JACKSON HOLE, Wyo. – Bette Midler wouldn’t normally be expected to trumpet her opinion on who should be the next chairman of the Federal Reserve.

This time is different.

A battle over what’s arguably the world’s most powerful economic post has turned into an unusually public struggle over two renowned economists: Fed Vice Chair Janet Yellen and former Treasury Secretary Larry Summers.

Chairman Ben Bernanke is expected to step down when his second term ends in January, and the contest to succeed him is sure to spark chatter at this week’s annual meeting of central bankers in Jackson Hole, Wyo. While the principals have kept mum, their warring camps have waged a battle that’s riled Congress, spawned opinion columns and sparked commentary from notables like the Divine Miss M.

Midler recalled that before the 2008 financial crisis, Summers resisted efforts to regulate the kinds of risky investments that helped ignite the crisis.

Sample Midler tweet: “HUH. The architect of bank deregulation, which turned straight-laced banks into casinos and bankers into pimps, may be next Head Fed: Summers.”

That’s just the public campaign.

There’s also been a whisper campaign suggesting that Yellen might lack the gravitas to be chairman — a job requiring enormous skills of persuasion as well as credibility with fellow Fed officials and global leaders. Yellen’s supporters regard such assertions as a sexist attack on someone who’d be the first woman to lead the Fed.

The Economist magazine described a rancorous battle of “name calling and innuendo.”

Participants at the Jackson Hole gathering, held in the picturesque shadows of the Grand Teton Mountains, will meet in a conference room to mull topics like “The Natural Rate of Interest, Financial Crises and the Zero Lower Bound.”

The hallways and grounds of the lodge are where conversation will likely take up the juicier succession battle — something the Fed, which will turn 100 in December, has never before witnessed. The selection of a chairman has long been a matter handled privately by a president and his most senior advisers.

“Most presidents strive for a smooth, quiet transition that doesn’t put markets on edge,” said David Jones, an economist and author of several books on the Fed. “Now, we have this knock-down, dragged-out fight, and nobody knows what will happen.”

The selections of the three most recent chairmen — Paul Volcker, Alan Greenspan and Bernanke — followed a familiar script: A search team quietly interviewed candidates. And then the president made his decision, typically after the White House had privately checked to be sure Wall Street had no strenuous objections.

Summers and Yellen both declined through spokesmen to speak publicly about the Fed post. At Jackson Hole, Yellen will moderate discussions but isn’t scheduled to address the conference. Summers, who has attended in the past, isn’t here this year.