Replacing New York Fed President Bill Dudley may be one of the most controversial Fed appointments in recent memory.

Dudley, who is in his mid-60s, announced his retirement last week, likely by the spring or summer, and speculation is already rife in markets about who will get his job.

Some call it the second-most important job in the Federal Reserve system. It’s so critical that during the creation of the Dodd-Frank financial reform legislation, some in Congress proposed to make it a presidential appointment.

The head of the NY Fed oversees supervision of the big money center New York banks and executes the market trades needed for the Fed to hit its benchmark funds-rate target. It was the bank that did most of the heavy lifting for the Fed to acquire the trillions in assets under the quantitative easing program, and it will be on the front line of selling those assets as the Fed now unwinds its balance sheet.

Most important, the NY Fed president is first among equals of the 12 regional bank presidents. The president serves as the vice chairman of the Federal Open Market Committee, which sets monetary policy, and always has a vote. The other regional presidents rotate as voters.

Dudley was part of a triumvirate with Fed Chair Janet Yellen and recently departed Vice Chairman Stanley Fischer who were at the core of Fed policymaking.

The opening comes at a time when the Fed is under pressure to appoint more diverse presidents. Of 135 regional bank presidents, six have been women (three from the Cleveland Federal Reserve) and three have been nonwhites (two from Minneapolis), according to Aaron Klein of the Brookings Institution. Eleven regional banks have never had a nonwhite president and eight of 12 have never been led by a woman.

Brookings Vice Chairman Glenn Hutchins, a private equity investor, is co-chair of the search committee along Sara Horowitz, head of the NY Fed board of directors. It will ultimately choose the next president, with approval from the Feds’ board of governors.

In announcing the search, which is expected to take six to nine months, the NY Fed said it hired national executive search firm Spencer Stuart and Bridge Partners, a search firm that specializes in diversity.

Diversity is not the only factor to consider. There’s the issue of whether the head of the NY Fed should be an economist, like Dudley. President Donald Trump nominated Federal Reserve Governor Jerome Powell, who is not an economist, to replace Yellen, who is. Some say there are enough economists at the Fed and that Trump, who has shown a certain antipathy toward the profession, could appoint an economist to the vice chairman’s position or some of the other vacant governor positions on the board. Others contend that monetary policy is a job for which a Ph.D. in economics should be a requirement.

Finally, there’s the issue of financial market and banking expertise. Both are essential at a time when the Fed is winding down its balance sheet, and there is a movement in Washington to revisit and likely ease up on the Dodd-Frank Act. A candidate from a large financial institution could be seen as beholden to the banks or markets.

• Peter Blair Henry: The youngest dean ever appointed to the NYU Stern School of Business, Henry, 48, holds a Ph.D. in economics from MIT and was a Rhodes Scholar at Oxford University. He’s a renowned expert in international finance, emerging markets and international debt. He has played a central role in moderating panels at the Fed’s marquis conferences in Jackson Hole, Wyoming.
• Peter Fisher: The former Treasury undersecretary for domestic finance in the Bush administration now teaches at Dartmouth. He previously headed the fixed income portfolio at BlackRock and spent 14 years at the NY Fed, including holding Dudley’s prior job as head of open market operations.
• Sandie O’Connor: The JPMorgan chief of regulatory affairs has worked closely with Fed Chairman-nominee Powell on several projects involving reforming financial markets. She previously was JPM’s treasurer. Because O’Connor is said to have good relationships with many outside of Wall Street, one Fed observer described her as the only banker who would be acceptable in a search where bankers generally may not be.
• Seth Carpenter: The UBS chief economist was assistant Treasury secretary in charge of financial markets in the Obama administration. He spent 15 years at the Fed, ending his career there as deputy director of the Division of Monetary Affairs. He holds a Ph.D. in economics from Princeton.

Brian Sack, D.E. Shaw chief economist, former head of the open market operations at the NY Fed.

Robert Kaplan, Dallas Fed President.

Lael Brainard, current Fed Governor.

Simon Potter, current head open market operations at the NY Fed.

Krishna Guha, vice chairman of Evercore ISI, former executive vice president at the NY Fed.