Rep. Maxine Waters, Rep. Nancy Pelosi, Federal Reserve Chair Janet Yellen and International Monetary Fund Managing Director Christine Lagarde toast at a celebration on Capitol Hill in honor of Women's History Month in March. (Photo courtesy Pelosi's office)

The two most powerful women in the global economy will take center stage together on Wednesday in Washington for the first time, their historic achievements a testament to the shifting gender dynamics in a field long fueled by testosterone.

International Monetary Fund managing director Christine Lagarde and Federal Reserve Chair Janet Yellen are the first females to serve in their positions. Lagarde took office in 2011, a camera-ready product of the corporate world who has graced the pages of Vogue. Meanwhile, Yellen took the helm at the central bank this year, a plainspoken economist who made her career at the University of California Berkeley.

But the women have staked out opposing sides in one of the most urgent policy questions facing the global economy. Under Lagarde's leadership,the IMF has stepped up its critiques of the Fed, particularly as the unwinding of the central bank's stimulus program could destabilize markets in the developing world. Yellen has maintained the Fed's first priority is the domestic economy.

At their appearance Wednesday at an IMF conference, the two women will take on a related issue: how countries should tackle instability in their own financial systems. The fund recently outlined half a dozen areas of “concern” in the United States, including fragmented oversight of the insurance industry and weaker underwriting standards for some leveraged loans. Yellen will deliver a speech that could push back against calls for the Fed to  pop nascent bubbles by hiking short-term interest rates. Lagarde will question her afterwards.

“I suspect that Yellen would be extremely happy to debate this issue,” said Roberto Perli, head of global monetary policy research at Cornerstone Macro. “Listening to the point of view of another institution is useful. [But] I wouldn’t expect that the views of another institution would be particularly influential in setting the direction of policy.”

The IMF has been sounding warnings about the risks of an unwieldy unwinding of the Fed’s aggressive support for the U.S. economy for more than a year. The mere hint in spring 2013 that the central bank was considering pulling back its stimulus was enough to throw global markets into turmoil. According to an analysis by the World Bank, about $64 billion in capital that had sought out higher returns in developing economies quickly reversed course, sending some markets plunging as much as 15 percent. The confusion was amplified by division among Fed officials over how the central bank should actually proceed.

In a speech last summer at the prestigious annual conference in Jackson Hole, Wyo., held by the Federal Reserve Bank of Kansas City, Lagarde channeled the frustration of many of the fund’s members

“People have legitimate concerns that communication about financial conditions could undermine market stability. Yet saying too little could well be worse, leading to market surprises,” she said. “Even if managed well, exit from [unconventional monetary policy] may well present other ... countries with an arduous obstacle course.”

Those fears flared up again in January, just before Yellen took the reins at the Fed. Political unrest in Turkey caused the lira to plummet, scaring off investors and leaving the country’s central bank scrambling. The turmoil coincided with the start of the Fed’s phaseout of its trillion-dollar bond-buying program, adding to the anxiety in the markets.

When Yellen took office the next month, one of her first challenges was to reassure global investors. Her arrival at an international meeting of economic leaders known as the Group of 20 in Sydney alongside Lagarde helped quell their fears, as the two walked side-by-side for the flashing cameras.

In an interview with Bloomberg TV the next day, Lagarde said she expected markets would continue to be volatile as the Fed withdrew its stimulus but that she was confident the concerns of emerging markets were being heard.

“She’s a very talented, very competent, very friendly woman that I greatly respect and admire,” Lagarde said of Yellen.

Peterson Institute senior fellow Edwin Truman said that the IMF has been short on concrete advice for the Fed but the debate alone is worthwhile.

“Having open conversation, whether it’s about the U.S. economy, the state of the world economy … does tend to reinforce certain messages,” he said. “That certainly is constructive even if you don’t have something you can point to.”

There are political as well as policy incentives for maintaining a strong relationship between the two institutions. The IMF is headed by a board of governors made up of representatives from each member country. In the United States, that responsibility falls to the Treasury Secretary -- but the Fed chairman is the alternate. Traditionally, both have wielded significant influence in IMF decisions.

A major reform of the IMF’s financing and governance structure agreed to by member countries four years ago has been stalled by partisan bickering in Congress, which must also approve the deal. Yellen could prove to be a key ally to the IMF in bridging the political divide, though the Fed has yet to weigh in on the issue.

“It’s not in Christine Lagarde’s interest to pick a fight with Janet Yellen,” Truman said.

But Yellen also has reason to tread lightly. Her husband, Nobel-prize winning economist George Akerlof, is a senior resident scholar at the IMF. And that means Lagarde is his boss.