Between 2001 and 2020, rents shot up by 150% ...

 at the same time CPI’s measure of housing costs grew by a mere 54%. 

Eugene Ludwig MarketWatch 27 May 2022

https://www.marketwatch.com/story/inflation-has-been-pummeling-the-middle-class-for-decades-but-the-out-of-touch-cpi-masks-this-reality-11653671201

Eugene Ludwig, a former U.S. comptroller of the currency, is chair of the Ludwig Institute for Shared Economic Prosperity and author of “The Vanishing American Dream.“

CPI Understated? Yes, by a lot.

I do not believe OER is only up 4.56%. Nor do I believe rent is only up 4.46%.

Moreover, home prices are not directly in the CPI, only OER and and Rent.

My Case-Shiller adjusted CPI is calculated by substituting the percentage change in the Case-Shiller national index for OER in the CPI.

The result is an adjusted annual CPI rise of 11.42%. 

That's a new record high for this data series.

Mish 31 May 2022

https://mishtalk.com/economics/case-shiller-home-prices-reach-new-record-high-but-this-is-rear-view-mirror-look

Real inflation is hard to measure

Tim Harford FT 4 January 2022

https://englundmacro.blogspot.com/2022/02/real-inflation-is-hard-to-measure.html