> Case Shiller home price index is another measure that shows 4X increase in housing costs since 2000. housing is a large component of cost of living

Case Shiller measures home prices (asset cost), not housing cost (rent expense, actual or forgone by choosing not to rent out a property you own.)

Also, the repeat sales method it uses has structural biases that favor increases.

That's specifically the Bay Area though, and inflation is a national average. Most other cities have not had that kind of housing price growth. I like to occasionally look at the sale prices of the houses I grew up in (partly because the listing photos are interesting to see how the new owners have redone the insides), and they've gone up about 2x since 2000, or annualized 3-4%.

Two examples: 3bd house in the Chicago suburbs, sold for $190,000 in 1999, and $420,000 in 2021. 5bd house in the Houston suburbs, sold for $290,000 in 2003, and $480,000 in 2022. If there were 5x price growth, these houses should be selling for $1m-$1.5m.

Here's a chart from 1997 to 2018 with prices with and without inflation adjustment: https://www.vitalsigns.mtc.ca.gov/home-prices