By Ann Saphir and Howard Schneider

(Reuters) -U.S. Federal Reserve officials got encouraging data on Friday suggesting inflation is cooling, news that helped ease doubts over how well monetary policy is doing its job after stronger-than-expected price increases earlier in the year.

But while progress on a month-to-month basis is increasingly clear, the road to the Fed’s 2% inflation goal – measured in year-over-year terms – is likely to be long, complicating discussions about when to cut interest rates.    “We are getting evidence that (policy) is tight enough,” San Francisco Federal Reserve Bank President Mary Daly told CNBC in an interview just minutes after a Bureau of Economic Analysis report showed inflation did not rise at all from April to May. “It’s really challenging to look anywhere and not see monetary policy working: we have growth slowing, spending slowing, the labor market slowing, inflation coming down.”

At the same time, Friday’s inflation data shows there’s still a lot more progress needed. From a year ago, the personal consumption expenditures price index rose 2.6%. The Fed’s target is 2%.

The Fed has kept its policy rate in the 5.25%-5.5% range since last July when it delivered what U.S. central bankers say will likely prove to be the last rate hike of an aggressive campaign begun in March 2022 to fight high inflation.

The central bank has said no rate cuts will be appropriate until policymakers gain more confidence that inflation is on a sustainable path to their 2% goal.

Traders on Friday bet that the latest inflation figures will firm up that confidence. Short-term interest-rate futures are now pricing in about a two-in-three chance that the Fed will deliver a first policy rate cut in September, with another one expected in December.

“May’s inflation print was well below the threshold the Fed needs to be comfortable and breaks the string of high inflation prints we’ve seen since the start of the year,” wrote Natixis economist Christopher Hodge.

But the optics for rate cuts could be challenging.

Even if inflation as measured from month to month rises slightly so that, annualized, it is in line with the Fed’s 2% target, the super-low inflation readings in the second-half of last year mean it would take until the end of the year to see progress in the year-over-year readings.

That could force Fed officials into a difficult debate over how to decide just when the month-to-month numbers provide enough signal to light the fuse on rate cuts and stop referring to inflation as “elevated” in their policy statement.

The Fed next meets on July 30-31.

Daly on Friday reiterated that inflation is still too high, and said she expects year-over-year inflation to potentially remain above 2% through the end of 2025. Earlier this week Fed Governor Lisa Cook said she expects inflation to go “sideways” this year, and fall more sharply next year.

Many Fed policymakers have lately stayed away from making clear pronouncements on when they may cut rates, referring instead to various scenarios that could mean a later, or an earlier, decision.

So far the Fed has kept rates on hold for longer than several previous episodes.

Atlanta Fed President Raphael Bostic is among the minority of U.S. central bankers who have been willing to put a time frame on a possible rate cut. “I continue to believe conditions will likely call for a cut in the federal funds rate in the fourth quarter of this year,” he said on Thursday.

PCE inflation peaked in June 2022 at 7.1%.

“The big picture for me is that there has been tremendous progress but there is still a distance to travel,” Bostic said, and the details of the inflation data will matter to the Fed’s assessment of further progress. “There have been periods when one or a small number of items move the headline number. I want to look through that and see if there are other dimensions that give us confidence…Even if the topline stays where it is.”

One detail Bostic and other Fed policymakers have their eye on is the share of goods and services whose prices are increasing at 5% or more. That share has fallen recently.

Fed Governor Michelle Bowman, among the more hawkish of U.S. central bankers, remains wary of reducing borrowing costs this year. Though central banks in other parts of the world have begun to reduce their policy rates, Bowman said the Fed would follow its own path.

“We’ve got…really strong employment and a strong labor market at the moment, but we haven’t quite reached our inflation goal, and we’ll continue to work toward that on our own pace,” she said on Friday.

(Reporting by Ann Saphir; Additional reporting by Howard Schneider and Michael S. Derby; Editing by Andrea Ricci)

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