"Given the focus on the relative slack in the labor market, given that inflation is falling rapidly and I expect it to continue to fall in the coming months, it would be a surprise if the Fed didn't start easing policy quickly, presumably at the September meeting," Baird said. "If they don't do that at the September meeting, the market will not accept it."

Fears of a slow Fed response

A brief rebound in weekly jobless claims, along with weaker other economic indicators, led some markets to briefly seek an emergency rate cut.

While that sentiment has dissipated, there are still concerns that the Fed will be slow to ease monetary policy, just as it was slow to tighten when inflation began to escalate.

Another tame inflation report "completely reassures the Fed that they can shift their focus from inflation to labor," said Tom Porcelli, chief U.S. economist at PGIM Fixed Income. "A few months ago, they could have shifted their focus from inflation to labor. Cracks are showing in the labor market backdrop."

With the dual reality of falling inflation and rising unemployment, the market has completely priced in a Fed rate cut at its Sept. 17-18 meeting. The only question is how much. Futures pricing is roughly split between a quarter or half percentage point cut and the possibility of a full percentage point cut by the end of the year, according to calculations by the Chicago Mercantile Exchange Group.

However, futures prices have diverged from expectations for much of this year. Market traders expected a rapid pace of cuts at the beginning of the year, then expected only one or two cuts until the most recent rate cut.

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