• Housing costs are the big factor keeping inflation high, according to the July CPI reading.

• Shelter costs posted a surprise jump, rising 0.4% compared to a 0.2% increase in June.

• The overall inflation rate fell to 2.9% in July, its lowest level since 2021.

Wednesday's consumer price index report showed inflation is decisively cooling in most areas of the economy, but one area remains particularly stubborn: housing.

There was much for investors to cheer in the latest consumer price index. Major stock averages rose broadly after the data, with the Dow up more than 200 points shortly after midday.

The good news was that goods prices fell yet again, with previously sticky areas like new and used auto inflation declining from the prior month. The other bright spot was in core services inflation, which Bank of America analysts note remains elevated but is definitely slowing.

The final piece of the puzzle seems to be housing.

July shelter costs posted a surprise jump, rising 0.4% compared to a 0.2% increase in June, and the shelter index has risen over 5% since July of last year.

"Heading into this report, the key factor for us was whether last month's deceleration in shelter would hold. The July CPI report indicated it did not," the BofA analysts wrote.

That rise has an outsize impact on the overall inflation reading, with the shelter index accounting for 90% of the rise in core CPI, the Bureau of Labor Statistics said Wednesday.

"[Shelter inflation] will offset some of the good news we saw from July PPI data on medical care services inflation when it comes to the PCE inflation report later this month," the BofA analysts wrote, referring to the release of the Fed's preferred inflation gauge on August 30.

Shelter costs account for 36% of the overall CPI, a far greater share than that of food or energy.

Yet, analysts say that since shelter costs have such an outsized impact and tend to lag behind actual real estate trends, the most recent shelter data may be keeping the CPI reading artificially high.

"[S]helter costs are also notoriously hard to measure accurately and are often perceived to move with a lag," Jim Baird, CIO of Plante Moran Financial Advisors, said in a Wednesday note.

In June, Federal Reserve Chair Jerome Powell said that when market-based rents increase sharply, there's a slower rollover for existing tenants than for new tenants, creating the delay.

"We've found now that there are big lags," he explained, adding that it may take years for the housing inflation index to reflect changes in the real estate market.