Inflation relief is finally coming to your grocery bill.

Prices of certain staple foods are falling at the fastest rate since 1951. For example: eggs whose prices have tumbled by nearly 14% since April, according to recent data from the U.S. Labor Department.

A slowdown in food prices also played a part in pushing headline inflation down to a two-year low of 4%.

Were it not for food and energy, May’s Consumer Price Index (CPI) wouldn’t have even budged. Core inflation, which excludes those volatile categories, climbed 5.3% vs. a year ago.

sticky core inflation

The “stickiness” of core prices suggests that inflation isn’t giving out just yet. And consumers are likely to feel the pinch for longer than most anticipate.

The good and bad of headline inflation

The last reading of headline inflation has both good and bad news.

First, the good: energy and food prices appear to be easing. Energy prices in May fell by a sharp 11.7% vs. a year ago, thanks to declines in gasoline and natural gas of 19.7% and 11%, respectively.

Lower oil prices also helped, with the West Texas Intermediate (WTI) price per barrel recently hovering below the $70 level.

Meanwhile, food prices in May inched higher by a modest 0.2%. So while food inflation has not disappeared, it’s definitely rising at a much slower pace than before.

Apart from that, the picture is not so rosy. Core inflation—which consists of less volatile products and services—remains elevated at 5.3% compared to a year ago.

Even though results were in line with economists’ expectations, that is of little comfort to consumers grappling with exploding costs of living, including housing.

In fact, a 0.6% jump in shelter prices was the biggest catalyst for the core CPI increase, comprising approximately 33% of the index. In May, rents went up 8.7% vs. a year ago, while overall shelter costs rose 8%.

Without shelter costs, May’s core CPI advanced by a mere 3.4%.

High core inflation tips off that inflation isn’t giving out yet. As MIT economist Kristin J. Forbes commented: “Big picture: We are making progress, but the progress is slower than expected. Inflation is somewhat more stubborn than we had hoped.”

Is it enough for the Fed?

The multi-trillion-dollar question is whether 4% headline inflation is enough of a justification for the Fed to pause hiking rates.

Fed Chair Jerome Powell isn’t convinced that inflation will subside soon—if for no other reason than “sticky” core prices. As such, he sees two more hikes by year-end.

“There’s a little further to go with rate hikes… It will be appropriate to raise rates again this year, and perhaps twice," Powell told the Senate Banking Committee on June 22.

All this suggests that the Fed’s historic inflation battle isn’t over, and neither is the consumer’s.