* Legacy rests on highlighting financial stability risks
* Could leave yet more power in hands of regional Fed banks
* Senate has not set a vote on three board nominees
(Adds details on Harvard, Fed quorum rules)
NEW YORK, April 3 (Reuters) - Federal Reserve Governor Jeremy Stein, who has spearheaded the debate over whether monetary policy should be used to combat asset bubbles, will step down next month, leaving another big hole in the ranks of the U.S. central bank.
Stein will leave on May 28 to return to his teaching post at Harvard University. He has served at the Fed for nearly two years, and made the move now because he risked losing tenure at Harvard had he stayed in Washington much longer.
The departure, announced on Thursday, will open up a second vacancy on the seven-person Fed board, assuming the U.S. Senate soon approves three nominees awaiting confirmation. The loss of Stein could complicate things for the board, which has been understaffed or in flux for years, as it attempts to reverse its most accommodative policy experiment ever.
Stein, 53, announced his departure in a resignation letter to President Barack Obama, which the Fed released publicly.
"During my time here, the economy has moved steadily back in the direction of full employment, and a number of important steps have been taken to make the financial system stronger and more resilient," he said in the letter. "There is undoubtedly more work to be done on both dimensions."
One of three governors on the Fed's financial stability committee, Stein's legacy will probably rest on his efforts to convince fellow policymakers that they should stand ready to raise interest rates to head off any dangerous asset-price bubbles that may arise.
He gave a speech more than a year ago suggesting that monetary policy, and not just regulation and supervision, should be a tool to deal with financial instabilities that threatened the economy. In what is now a famous line within Fed circles, he said policy "gets in all the cracks" that regulation might not.
The suggestion broke from monetary tradition and appears to have won partial support from Fed Chair Janet Yellen and her predecessor Ben Bernanke, among some others.
Yellen has acknowledged that persistently low rates can incite the development of bubbles, telling Congress in a February testimony that the central bank "can't take monetary policy off the table as a tool used to address it."
On Thursday, Yellen said Stein "served as an intellectual leader" at the Fed. "His understanding of monetary policy and markets as well as his expertise in banking and financial regulation has proven invaluable," she said in a statement.
Stein broke from the "party line" on dealing with financial instabilities, said Carl Tannenbaum, a former Fed official who is now chief economist at Northern Trust. "It was nice to have a very talented scholar on the board to think through these things."
Stein will return to the Boston area where his family remains. Though he might have stayed as governor for a year longer, especially given the unfilled positions on the Fed board, Harvard's rigid tenure policies prompted the resignation.
While Fed governors are appointed to 14-year terms, very few serve them in full. Stein himself was appointed by Obama in May 2012 to serve an unexpired term that ends in 2018, and that will now have to be filled by someone else.
The Senate Banking Committee has yet to schedule a vote on three nominees: sitting Governor Jerome Powell, whose term expires this year; former top U.S. Treasury official Lael Brainard; and former Bank of Israel Governor Stanley Fischer, who would become Yellen's vice chair.
The panel would have to sign off on the nominations before the full Senate can grant its final approval.
With the nominees yet to be confirmed and Stein on his way out, Yellen and Governor Daniel Tarullo are providing the only stability on the Fed board, whose members have permanent votes on monetary policy. Bernanke and former Governors Sarah Bloom Raskin and Elizabeth Duke have all left in the last eight months.
"The Federal Reserve, which has lots to do, will now be badly shorthanded," said Alan Blinder, a former Fed vice chair who is now an economics professor at Princeton University. "The remedy is clear: the Senate should hold votes on Fischer, Brainard, and Powell quickly."
The Fed can still make emergency decisions with fewer than five governors thanks to a 2003 rule change that requires a simple majority of even a depleted board for a quorum.
But the empty offices not only leave more work to sitting governors and their staff, but they effectively give more power to the heads of the Fed's 12 regional branches, who rotate through voting positions each year.
At the last policy-setting meeting in March, five of the nine voters were from regional Fed banks, who generally tend to be more hawkish than governors. Stein himself is considered perhaps the most hawkish member of the board, meaning he is seen as less willing to keep stimulating the economy in the face of possible problems the monetary accommodation could cause.
The Fed has kept interest rates near zero for more than five years and likely plans to keep them there until 2015 to encourage investment and hiring in the world's largest economy. This year, in a nod to stronger growth and employment, it started scaling back an aggressive bond-buying program.
(Additional reporting by Timothy Ahmann in Washington; Editing by Andrea Ricci and Leslie Adler)