Elizabeth Duke’s resignation from the Federal Reserve Board and Chairman Ben S. Bernanke’s potential departure in January could set off a series of vacancies and appointments that give President Barack Obama the opportunity to leave his mark on the Fed for a decade or longer.

Duke announced Thursday she is leaving the board in August, and Obama signaled last month that he expects Bernanke to leave when his current term expires next year, saying the central bank chief had stayed in his post “longer than he wanted.”

“There’s an opportunity for the president to shape the composition of the board for a long time,” said Roberto Perli, a Washington-based partner for Cornerstone Macro LP and a former senior staff economist in the Fed’s division of monetary affairs. “Obama is unlikely to nominate someone who differs from the current policy framework. It cements the fact that monetary policy is likely to remain very accommodative for the next couple of years, if not longer.”

The pending vacancies at the Fed will require confirmation by the Senate, which has posed an obstacle to previous financial regulatory appointments by Obama, including at the central bank. Nobel-prize winning economist Peter Diamond was unable to win confirmation to the central bank in 2010 amid Republican opposition. The Senate approved Bernanke for his second term with the thinnest margin of any recent chairman, as senators registered outrage at bailouts during the financial crisis.

Senate Gridlock

With Senate gridlock repeatedly thwarting Obama’s agenda, any appointments could be a challenge, said Michael Hanson, senior U.S. economist at Bank of America Corp. in New York.

“There’s a little risk of course, given how productive the Senate has been in recent years, that we end up with a very short-handed Fed,” said Hanson, a former Fed economist. “That could be a problem.”

The first task is filling Bernanke’s seat with a chairman who will serve through 2018. Economists in a June 19-20 Bloomberg survey assigned 65 percent odds that Obama will pick Janet Yellen, the central bank’s current vice chairman.

If Yellen becomes chairman, that would leave open the influential number-two position at the central bank. If Obama instead opts to appoint one of his former advisers, such as former Treasury Secretaries Lawrence Summers or Timothy F. Geithner, then Yellen may depart the central bank when her term as vice chairman expires in October 2014.

Obama also confronts another opening on the board: Governor Jerome Powell’s term expires the same month as Bernanke’s, in January 2014.

Obama’s Opportunity

The Duke and Powell seats present a particular opportunity for the president because of the length of a Fed governor’s tenure. Duke’s replacement will have an appointment that lasts through 2026 and the nominee for Powell’s seat will have a term that lasts through 2028.

Even with Obama’s four potential appointments to the Fed board, including the top two officials, there are limits to the president’s influence on future policy. Obama has no say in who serves as president of the 12 regional Fed banks. The Fed’s presidents rotate voting on the Federal Open Market Committee with five voting in any given year. The seven governors always vote on monetary policy.

“Even though you have a lot of appointments, it’s a smaller percentage of the FOMC group,” said former Richmond Fed President J. Alfred Broaddus. The presidents are often more vocal in their views, he said: “Just look around, the people who were dissenting and making noise are not the governors.”

Banking Background

Duke’s seat in the past has been filled by someone with a “background in banking” and “the person they may want to replace her may have that same background,” Hanson said.

Duke took over an unexpired term at the Fed that had previously been filled by Susan Bies, a former banker at First Tennessee National Corp. Bies was appointed by President George W. Bush in 2001 and left the Fed in 2007, before her full term expired.

Press secretary Jay Carney said today he had no personnel announcements to make on a replacement for Duke. He declined to say whether there will be any effort by the president to nominate a successor before the August recess by Congress.

Appointing a high-profile economist to one of the open seats could strengthen the Fed’s credibility, Hanson said.

“If you have someone who is a face of the committee, not upstaging the chairman or chairwoman, but giving an explicit message that the Fed is committed to its path, it helps credibility,” Hanson said.

Bank Supervision

By statute, the Fed has two vice chairmen, though the second seat has never been occupied. The Dodd-Frank Act overhauling U.S. financial regulation created a second vice chairman’s position at the Fed focused on bank supervision. The vice chairman of supervision seat has been empty for more than 1,000 days.

Fed Governor Daniel Tarullo has taken the lead on regulation, though he has not been appointed to the vice chairmanship.

“Given the fact that the Fed will still be in uncharted territory implementing financial reforms and dealing with the exit from a more than $3 trillion balance sheet, I think there’s a role to be played by the board of governors,” said Sarah Binder, a senior fellow at the Brookings Institution who researches the relationship between the Fed and Congress. The appointments may be contentious, Binder said.

“Republicans still want to see a much tighter monetary policy and more quickly,” said Binder. “Democrats, when they pay attention to the Fed, understand it’s the only sort of stimulus in town and they’ll want commitments that the Fed is not going to withdraw that level of stimulus.”

Once Bernanke and Duke leave, none of the governors who served during the height of the financial crisis will remain at the central bank. Yellen was the San Francisco Fed President during the financial crisis. She didn’t join the board of governors until October 2010.