Yellen, speaking Friday at the central bank's annual summit in Jackson Hole, Wyoming, touted how a regulation revamp following the financial crisis has helped strengthen the system. She said the crisis "demanded action" and said the reforms "have made the system safer."
That, however, is just the opposite of what Trump has been preaching. The president has long bemoaned the handcuffs he sees Dodd-Frank and other reforms have put on banking, and is unlikely to want a Fed chair at odds with his thinking.
"When push comes to shove, would Trump, who put Scott Pruitt in charge of the EPA and Rick Perry in charge of the Energy Department, really keep on someone who defends financial regulation as strongly as Yellen just did?" Paul Ashworth, chief U.S. economist at Capital Economics, said in a note.
The initial reaction among pundits is that Gary Cohn may just have moved to the front of the line. For months, the head of the National Economic Council has been pushed as a likely Yellen successor, and her speech Friday may have cemented the move. Yellen's term expires in February, and Trump has not said whether he will reappoint her.
Cohn and Yellen are of like minds when it comes to low rates, but diverge on regulations.