The U.S. unemployment rate may need to reach as high as 7.5%, double its current level, to end the country's outbreak of high inflation, according to new estimates from a team of researchers including two staff economists from the International Monetary Fund.

That would entail job losses of perhaps 6 million people, but the research found that only under "quite optimistic assumptions" about the behavior of the U.S. job market and inflation would the U.S. Federal Reserve be able to tame current price pressures with a smaller blow to employment.

As of June Fed officials at the median projected unemployment would need rise to only 4.1% by the end of 2024 for inflation to drift back towards the central bank's 2% target. The jobless rate in August was 3.7%.

"If either the labor market doesn't behave, or (inflation) expectations don't behave, the small increase in unemployment the Fed projects won't be enough. Either inflation will stay substantially higher, or we will have higher unemployment and a substantial economic slowdown," Johns Hopkins University economics professor Laurence Ball said in a summary of the research distributed as part of a Brookings Institution economic conference.

The paper, co-authored by IMF economists Daniel Leigh and Prachi Mishra, is part of an intensifying debate over just how much economic "pain," as Fed Chair Jerome Powell recently called it, may be needed to control the worst breakout of U.S. inflation since the 1980s.

The central bank is raising interest rates at the fastest pace since that era, when then-Fed chair Paul Volcker used an intense crackdown on credit to break consumer price increases that at one point exceeded 14% annually. But success came at the cost of recession and, as firms adjusted to the slowed economy and laid off workers, an unemployment rate that exceeded 10%.

Fed officials insist this time is different - their preferred measure of inflation may have peaked already at just over 6%, for instance - and still feel inflation can be beaten without a substantial rise in unemployment or a recession.

New Fed projections to be issued in two weeks are likely to show the outlook getting less benign, with analysts expecting the projections from the 19 Fed policymakers will reflect a longer and tougher battle to control inflation, and higher unemployment, than they foresaw in June.

But just how high is up for debate.

Economists and policymakers have sparred in recent weeks over whether the Fed's "soft landing" aspirations are altogether passe or still credible. Former Treasury Secretary Lawrence Summers for example has used the 7.5% figure also, a number the researchers incorporated into their scenarios along with the lower unemployment rate projected by the Fed in June, and a middle ground 5.3% unemployment rate the IMF has forecast.

For the Fed's best-case, the U.S economy would have to behave differently than it has in recent decades and some Fed policymakers have laid out arguments for why that is not unreasonable to expect.

Ball and his co-authors, looking at how inflation might behave under different rates of unemployment, did not rule that out altogether.

But the only outcome that "robustly" brought inflation under control, they concluded, was the one involving "a painful and prolonged increase in unemployment."