“The economy is humming along,” said Julia Coronado, president of MacroPolicy Perspectives, a New York economic research firm. “The markets are humming along. Given all the other stuff that’s going on, why mess with that?”
Mr. Trump is considering four candidates to replace Ms. Yellen. On that short list: Gary D. Cohn, the president’s chief economic adviser; Jerome H. Powell, the only Republican on the Fed’s board of governors; John B. Taylor, a Stanford University economist who has criticized the Fed for raising interest rates too slowly; and Kevin Warsh, a former Fed governor and a fellow at the Hoover Institution.
“Honestly, I like them all,” Mr. Trump said Tuesday. He added that he would choose a nominee “over the next very short period of time.” The White House would like to make the nomination before he departs for a 12-day trip to Asia in early November. Ms. Yellen’s term ends in early February, and the next chairman must be confirmed by the Senate.
Ms. Yellen, 71, has spent almost two decades at the Fed. She was a Fed governor in the mid-1990s, then returned to the Fed as president of the Federal Reserve Bank of San Francisco in 2004. She became vice chairwoman in 2010 and chairwoman in 2014.
During her four-year term, the unemployment rate has fallen to 4.2 percent while inflation has remained below 2 percent. Both metrics are close to the levels the Fed regards as ideal. Indeed, it has seldom come closer. She also has presided over the gradual reduction of the Fed’s stimulus campaign, which was implemented in the wake of the 2008 financial crisis, as the economy struggled through a bruising recession with persistent unemployment that peaked at 10 percent in October 2009.
Ms. Yellen’s calm and careful leadership style has won fans, both inside and outside of the Fed. John Williams, president of the San Francisco Fed, said that Ms. Yellen had been effective in building a consensus about the direction of policy among Fed officials, and in communicating policy to the markets and the public.
“When she came in there was a lot of concern about how would we unwind our policies and would that be disruptive and difficult, especially in the context of a global economy where other central banks were going in the other direction,” he said. “Now it’s almost like, ‘That was easy!’ But it wasn’t. It took hard work.”
Some of the other candidates, notably Mr. Taylor and Mr. Warsh, have argued the Fed should be raising interest rates more quickly. But financial regulation is the area in which a new chairman likely would make the largest changes. The Fed supervises the nation’s largest banks and oversees the broader financial system.
Mr. Trump wants to loosen financial regulations, which he regards as an impediment to economic growth. Ms. Yellen, who played a key role implementing the new banking rules after the 2008 crisis, has acknowledged room for improvement. But in a high-profile speech in August, she also issued a warning against going too far.
The Treasury secretary, Steven Mnuchin, has argued that installing a new Fed chairman would help Mr. Trump achieve his goal of reducing regulation.
Charles W. Calomiris, a finance professor at Columbia University, said that Ms. Yellen’s approach to regulation was reason enough to replace her. “It’s not just that regulation is excessively costly and complex,” he said. “It’s also failing to achieve its objectives.”
But Ms. Yellen has faced relatively little public criticism. Mr. Trump criticized her on the campaign trail, but he has praised her since taking office.
House Republicans have been among Ms. Yellen’s fiercest critics, regularly calling on her to increase interest rates and to reduce financial regulations.
Representative Jeb Hensarling, the Texas Republican who chairs the House Financial Services Committee, sent a letter to Ms. Yellen in February demanding that the Fed stop crafting regulations until Mr. Trump appointed a new vice chairman for supervision.
Mr. Trump’s choice, Randal K. Quarles, who was sworn in last week, will oversee the Fed’s regulatory work, including its stress tests of large banks.
Mr. Hensarling also has criticized Ms. Yellen’s approach to monetary policy. But he has not commented on whether Ms. Yellen should be nominated for a second term, and a spokeswoman did not respond to an email on Wednesday.
A spokeswoman for Senator Michael D. Crapo, the Idaho Republican who chairs the Banking Committee, said he had not taken a position on Ms. Yellen’s candidacy.
Even some of Ms. Yellen’s critics favor her reappointment.
“She is an intelligent and levelheaded individual,” said Deborah J. Lucas, an economics professor at M.I.T. who has criticized the Fed’s bond purchases. “I trust her to make prudent decisions, particularly when it matters most, which is if there is another crisis. Continuity and experience seem especially valuable right now.”
Presidents in recent decades have generally decided to reappoint Fed chairmen, even from the opposing political party, on the theory that stability would comfort markets. Ronald Reagan, the last Republican president to inherit a Fed chairman who was a Democrat, thought seriously about replacing Paul A. Volcker in 1983, but ultimately decided to nominate Mr. Volcker to a second term. “The financial market seems set on having him,” Reagan wrote in his diary. “I don’t want to shake their confidence in recovery.”
President Clinton nominated Alan Greenspan in 1996 and in 2000 and President George W. Bush nominated Mr. Greenspan to a fifth term in 2004, before tapping Ben S. Bernanke to begin in 2006.
President Obama nominated Mr. Bernanke for a second term in 2010. When Mr. Bernanke stepped down in 2014, Mr. Obama named Ms. Yellen.
The last Fed chairman who did not serve a second term was G. William Miller, who is widely regarded as the least effective leader in the Fed’s modern history. Mr. Miller was also the last person without an economics degree to run the central bank. He was nominated by President Carter in 1978. Both unemployment and inflation were high and rising, and he was replaced after just 17 months by Mr. Volcker.