WILLIAM BRANGHAM: Now the latest in the Federal Reserve's campaign to raise interest rates and bring down inflation.

That effort is almost a year-and-a-half-old now.

At the same time, Fed Chair Jay Powell wants to tame inflation without tipping the economy into a recession, which is a tall order.

Economics correspondent Paul Solman helps us unpack the thinking behind the Fed's moves.

PAUL SOLMAN: As expected, the Federal Reserve raised its key lending rate again today after a pause in June to the highest level in 22 years.

Chair Jay Powell: JEROME POWELL, Federal Reserve Chairman: Powell inflation has moderated somewhat since the middle of last year.

Nonetheless, the process of getting inflation back down to 2 percent has a long way to go.

PAUL SOLMAN: A long way to go, despite signs that inflation is ebbing.

EDWARD AL-HUSSAINY, Columbia Threadneedle: Rental inflation, the cost of housing, which was rising very rapidly in the course of 2021-2022, is now reversing.

PAUL SOLMAN: And even wages are moderating, says analyst Ed Al-Hussainy.

EDWARD AL-HUSSAINY: Wage growth as well peaked about a year ago.

It's decelerating.

It's not decelerating as fast as inflation, but it is decelerating.

People have come back into the labor force from the sidelines, particularly women.

So the size of the pool of people available to work is higher today than it was in 2019, and that's taking a lot of pressure off of wages, and, therefore, inflation that's related to services that is connected to the labor market.

PAUL SOLMAN: No wonder then that the Consumer Price Index was up just 3 percent in June.

A year ago, it was embracing 9.1.

But Chair Powell worries about putting too much stock in one month's data.

JEROME POWELL: The June CPI report, of course, was welcome, but it's only one report, one month's data.

Inflation repeatedly has proved stronger than we and other forecasters have expected.

And at some point, that may change.

We have to be ready to follow the data.

And given how far we have come, we can afford to be a little patient, as well as resolute, as we let this unfold.

EDWARD AL-HUSSAINY: We are not sure that the inflation story is finished.

PAUL SOLMAN: Moreover, adds Ed Al-Hussainy: EDWARD AL-HUSSAINY: And we're not sure that higher inflation is not being embedded in the economy, in the psychology of people's everyday decision-making.

PAUL SOLMAN: In short, our inflation expectations, as shoppers, as workers, they really matter, says economist Julia Coronado.

JULIA CORONADO, MacroPolicy Perspectives: For the Fed, that inflation psychology is a very important element of inflation dynamics.

If we believe that the Fed is going to control inflation, that gives rise to behavior that reinforces that low inflation.

Companies stop raising prices.

People stop demanding cost-of-living increases.

And that, in turn, helps sort of lock in lower inflation.

PAUL SOLMAN: So the Fed thinks it's doing it's duty, trying to discourage us from spending in order to slow down economic activity, says former Fed official Krishna Guha.

KRISHNA GUHA, Vice Chairman, Evercore ISI: The Fed has promised to deliver 2 percent inflation.

Now, that doesn't mean they have to be inflation nutcases and crash the economy to get inflation back to 2 at the very earliest opportunity.

But they do need to seriously commit to get it there over the next few years.

PAUL SOLMAN: To maintain credibility.

But Guha admits prices rose for reasons that had nothing to do with the Fed.

KRISHNA GUHA: The big forces that drove inflation higher were coming, obviously, from fundamental shocks to the economy.

PAUL SOLMAN: The forces you have heard here and elsewhere beaten drumlike, COVID, supply chains, Ukraine, corporate opportunism, stimulus checks.

KRISHNA GUHA: A big part of the process by which inflation hopefully eventually returns to target is just that those big shocks dissipate and the dislocations in the economy gradually sort themselves out.

PAUL SOLMAN: In which case, says Ed Al-Hussainy: EDWARD AL-HUSSAINY: And the mystery is whether the Fed had anything to do with it.

PAUL SOLMAN: But, even so, the Fed's using, well, the standby arrow in its quiver, targeting higher interest rates, even at the risk of recession, to hit its bullseye, 2 percent inflation.

EDWARD AL-HUSSAINY: Think about the problem the Fed is trying to solve is this.

Let's pick a number for inflation that will be immaterial to people's everyday decision-making, to how they bargain for wages, how they make consumption and purchasing decisions around large items like cars or homes.

Does the Fed have the luxury to re examine the target in today's environment?

Categorically, the answer is no.

PAUL SOLMAN: Finally, a looming question: Is this likely to be the last Fed rate hike for a while?

EDWARD AL-HUSSAINY: The Fed's tightening cycle is coming to an end.

They are very likely to pause in the course of the next several meetings.

And that's a world away from where they were six to 12 months ago.

PAUL SOLMAN: For his part, Powell was noncommittal about what the Fed might do at the next meeting.

JEROME POWELL: In September, we're going to look at two additional job reports, two additional CPI reports, lots of activity data.

And that's what we're going to look at.

And it's really dependent so much on the data.

And we just don't have it yet.

PAUL SOLMAN: But, by September, they will.

For the "PBS NewsHour," Paul Solman.