U.S. President Donald Trump speaks as Jerome Powell, governor of the U.S. Federal Reserve and Trumps nominee as chairman of the Federal Reserve, left, listens during a nomination announcement in the Rose Garden of the White House in Washington, D.C., U.S., on Thursday, Nov. 2, 2017. Andrew Harrer| Bloomberg | Getty Images

Federal Reserve Chairman Jerome Powell has made clear the Fed will not bend to the will of President Donald Trump, and so far the central bank appears to be winning. In a town where Trump has succeeded in getting his way with many institutions, influencing policy at the Federal Reserve hasn't been one of them. That was evidenced Thursday when Stephen Moore became the second of two controversial potential Trump nominees to remove himself from the process, not a surprise in Washington where it appears he would not receive sufficient support in the Senate. But Trump is likely to try again, since the Fed and Powell have not listened to his calls to lower interest rates or embark on a program of quantitative easing, a policy the Fed initiated during the financial crisis and has since retired.

"Trump views loyalty over anything else and he needs people on the Fed who are loyal to him, and he will look for someone else in the same loyalty mode as Herman Cain and Stephen Moore," said Tom Block, Washington policy strategist at FundStrat. "As has been pointed out by many, Trump's earlier choices have been solid economists who have earned their seats. Then he tried to put someone loyal across at the Fed, and he's having a hard time finding someone." Moore said he was bowing out because attacks on his character have become untenable for himself and his family. Block said several Republican women senators, including Iowa Sen. Joni Ernst, were unlikely to support him because of controversial remarks he made about women. But the exit of Moore was viewed as a positive by those who believed Trump was trying to politicize the Fed.

'Picked for their acumen'

"The failure of the two potential nominees to gain traction, I think, suggests there's a strong bipartisan support for continued independence of the Fed and Fed policy because the fact that senators came back and said this doesn't seem quite right, gives you an indication that there are places where you can inject politics and places where you would prefer it not to go," said Barclays chief U.S. economist Michael Gapen. "We think nominees to the Federal Reserve board should be picked for their acumen and monetary policy bona fides, not for their political stripes." Moore and Herman Cain, a former pizza restaurant executive, who withdrew previously, were criticized for changing their prior hawkish tones to fit with Trump's demands for easier Fed policy. Cain, a GOP presidential candidate in 2012, had presented a tax plan at the time that advocated a return to the gold standard, and Moore had been his adviser. Both candidates did have some related experience. Moore holds a master of arts in economics from George Mason University. He also served as a fellow at the Cato Institute, the Club for Growth, and the Heritage Foundation and was formerly on The Wall Street Journal editorial board. Cain was a chairman and deputy chairman at both the Omaha branch of the Federal Reserve Bank of Kansas City and the Federal Reserve Bank of Kansas City.

Stephen Moore Anjali Sundaram | CNBC

As the Fed met earlier this week, Trump tweeted criticism of the Federal Reserve's policy and called for a 1 percentage point rate cut and a return to financial crisis policy, quantitative easing. He blamed the Fed for holding back the economy. Moore has been supportive of rate cuts in recent comments. Powell has publicly said the Fed is not influenced by the White House, and yesterday he made it clear the Fed was not considering interest rate cuts. When he spoke to the media following the Fed's meeting, he reiterated the Fed was patient and not ready to move in either direction. He also said the Fed does not see low inflation as a persistent problem that would require a policy change. In other words, he signaled there was no rate cut now under consideration by the Fed. "Powell said the Committee isn't worried about too low inflation which appears to rule out a rate cut for now. This is going to make the Trump administration a little cross as they try to engender faster rocket ship growth that can put the President back in the White House for a second term," MUFG chief financial economist Chris Rupkey wrote, following Wednesday's briefing by Powell.

Protecting the reserve currency

If Powell did appear to be influenced by the president, it would be a negative for financial markets. "Because [the dollar] is the reserve currency and will remain the reserve currency, it is imperative that we have a sound monetary structure that the independent Fed has done a good job of maintaining," said Block. The risk is that even thought the Fed does not respond to Trump's criticism, his tweets and other attacks could harm the Fed's credibility. "The perception in financial markets have been warped about what the Fed's motivation is because of the president's rhetoric," said Diane Swonk, chief economist at Grant Thornton. When Powell and the Fed signaled they would pause in the rate hiking cycle following the December hike, it was because of economic signals, not Trump's calls for easier policy, she said.