Wages climbed 5.1 percent, a still-rapid pace as Fed awaits slowdown.

Wages continued to climb rapidly last month, offering little encouragement to the Federal Reserve as policymakers hope for a slowdown in pay gains that might allow inflation to moderate.

Average hourly earnings picked up by 5.1 percent in the year through June, moderating slightly from 5.3 percent in the year through May. Economists in a Bloomberg survey had expected a slightly bigger cool-down, to 5 percent.

Fed officials spent the years before the pandemic cheering every strong wage number, but recent pay gains have been fast enough that they would make it difficult for rapid inflation to slow toward the central bank’s 2 percent annual goal. That is because as companies pay more, they typically try to cover their costs by raising prices.

“Wages are not principally responsible for the inflation that we’re seeing, but going forward, they would be very important, particularly in the service sector,” Jerome H. Powell, the Fed chair, said at his news conference in June. He has repeatedly made the case that slowing the job market is necessary to put it on a more sustainable longer-run path.

“If you don’t have price stability, the economy’s really not going to work the way it’s supposed to,” he added in June. “It won’t work for people — their wages will be eaten up.”

Wages are already failing to keep pace with price increases for most people.

The Fed is raising interest rates to cool down the economy to bring inflation under control, and slowing demand should weigh on hiring and pay. The question is how much wage growth moderation is needed to ease inflation concerns.

Economists at Goldman Sachs have estimated that using their wage growth tracker — which has been running a few tenths of a percent higher than the average hourly earnings estimate — pay gains probably need to slow to about 3.5 percent to be consistent with the Fed’s inflation goal.