But some of Ms. Yellen's critics remain wary. They worry that she would not be sufficiently concerned about the possibility that inflation will accelerate as the economic recovery gains strength. If nominated, she could face opposition from Senate Republicans who have repeatedly expressed concern that the Fed's campaign would destabilize financial markets and make controlling the pace of inflation more difficult.
"I think people read Janet Yellen's speeches as saying that she puts a higher weight on joblessness compared to inflation" than the typical member of the Fed's policy-making committee, said Vincent Reinhart, formerly the head of the Fed's monetary policy staff and now the chief United States economist at Morgan Stanley. "And that includes Ben Bernanke."
He added, however, that her nomination would be unlikely to shake financial markets because she already exercises considerable influence, so any shift in policy would most likely be modest.
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Moreover, Ms. Yellen's personal qualities, highlighted by the 1996 episode, have helped her win supporters even among her ideological opponents.
"She makes an argument on the merits and she sticks with it," said Alan Blinder, an economics professor at Princeton nominated to the Fed alongside Ms. Yellen in 1994. "And she's good at articulating an argument in a way that doesn't leave people on the other side hopping mad at her."
Despite their disagreement at the time, Mr. Greenspan said that he continued to hold Ms. Yellen in high regard. "I did listen to her more carefully because she articulates her position in a way that you can follow it analytically," he said in an interview. "Intuitions are useless. Janet's conversation and her presentations were factually based, and that always got my attention."
If confirmed, Ms. Yellen would become the first woman to lead a major central bank. She is 66, seven years older than Mr. Bernanke. She would be 71 by the end of a four-year term as chairwoman. But she remains in good health, and friends say that, like other prominent women of her generation, she regards herself as being in the prime of a late-blooming career. Nor would she be the oldest person to lead the Fed. Mr. Greenspan began his fifth and final term in 2004 at 78.
Ms. Yellen, slight, white-haired and described by one colleague as a "small lady with a large I.Q.," does not loom like Paul Volcker nor cut like Mr. Greenspan. Her personal style more closely resembles Mr. Bernanke's soft-spoken manner. The force of her arguments can catch people by surprise.
Kevin Hassett, a staff economist at the Fed when Ms. Yellen arrived in 1994, recalled that she started to eat lunch regularly in the staff cafeteria to subvert the hierarchical system that limited communication between Fed governors and the vast army of research economists. Other governors had tried to change the rules but Ms. Yellen, he said, found a way around them.
"It showed a kind of grace and wisdom that is very unusual in Washington," said Mr. Hassett, now a fellow at the right-leaning American Enterprise Institute.
Mr. Hassett is among those who worry that Ms. Yellen does not place a sufficient emphasis on controlling inflation. "But I hold her in the highest possible regard," he said. If the Obama administration is "going to pick a Fed chair that thinks the way they do, then Janet Yellen would be the best possible choice."
There has been no official word from the White House or Mr. Bernanke that the Fed will have a new chairman next year. The decision is up to Mr. Obama, and aides say he has not yet focused on who he wants in the job.
But Mr. Bernanke may have signaled his departure last week when the Fed announced that he planned to skip an annual summer conference in Jackson Hole, Wyo. The Fed's chairman has attended the event in each of the previous 25 years.
People who have spoken with Mr. Bernanke say he is tired after leading the Fed through eight years that were mostly consumed by crisis. Mr. Bernanke has also sought to make monetary policy more transparent and predictable, dispelling the image of the Fed chairman as a kind of artist. "I don't think that I'm the only person in the world who can manage the exit" from the Fed's current policies, he said last month. The only way to prove that point would be to let someone else do it.
President Obama, for his part, has the opportunity to nominate the first Democrat to lead the Federal Reserve since President Carter chose Mr. Volcker in 1979 — and the person he selects will serve a term that extends two years beyond his own.
Ms. Yellen has avoided questions about her future, but she, too, appeared to address the subject indirectly this month. Asked about the dearth of female economic policy makers, she responded that it was "something we're going to see increase over time, and it's time for that to happen."
She declined a request to be interviewed for this article.
