GEOFF BENNETT: Inflation cooled somewhat last month.

That's according to new numbers from the Bureau of Labor Statistics.

The Consumer Price Index rose at an annual rate of 3.4 percent.

That's in line with expectations.

But, overall, inflation hasn't yet come down quite to the levels that many people have been hoping for.

Our economics correspondent, Paul Solman, has the story.

PAUL SOLMAN: The latest CPI data prices, of goods and services did rise last month, but at a slightly slower pace.

CHRISTOPHER CONLON, Associate Professor of Economics, New York University Stern School of Business: I think this is good news, particularly because what the Federal Reserve generally looks at is core CPI, and that's down to 3.6 percent year-on-year, which is actually the lowest level since April 2021.

PAUL SOLMAN: Core CPI, in other words, explains New York University's Chris Conlon, everything but food and fuel prices.

CHRISTOPHER CONLON: One of the things that's been pushing up CPI this month has been the increase in gasoline prices.

PAUL SOLMAN: But we shouldn't necessarily be looking at that?

CHRISTOPHER CONLON: yes, I think there are a lot of reasons why gasoline prices tend to be volatile, particularly this time of year, that have nothing to do with sort of overall inflation.

Crude prices are actually been heading downward.

PAUL SOLMAN: And food prices can be similarly jumpy, for short-term reasons, in contrast to the longer-term causes of, say, the great COVID inflation that started all this, though, by now, you may be as tired of hearing them and seeing the footage as we are, backed-up supply chain ships due to the stuck-at-home spending spree, stimulus checks, labor shortages, firms hiking prices above their own costs.

But, today, that's pretty much behind us, according to the Harvard Business School's Alberto Cavallo.

ALBERTO CAVALLO, Professor of Business Administration, Harvard Business School: Goods inflation has come down significantly.

And we are back to pre-pandemic levels.

What still remains is the impact of shelter inflation, or rents, which is a category that tends to lag a lot.

PAUL SOLMAN: Shelter costs, measured mostly by rents, are more than a third of the CPI and a clear source of lag, says Cavallo.

ALBERTO CAVALLO: Landlords putting their houses, for rent, they don't have a very good idea of what's happening with supply, with demand.

They may test high rents for a while, and it takes longer for them to internalize and realize that the conditions will require lower rents.

And, naturally, that makes the inflation rate take longer to come down.

MAN: Go, NASA.

PAUL SOLMAN: Economists have a phrase to describe this, says Chris Conlon, rockets and feathers.

CHRISTOPHER CONLON: When costs go up, prices go up like a rocket.

They go up really fast.

And when costs go down, prices fall like a feather, that is, they float to the ground really slowly.

PAUL SOLMAN: But though inflation has swooned since peaking above 9 percent in 2022, we remain preoccupied.

Why?

STEFANIE STANTCHEVA, Professor of Political Economy, Harvard University: People tend to associate inflation with a bad economy.

We feel like it is eroding our living standards.

PAUL SOLMAN: Harvard researcher STEFANIE STANTCHEVA.

STEFANIE STANTCHEVA: When I ask people what emotions do you feel when you see rising prices, predominantly, it's very negative emotions such as anger, fear, and stress.

And while they're quite widespread, they're especially concentrated among lower-income respondents.

PAUL SOLMAN: And, crucially, that's because inflation hits different folks differently, says Cavallo.

ALBERTO CAVALLO: We all tend to focus on what we call average inflation for an average consumer.

But each one of us experiences an actual different inflation based on the products we do buy.

We have, for example, low-income households consuming a lot more food than high-income households.

If there's suddenly a lot of inflation in food, the low-income households actually experience more inflation.

PAUL SOLMAN: So, yes, the data show price hikes tapering, but not for everyone equally, echoes Stantcheva.

STEFANIE STANTCHEVA: We know there's inflation inequality, where the basket of goods that people consume will vastly shape the inflation experience.

So, I think this is very important to bear in mind when thinking about people's stress responses, reactions, lived experience that might just not well be captured by our official statistics.

PAUL SOLMAN: Which may help explain why consumer sentiment sank in may, many Americans feeling that inflation hasn't dropped fast enough and could even get worse.

For the "PBS NewsHour," Paul Solman.