My experience with people complaining about CPI is usually simply that the numbers don't match their feeling.
Looking at the description [1] is really interesting:
> The shelter component of the CPI includes two major items: rent of primary residence and owners' equivalent rent (OER). Rent of primary residence, or simply rent, refers to the cost of renting a place on the market. [...] OER refers to the amount of rent that a homeowner would be paid if they were renting out their own home in the market. [...] is calculated by splitting the non-recurring cost of buying a home real estate into rental payments
I got a bit tired reading [2] for more details, as it isn't even my countries CPI...
> The expenditure weight in the CPI market basket for OER is based on the following question that the CE Survey asks of consumers who own their primary residence: “If someone were to rent your home today, how much do you think it would rent for monthly, unfurnished and without utilities?”
Left me a bit unsatisfied, but I'll keep it at that. The followup question would be how much rent prices deviate from housing prices. I am sure that has a lot of data though.
[1] https://en.macromicro.me/charts/24/cpi-house
[2] https://www.bls.gov/cpi/factsheets/owners-equivalent-rent-an...