Inflation is likely to fall short of the Fed’s preferred 2 percent annual pace for the seventh straight year.

Rising wages can lead to inflation, if companies find the money by increasing prices. But companies also can find money by curtailing profits, giving workers a larger share of the pie without increasing inflation.

Jon Faust, now a senior adviser to Mr. Powell, warned in a 2015 paper that the central bank would need to be careful as it raised interest rates to make sure it was fighting inflation rather than protecting the profit margins of corporations and the dividends of shareholders.

“A central bank intending to lean against inflationary winds could inadvertently end up resisting secular forces toward income equality,” wrote Mr. Faust, then an economist at Johns Hopkins University. The paper, written with Eric Leeper, was presented at the Fed’s annual Jackson Hole symposium.

There are various ways to measure the share of economic output claimed by workers, but all show the same basic pattern: A sharp decline during the first decade of the present century, followed by a period of stagnation, followed by a mild recovery that began around 2015. Over the last year, however, as the Fed has raised rates, the level of the “labor share” has stagnated.

Julia Coronado, the president of MacroPolicy Perspectives, said she expected the Fed to take a break after raising rates Wednesday to wait for clearer evidence of inflation. “I think that is their intention,” she said. “They want to pause on benign inflation and let things run strong.”

Mr. Leeper, the co-author of the 2015 paper, said in an interview that it was impossible to determine from the available data if the Fed’s rate increases were weighing on wage growth. But he added that he was confident that the Fed was mindful of the difference between rising prices and falling profits — not least because Mr. Faust now works at the Fed. “I think you can be sure that they’re carefully trying to decompose this in the way that we’re talking about,” Mr. Leeper said.