Has the inflation battle been won? Not yet.

Inflation is beginning to decline significantly for US consumers. Gas is cheaper, eggs are about half their January price, and prices are no longer rising as fast for a wide variety of products.

But at least one person has yet to express his relief: Jerome H. Powell, the chairman of the Federal Reserve.

The Fed has been engaged in an aggressive war on inflation for the past 15 months, raising interest rates above 5 percent in an effort to get price increases back to a more normal pace. Last week, the officials announced they were skipping a rate hike in June, giving them more time to see how the changes already in place in the economy play out.

But mr. Powell stressed that it was too early to declare victory in the battle against rapid price increases.

The reason: While cheaper gasoline and slower food price adjustments have contributed to headline inflation falling since its four-decade peak last summer, food and fuel costs tend to fluctuate a lot. That obscures underlying trends. And a measure of “core” inflation that takes away food and fuel shows surprising staying power as a range of purchases from dental care and hair styling to education and auto insurance continue to rapidly increase in price.

Last week, Fed officials sharply revised their forecast of how high core inflation would be by the end of 2023. They now see it at 3.9 percent, higher than the 3.6 percent they predicted in March and nearly twice their inflation target of 2 percent.

In short, the economic picture plays out on a kind of split screen. While the strongest price hikes appear to be over for consumers – a relief to many, and a development that President Biden and his advisers have celebrated – Fed policymakers and many outside economists see continued cause for concern. Between the subtle signs that inflation could persist and the surprising resilience of the US economy, they believe central bankers may need to do more to cool growth and curb demand to prevent unusually high price increases from becoming permanent.

“Broad picture: We are making progress, but progress is slower than expected,” said Kristin J. Forbes, an economist at the Massachusetts Institute of Technology and former Bank of England policymaker. “Inflation is a bit more stubborn than we had hoped.”

A new consumer price index inflation report last week showed that inflation continued to decline sharply overall in May. That metric helps fuel the Fed’s preferred metric, the Personal Consumption Expenditures Index, which is used to define its 2 percent target. The new PCE figures will be released on June 30.

White House officials, who have spent months on the defensive about the role pandemic spending under Biden played in fueling demand and price increases, have greeted the recent cooling in inflation with enthusiasm.

“We have seen a very large reduction in inflation, by more than 50 percent,” Lael Brainard, the director of the White House National Economic Council, said in an interview. She added that inflation’s current trajectory offered cause for optimism that it could return to normal fairly quickly as the economy slowed, and expressed hope that knocking it down would not necessarily require a large rise in unemployment – something that historically accompanied the campaigns of the Fed. fight inflation.

“The employment picture is very sustainable,” she said.

But many economists are less optimistic. That’s partly because most of the factors that have contributed to inflation’s fall so far have been widely expected, some sort of low-hanging fruit of disinflation.

Supply chains were tested by the pandemic and have since healed, slowing the rise in commodity prices. An increase in oil prices linked to the war in Ukraine has faded.

And there may be more to come: Rents rose from 2021 as people moved out on their own or moved during the pandemic. They have since cooled off as landlords discovered that tenant demand was not strong enough to support ever-increasing prices, and the moderation is slowly being reflected in official inflation data.

What remains are relatively rapid price increases of services outside housing. This is a broad category and includes purchases that are often labour-intensive, such as hospital care, school fees and sports tickets. Those prices tend to rise as wages rise, both because employers try to cover their higher costs and because consumers who earn more can pay more without pulling out.

“The big action is behind us,” said Olivier Blanchard, a former International Monetary Fund chief economist who is now affiliated with the Peterson Institute. “What remains is the pressure on wages.”

At a press conference last week, Mr. Powell that in the measure of inflation that excludes food and energy “you just don’t see much progress.” important part of curbing the remaining price increases.

There are early signs that a slowdown in the labor market is underway. The Employment Cost Index measure of wages, which the Fed closely monitors, is climbing much faster than before the pandemic, but has slowed from the mid-2022 peak. A measure of average hourly wage has dropped even more noticeably. And jobless claims have risen in recent weeks.

But hiring has remained robust and the unemployment rate is low. That’s why economists are trying to figure out if the economy is cooling down enough to guarantee that inflation will return to full normalcy.

Cylus Scarbrough, 42, has witnessed both characteristics of today’s economy: rapid wage growth and rapid inflation. Mr. Scarbrough works as an analyst for a homebuilder in Sacramento, and he said his skills were in such demand that he could quickly get a new job if he wanted to. He received a 33 percent raise when he joined the company two years ago, and his salary has continued to rise since then.

Still, he’s racking up credit card debt because of higher inflation and because he and his family are spending more than before the pandemic. They’ve been to Disneyland twice in the past six months and eat out more often.

“It’s something about: You only live once,” he explained.

He said he was fine with spending outside of his budget because he bought a home just at the start of the pandemic and now has about $100,000 in equity. In fact, he’s not even that worried about inflation these days – he noticed it much more when gas prices were rising rapidly.

“That was the time when I really felt that inflation was affecting our budget,” said Mr. Scarbrough. “I feel more comfortable with it now. I don’t think about it every day.”

Fed officials are not yet comfortable, and they can do more to curb price increases. Officials last week forecast they would raise interest rates to 5.6 percent this year, making two more quarter-point moves that would push rates to their highest level since 2000.

Investors doubt that will happen. Given the recent cooling in inflation and signs that the labor market is beginning to crack, they are expect another rate increase in July — and then outright rate cuts early next year. But if that bet is wrong, the next phase of the fight against inflation could be the most painful.

As higher borrowing costs prompt consumers and businesses to pull out, this is expected to translate into fewer hires and fewer job opportunities for people like Mr. Scarbrough. The delay could put some people out of work altogether.

Fed policymakers estimate that unemployment will rise to 4.5 percent by the end of next year — slightly higher than the 3.7 percent now, but quite low historically. But Mr Blanchard thinks the unemployment rate may need to rise by one percentage point “and probably more”.

Jason Furman, a Harvard economist, said he thought unemployment could go even higher. While not his prediction, he said that in a bad scenario, it would “possibly” take about 10 percent unemployment to bring inflation back to normal. That’s how high unemployment rose at the worst point of the 2009 recession, and inflation fell by about two percentage points, he noted.

In any case, Mr Furman warned against jumping to conclusions about the future path for inflation based on progress made so far.

“People have been so insanely premature to keep proclaiming victory over inflation,” he said.