There are other potential candidates for the job, including Roger W. Ferguson Jr. and Professor Blinder, both former Fed officials, and economic advisers to Mr. Obama including Timothy F. Geithner and Lawrence H. Summers. But Ms. Yellen appears to be the front-runner in a race that has not actually started quite yet.
None of the other obvious candidates possess the same combination of academic credentials and policy-making experience. No Fed chairman has been as deeply steeped in both the theory and practice of central banking.
"In the realm of plausible candidates, she is by far the best," said Christina Romer, a former chairwoman of Mr. Obama's Council of Economic Advisers who is an economics professor at the University of California, Berkeley. She has known Ms. Yellen for years and counts her as a friend.
Asked who else she would recommend that the president consider for the job, Ms. Romer responded, "I would stop after No. 1."
Ms. Yellen, born in Brooklyn in 1946, has said that she became interested in economics as a way of thinking logically about how to help people. She studied at Yale under the Nobel laureate James Tobin, a leading proponent of the view that governments could mitigate recessions. Professor Tobin, now dead, told Business Week magazine in 1997 that Ms. Yellen had "a genius for expressing complicated arguments simply and clearly."
She built an academic career at Berkeley together with her husband, the economist George A. Akerlof, whom she met in a Fed cafeteria. Much of their work together highlighted flaws in the economic theory that markets operate efficiently, a theory that basically treats government policy as inherently costly. Their work showed that government, including central banks, could indeed adopt economic policies that improved people's lives.
Colleagues and people familiar with their work said that Professor Akerlof, who shared the Nobel in economics in 2001 with Joseph E. Stiglitz and A. Michael Spence, was the more creative thinker, while Professor Yellen was more rigorous.
"George can sometimes go off in a direction that is untethered from the real world, and Janet was better at bringing it back," said Professor Romer, who joined the Berkeley economics faculty with her husband and collaborator, David Romer, about a decade after Ms. Yellen and Mr. Akerlof.
In 1994, the Clinton administration nominated Ms. Yellen to the Fed on the recommendation of Laura D'Andrea Tyson, a colleague at Berkeley then serving as the head of the Council of Economic Advisers.
Ms. Yellen and Professor Blinder were chosen to check the Fed's tendency to curtail growth for fear of inflation. But in an unlikely twist, Mr. Greenspan became the strongest advocate for letting the economy grow more quickly, and Ms. Yellen helped provide intellectual justification for keeping interest rates low.
"She was much more aware of the current state of academic literature on fairly technical issues," Mr. Greenspan recalled. "I found her very useful in that regard."
At the time of the 1996 debate, inflation had fallen to a relatively stable pace of about 3 percent a year, eliminating much of the unpredictability that had plagued the economy. Mr. Greenspan saw clear benefits in pushing all the way to zero. But some economists worried that lower inflation might result in permanently higher unemployment, by making it difficult to adjust wages. And it would bring the economy dangerously close to deflation, the destabilizing condition in which falling prices freeze economic activity as people anticipate lower prices.
"I believe that heading toward 2 percent inflation would be a good idea, and that we should do so in a slow fashion, looking at what happens along the way," Ms. Yellen said at the 1996 meeting. The debate continued for years; the Fed finally adopted a 2 percent inflation target last year.
But Laurence H. Meyer, a former Fed governor, recalled the 1996 meeting as a turning point. "She was the one who really brought the story that inflation could be too low," said Mr. Meyer, a senior adviser at MacroEconomic Advisers. "And she was very effective. Once she said it, it seemed so obvious and sensible."
Ms. Yellen began a second stint at the Fed in 2004 when she was named president of the Federal Reserve Bank of San Francisco. She has played a leading role in the Fed's movement to provide "forward guidance" about the path of policy over the next several years, persuading investors that it is safe to accept lower interest rates.
But it is easy to overstate her differences with those more focused on inflation. "I think I am as committed to price stability and the attainment of price stability as any member of the F.O.M.C.," a reference to the Federal Open Market Committee, Ms. Yellen said at a 2010 luncheon in Los Angeles. "When the time has come, am I going to support raising interest rates? You bet."