Kansas City Fed's Schmid says inflation 'stubborn' and 'sticky,' policy rate not restrictive

Kansas City Federal Reserve President Jeffrey Schmid said Thursday that inflation is still too high, though he stopped short of calling for an interest rate hike.

Speaking from the central bank's annual symposium in Jackson Hole, Wyoming, that the Kansas City Fed hosts, Schmid said in a CNBC interview that inflation has proven resilient.

"It's still stubborn and it's still sticky, and ... we've got to continue to find ways to break through," he said on " Squawk Box ." "We're going to have our work cut out for us as we move into the [Federal Open Market Committee] cycle."

The comments came the day after the Commerce Department reported that the Fed's primary inflation gauge showed core prices, which exclude food and energy, rose 3.3% from a year ago, well above the central bank's 2% target.

Coupled with an economy that grew at 1.5% in the second quarter and an unemployment rate sitting at 4.1%, Schmid said it's not clear that the Fed's current policy rate target of 3.5%-3.75% is restrictive.

"I don't know what we're restricting currently with the rate policy that we're at today," he said. "I do know moving the rate does change behaviors in the market in a macro level market."

Schmid does not vote this year on the FOMC, though he still gets to express his views at meetings. When he was a voter last year, he twice dissented against rate cuts.

However, Schmid said he is not sure whether he would support a rate increase now.