Oh, you're assuming that CPI is computed in a rational scientific way. And that "housing" means housing. Neither is true.

Let's take a deep dive into how CPI housing is computed. You would think it could just be "track the price of every home sale in the US", or "track the price of every new rental". Ah, my naive friend, the US Bureau of Labor Statistics lives in the year 1900 as if data, electricity, compute, and statistics don't exist. Anyway, those numbers would be too scary and too objective.

First, the real kicker, CPI housing doesn't measure the cost of a house! At all. Their rationale is that the a house is an investment. So it has no relationship to the Case-Shiller index at all.

What do you measure if you don't measure the cost of housing? Well, you're left measuring rents, but that's not satisfying when a lot of people buy a home. So.. why don't we measure the imaginary rent that someone thinks that their house that they bought 30 years ago might be able to fetch.

3/4ths of the housing index is computed from a single quantity called the "Owners’ equivalent rent of residences". They ask people in a survey: “If someone were to rent your home today, how much do you think it would rent for monthly, unfurnished and without utilities?”

Let that sink in for a moment. People who aren't renting their home. Who aren't real estate agents. Who have no idea what the cost to rent their home is. Who are homeowners and haven't rented a home in decades probably. "Bob, what do you think this would rent for?" "Ugh, $1400/month" Great! Let's base our entire understanding of the economy on the random answers of clueless people.

But, remember, the Bureau of Labor Statistics needs to do everything like we're in the pre-electricity era cruising around on the latest model of horse. So they can't ask too many people. Only a few thousand people, and they keep asking the same people over and over again. Seriously, they ask the same few thousand people every 6 months what their rent is and what their imaginary rent is. They even admit this doesn't change much. And they admit this means all the data they get is garbage, it's too skewed by the particular properties of those few thousand people they randomly selected once.

They could just ask 100,000 people or at least pick a different group of a few thousand every time? And then everything averages out eventually.

Doing that with your horse and buggy is way too hard. Instead they adjust the junk responses they get for the type of housing, quality, etc. With a whole bunch of magic numbers that come from yet another survey of clueless people, the Department of Energy’s Residential Energy Consumption Survey, which was last run in 2020 (although I think housing CPI is computed with the 2015 run) and asked about 5000 households a bunch of questions + got some billing info from their utilities.

They compute monthly CPI with an amazing formula that I think is the only use of a 6th degree square root I've ever seen in statistics (and I have CS/math degrees and do ML research; it's probably legit, but I'm not working backwards to figure out how they derived this).

Oh, we're done yet! Housing also gets older all the time, we need to correct for this. That's a whole pdf. That I've never read. And I'm not sacrificing my sanity for HN. https://www.bls.gov/cpi/quality-adjustment/updating-housing-... But it has a model from January 1997 with 110 degrees of freedom. That's not confidence inspiring to say the least.

Ok, so we ask clueless people to give us meaningless numbers that we then adjust based on complex largely meaningless formulas to compute an imaginary rent that doesn't exist instead of just looking at the actual cost of housing. How could this get worse? With the magic of "imputation"! A beautiful word from statistics that means "Oh, we didn't collect enough data and we have no idea what the actual number should be, so we're just going to make a number up and pretend like it's a data point we gathered based on some idea of what we think it ought to have been". Because the best data is the data you make up according to your gut.

Feel free to read the horror show for yourself https://www.bls.gov/cpi/factsheets/owners-equivalent-rent-an...

No one with two neurons to rub together would ever adopt this methodology in the modern world.

Of course none of these numbers match any of the reality that anyone experiences. Their documentation on how anything is computed reads like standup comedy.