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Stocks fell on Friday after Fed Chair Kevin Warsh warned about sticky inflation. Reuters

Stocks fell on Friday after Federal Reserve Chair Kevin Warsh warned about stubborn inflation in his speech at Jackson Hole.

The Dow Jones Industrial Average edged down 0.02%, while the S&P 500 dropped 0.25%. The tech-heavy Nasdaq Composite underperformed, falling 0.52%. However, the S&P 500 closed the week in green.

Warsh said on Friday that even though recent inflation readings have been "better than expected, they do not tell me that underlying trends have meaningfully improved." He claimed that if the trend doesn't move down in the future, the central bank will have "work to do."

However, he did not offer guidance about the central bank's next moves, speaking against "oversharing" policy deliberations.

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During a passage of his speech, Warsh said forward guidance "has overstayed its welcome" and "should not indulge a regime where market participants are looking at the Fed for their next trade."

Warsh went on to propose an "explicit reaction function" noting that the Fed chair "should tell us his interest rate path—if, say, the data were to come in hot or cold."

However, he then issued a warning: "our knowledge just doesn't extend that far—at least not yet—and the factors most relevant to the proper conduct of monetary policy change over time."

"In my term as Chairman, my colleagues and I will endeavor to construct more reliable models and more robust rules to guide policy decisions. We'll do this knowing that accuracy in economic forecasting is still just an aspiration. With so much changing so fast in geopolitics, global supply chains, and technology, it's wise to be modest about what we can and cannot know," Warsh added.

Elsewhere, Warsh expressed confidence in the economy, saying it "appears to have strengthened." He also lauded economic benefits from AI and said business and consumer spending has held up.

Chances of a rate hike by the Federal Reserve jumped more than 20 points after the remarks, according to the CME Group's FedWatch tool. They now stand at 57.5%, compared to 35.4% on Thursday. That means markets now believe there is a higher chance that the Fed hikes rates than not in its next meeting in mid-September.