It is common knowledge that the homeownership component of the CPI consists of owner’s equivalent rent instead of the real cost of homeownership. As described in this New York Times article, this was done back in 1983, for what some would say were dubious reasons:
Until 1983, the bureau measured housing inflation by looking at what it cost to buy and own homes, considering factors like house prices, mortgage interest costs and property taxes. But given the shifts in interest rates and housing prices, those measures could show big bounces from month to month. Besides, homes are a strange hybrid of a consumable good and a long-term investment. As part of a long-running evaluation, the bureau wanted to “separate out the investment component from the consumption component” of the housing market, said Patrick C. Jackman, an economist at the bureau.
Not coincidentally, taking home prices out of inflation reporting seems to have had a very calming effect on reported inflation,
