On Thursday, investors will digest one of the most important data points that will shape future Federal Reserve interest rate policy: June's Consumer Price Index (CPI).

The inflation report, set for release at 8:30 a.m. ET, is expected to show headline inflation of 3.1%, a deceleration from the 3.3% rise seen in May. This would be the smallest annual rise since January as another drop in energy prices likely contributed to further downward pressure on headline CPI.

Over the prior month, consumer prices are expected to have risen 0.1%, a slight uptick from May's flat monthly reading.

Meanwhile, on a "core" basis, which strips out the more volatile costs of food and gas, prices in June are expected to have risen 3.4% over last year and 0.2% over the prior month, unchanged from May, according to Bloomberg data.

"We expect the June CPI report to be another confidence builder following the undeniably good May report," Bank of America economists Stephen Juneau and and Michael Gapen wrote in a note last week.

The economists said while the anticipated numbers are "not quite as low as May, it would be a good print for the Fed."

Thursday's inflation data arrives at a critical moment for the central bank after slowing job market growth, coupled with recent testimony from Federal Reserve chair Jay Powell, have kept rate cut hopes alive.

Powell, who will wrap up his semiannual policy update to Congress on Wednesday, has largely stuck to his data-dependent narrative — a positive sign given recent positive data. On Tuesday, he told the Senate Banking Committee that although there's been evidence of cooler inflation, the Fed still needs more "good data" to be confident that inflation is moving towards its 2% target.

Core inflation has remained stubbornly elevated due to higher costs of shelter and core services like insurance and medical care. In May, non-housing services "surprisingly edged down in May, owing in large part to a slight decline in motor vehicle insurance," Bank of America's Juneau and Gapen noted.

But the economists expect the category (and motor vehicle insurance) to have increased in June, indicative of the "bumpy" path forward when it comes to price stabilization.

"Non-housing services inflation should moderate over time given cooling services wage inflation; however, a sustained period of deflation is unlikely," they warned.

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