn fell out of the top slot. Cohn, the director of the National Economic Council, had been seen as a front-runner until he was critical of the president's reaction to violence by white nationalists in Charlottesville, Virginia.
Yellen and Warsh are now running neck and neck on the PredictIt betting website, with Cohn a distant third.
Politico points out that Warsh's ties to the White House are strong. He is married to the granddaughter of Estee Lauder, and is son-in-law of Ronald Lauder, a longtime close business associate of Trump.
The article also noted Warsh's ties to Wall Street. Warsh spent seven years at Morgan Stanley, where he was vice president in the mergers and acquisitions department, before joining the Bush White House in 2002 as an economic policy advisor. Four years later, he was appointed to the Federal Reserve at age 35, the youngest governor ever.
Warsh was also a member of President Trump's now disbanded Strategic and Policy forum, a group of mainly CEOs who were working with the White House on economic and policy issues. According to one observer, Warsh had credibility with the group and "acted like a Fed chairman."
"I think Kevin Warsh has a very good chance. He's a former Fed governor. He was there during the crisis. He knows why they did what they did. He didn't agree with the post-crisis continual unconventional policy. He's been very critical of the Fed forecasts. If anyone is going to come in as a non-economist and be able to challenge the Fed staff, it would be Warsh," said Diane Swonk, CEO of DS Economics.
President Donald Trump has said Yellen was a possibility, but the Fed chair, during her press briefing Wednesday, declined to comment on whether she would be interested in staying on.
"I have said that I intend to serve out my term as chair and that I'm really not going to comment on my intentions beyond that. I will say that I have not had a further meeting with President Trump. I met with him early in my term, and I've not had a further meeting with him," Yellen said.
Last week, Treasury Secretary Steven Mnuchin said Yellen was a potential candidate but there were lots of "great people" being interviewed. Trump said Yellen was doing a "good job" in July, when he also mentioned Cohn as a possible replacement.
Also reported to have been considered are Stanford University economist John Taylor, former Fed governor Lawrence Lindsey, and former BB&T CEO John Allison. Also believed to be in the running is Randal Quarles, nominated by Trump as the first-ever Fed vice chair for supervision. He awaits confirmation by the Senate.
"I suspect that perceptions are changing about the possibility of Yellen returning because she continues to stick her heels in on regulatory issues. Trump wants to deregulate, and Yellen's made it clear that's a line in the sand … and she repeated that yesterday and made it clear her position was quite different than President Trump. That creates an awkward situation on both sides here," said Ward McCarthy, chief financial economist at Jefferies. "The president is going to want to appoint someone who is going to embrace his deregulatory aspirations and she may not want the job if she's going to be pushed in that direction."
At a press briefing after the Fed released its post-meeting statement Wednesday, Yellen did comment about keeping tougher rules in force.
"We put in place, since the financial crisis, a set of core reforms that have strengthened the financial system. And in my personal view, it's important they remain in place. And those core reforms are: more capital, higher quality capital, more liquidity, especially in systemically important banking institutions. Stress testing and resolution plans, and those four prongs of improvements in banking supervision have really strengthened the financial system," Yellen said at the briefing.
Swonk said the Fed chair has a lot of latitude to regulate within the law, and the next chairman could have a more laissez-faire attitude about regulating banks even if Dodd-Frank legislation remains in place.
"You can tweak things like the Volcker rule in your interpretation of the law, and that's where personnel-driven deregulation comes into play," she said. "It's the nuance—how much regulation. How far do we regulate? What do we consider bank capital? All of those things fall into a gray area."
McCarthy said Warsh would be different on the regulatory front but also possibly on the latest steps the Fed announced to unwind its massive $4.5 trillion balance sheet. The Fed announced a process of winding it down by tapering the amount of purchases it makes on a monthly basis to cover maturing Treasury and mortgage securities. By next year, its goal is to reduce the amount of purchases by $50 billion a month, which would allow for a gradual shrinking of the balance sheet.
"What Kevin Warsh, I think, primarily represents is a change in the regulatory environment, and Kevin Warsh has been one of the harshest critics of the Fed's expansion of the balance sheet. The primary questions were he to be appointed, you'd have to wonder if the current balance sheet normalization process happens fast enough to make him happy," said McCarthy.
He said the program may be difficult to change if it proves to work once it's in place. "If I were in her shoes, I would be disinclined to come back, not just because of the regulatory issues but because she's accomplished so much. … She finished tapering. She started rate normalization and now she started balance sheet normalization," said McCarthy.
Strategists have said they have been surprised by how much guidance the Fed provided on the balance sheet reduction ahead of the announcement, and there's been little market reaction to it.
"I think there are a lot of people like me who get frustrated with her periodic bouts of indecision. They did this [balance sheet reduction plan], McCarthy said. "Her record on rate normalization has been a little more spotty. I think it's the right thing to do and she deserves a lot of credit for pulling forward balance sheet normalization. They were talking about it for 2018. … She pulled it forward, and she pulled it off."