“The nearly 1% move lower in inflation from April to May is a feather in the cap for the Fed, which appears to be achieving its mandate of widespread price stability,” Peter Essele, head of portfolio management at the RIA-independent broker/dealer Commonwealth Financial Network, told Fortune.

David Bahnsen, chief investment officer at The Bahnsen Group, a wealth management firm, went further, telling Fortune that his interpretation of the data shows “inflation has been defeated.”

Not every economist agreed with them, however. The field is largely split on whether to be encouraged or not about year-over-year inflation falling to 4%, the lowest point in over two years. Seeing why this mostly positive report is so controversial requires looking between the lines.

The good, the bad, and the ugly

The latest drop in inflation was mainly caused by falling energy and airfare prices. Energy prices dropped 11.7% year over year in May amid falling prices at the gas pump. The average price for a gallon of gasoline in the U.S. is now $3.59, down 28% from a year ago, according to the American Automobile Association. And there were even some outlandish drops within CPI segments in May, like the stunning collapse in the price of eggs even as food prices rose.

However, many areas of the economy still experienced persistent inflation last month. Food, shelter, and transportation prices all increased in May. Food prices jumped 6.7% from a year ago, driven by rising prices for fruit and vegetables, as well as nonalcoholic beverages. And shelter prices rose 8% year over year, even though median home prices fell in the first quarter, suggesting that rent is a difficult beast to tame.

Bahnsen thinks the CPI’s shelter data is a bit misleading, however. “Most of the inflation we are seeing is coming from housing, but it takes time for home price declines to show up in the CPI data, so today’s 4% inflation rate is actually much closer to the 2% Federal Reserve target,” he said, noting this is why he believes the Fed’s war has been won.

Julia Pollak, ZipRecruiter’s chief economist, said that the inflation data is also “encouraging news for the labor market” as she believes it will allow the Fed to pause rate hikes for the rest of the year and even begin lowering rates in 2024.

“The largest risk to the economic outlook—that inflation would prove sticky, requiring the Fed to throw even more cold water on the economy—appears to have receded,” she wrote in a Wednesday note. “Disinflation is well underway—and measures using real-time, private-sector data, such as the truflation rate, suggest we’re even further along in returning to the Fed’s 2% inflation target than official data shows.”

Just a head fake?

Although economists widely agree that the latest CPI data is a sign the Fed will pause its interest rate hikes this month, inflation is still well above the Fed’s 2% target. And some experts argue that disturbing trends in core inflation, a figure which excludes volatile food and energy prices, could spoil the Fed’s party. While year-over-year headline inflation fell to 4% in May, core inflation remained higher than most economists would like, at 5.3%. 

“Don’t get sidetracked by falling headline inflation. The real story from today’s release is that core inflation remains persistently elevated,” Morning Consult chief economist John Leer told Fortune. “Despite the Fed’s aggressive increases in interest rates beginning last spring, core CPI has actually trended higher since last October. The Fed may pause hiking rates tomorrow, but it will have to raise rates again if it hopes to tame inflation.”

It isn’t just economists like Leer who fear the Fed may have to raise rates again later on this year in order to quash core inflation. Jim Smigiel, chief investment officer at SEI, which manages, advises, or administers approximately $1.3 trillion in assets, said that core inflation came in “hotter than expected” in May, which means more rate hikes—that investors aren’t anticipating—will eventually be necessary. 

“In our view, market expectations are too settled on the pause at this point and the Fed will not want to surprise investors. However, with core still running with a 5-handle, the next move from the Fed is another hike in July and perhaps one more after that (which is not priced in at this point),” he warned.

In other words, dear reader, wait and see. This fight isn’t over yet.