The Fed chair is not an executive branch position so the president cannot fire Yellen at will. In a 1935 Supreme Court decision, Humphrey's Executor v. United States (295 U.S. 602), the court ruled that an officer who is not in an executive branch position may be removed only with procedures consistent with statutory conditions enacted by Congress. They cannot be removed solely for political reasons. So if Yellen can indeed be removed "for cause" then Congress needs to identify what that "cause" is and Yellen has to violate it. Did she?
My original point was that ‘for cause’ would *not* include policy differences, so the Fed Chair does not serve at anyone’s ‘pleasure’. Financial markets and the Fed itself pretty much rule themselves.