September's Consumer Price Index (CPI) will serve as the latest test of whether inflation will continue to ease as the Federal Reserve debates its next interest rate decision.

The report, set for release at 8:30 a.m. ET on Thursday, is expected to show headline inflation of 2.3%, a deceleration from August's 2.5% annual gain in prices, which marked the lowest annual rate since early 2021. Over the prior month, consumer prices are expected to have risen 0.1%, down from the 0.2% increase seen in August.

On a "core" basis, which strips out the more volatile costs of food and gas, prices in September are expected to have risen 3.2% over last year, unchanged from August's increase. Economists expect monthly core price increases to slow slightly, estimating an uptick of 0.2% compared to August's 0.3% gain in prices, according to Bloomberg data.

Inflation, although moderating, has remained above the Federal Reserve's 2% target on an annual basis.

But the Federal Reserve has recently shifted its attention to the state of the labor market, which has been surprisingly resilient in the face of high interest rates.

Data from the Bureau of Labor Statistics released Friday showed the labor market added 254,000 payrolls in September, more additions than the 150,000 expected by economists, while the unemployment rate fell to 4.1% from 4.2%.

The strong report altered expectations about the path forward for interest rates, with markets now pricing in a smaller 25 basis point cut in November rather than another jumbo 50 basis point cut.

Read more: What the Fed rate cut means for bank accounts, CDs, loans, and credit cards

"We think the bar for the Fed to not cut rates at all in November is high," Citi economist Veronica Clark wrote in a note to clients on Monday. "Ultimately, we expect a still subdued inflation backdrop and a reemergence of weaker labor market trends in the next few months will have officials cutting rates by 50bp in December after a smaller 25bp cut in November."

A hot reading could still spook markets, though.

"Good news is good news for stocks as long as inflation doesn't flare up again," Bank of America equity strategist Ohsung Kwon wrote on Monday. "Following the blowout jobs report last Friday, we believe the importance of CPI this week has risen."

"While stocks should be able to withstand a slight upside surprise in inflation given improving macro data, a sizeable surprise could bring uncertainty on the easing cycle and more volatility into the market," he warned.

Sticky shelter, core services

Core inflation has remained stubbornly elevated due to higher costs for shelter and core services like insurance and medical care.

"We see some risks of stronger inflation in large components like owners’ equivalent rent relative to our forecasts," Citi's Clark said. Owners' equivalent rent is the hypothetical rent a homeowner would pay for the same property.

Bank of America added sticky rent inflation and an uptick in lodging away from home, used car prices, and airfares will likely translate to a firmer core reading in September month over month after the latter two categories saw price declines in August.

"While we expect core CPI to be on the firmer side of recent readings in September, our forecast does not change our medium-term outlook for further disinflation," Bank of America economists Stephen Juneau and Jeseo Park wrote in a preview of the data. "A cooler labor market coupled with anchored inflation expectations should keep disinflation on track."

"That said, there are some upside risks to consider, including the East coast port strikes, rising oil prices and higher shipping costs," the duo added. "We think these risks would contribute to a more gradual disinflationary process than we currently expect."

Alexandra Canal is a Senior Reporter at Yahoo Finance. Follow her on X @allie_canal, LinkedIn, and email her at alexandra.canal@yahoofinance.com.

Click here for the latest stock market news and in-depth analysis, including events that move stocks

Read the latest financial and business news from Yahoo Finance.