Housing costs are still a key driver of inflation, according to the latest data from the Bureau of Labor Statistics released Wednesday, even as the residential market stabilizes.

The shelter component of the March Consumer Price Index (CPI) — which makes up a third of the overall inflation index — rose 0.6% over the last month after rising 0.8% in February. On a yearly basis, shelter climbed 8.2% in March.

The shelter index consists of what rent prices and what a homeowner would pay to rent an equivalent apartment, known as owners' equivalent rent, which gained 0.5% over the last month.

The index for shelter was "by far the largest contributor" to the monthly increase in the index for all items excluding food and energy, according to the Bureau of Labor Statistics report. Consumer prices rose at the slowest pace since May 2021.

“Shelter costs posted their smallest gain since April 2022, up 0.56%, with rent prices and owners’ equivalent rent up 0.5%, their smallest advance since March 2022 and May 2022, respectively. Excluding shelter costs, services prices were unchanged on the month,” Gregory Daco, Chief Economist at EY, wrote following the release.

"This is reassuring in two ways. First, it indicates that we may have passed peak sequential momentum in CPI shelter cost. Second, it points to strong disinflationary forces in the coming months as housing cost pressures ease significantly on the back of a sharp pullback in housing demand. This slowdown may surprise many on the downside once it gets underway,” he added.

This data from the BLS comes after real-time data from RealPage showed apartment demand has rebounded back into positive territory this year, but less quickly than supply.

The apartment market across the U.S. added 19,243 net new renters during the first three months of the year, according to RealPage data. That's an upbeat turnaround from the 114,000 net renters lost in 2022 but still short of the 95,237 new units set to deliver soon.

“When you look at U.S. apartment occupancy and rents right now, they suddenly look pretty normal on the surface,” RealPage Senior Vice President and Chief Economist Jay Parsons said. “Obviously how we got here was unprecedented, and the road from here remains uncertain. But apartment fundamentals right now are still in very solid shape, even if it’s nothing like the crazy highs of early 2022.”

While more space was leased than vacant this quarter, it doesn't reverse the three previous quarters of negative net absorption, where more apartments sat vacant than occupied. As result, occupancy rates continue to trend downward, coming in at 94.7% in March and matching pre-pandemic averages.

The story was the same for rents. In March, asking rents for those signing a new lease climbed 0.3%, marking the largest monthly increase since August.

Still, this was only half the average increase seen during the month of March over the last decade, RealPage data found. On a yearly basis, asking rents rose 3.9%, the first time falling below 4% since April 2021.

Fed officials and economists have expected housing inflation to moderate this year, but more slowly than private data suggests.

"The housing services is really a matter of time passing," Federal Reserve Chair Jerome Powell said in a press conference last month. "We continue to see the new leases being signed at much lower levels of inflation."

Dani Romero is a reporter for Yahoo Finance. Follow her on Twitter @daniromerotv

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