Cleveland Federal Reserve President Beth Hammack said Friday that persistently high inflation might be changing how businesses set prices-which could make the Fed's job of bringing inflation backto its 2% target more difficult.

Speaking on PBS NewsHour, Hammack described what she calls an "inflationary mindset" in which consumers and businesses become increasingly accustomed to persistent price increases. She gave an example of one retailer in her district that began raising prices more than current input-cost increases because it expected more inflationary shocks to eventually arrive.

"They know there'll be more inflation coming, they just don't know from where," she said. "And they want to maintain their margins."

Such behavior could make it more difficult for the Fed to bring inflation down, Hammack said, if expectations of future costs increases begin influencing pricing decisions today. She stressed that inflation expectations remain anchored around the Fed's 2% goal, but said preserving that anchor is critical.

Hammack's comments came after the September jobs report-released Friday morning-showed weak hiring, with the unemployment rate little changed at 4.2%.

Hammack played down the significance of any single monthly payroll number. She said that employment remains around her estimate of maximum employment, while inflation concerns her more.

The personal consumption expenditures price index rose 3.4% from a year earlier in August, well above the Fed's goal.

Hammack pointed to growing financial strain among lower-income households, as well as shortages of skilled workers, particularly electricians, for businesses in her district amid growing demand from data-center and construction projects.

The Fed will get two more major readings on inflation before its next Oct. 27-28 policy meeting: the September consumer price index and producer price index readings, which will be released Oct. 14 and 15, respectively.