It appears that the Consumer Price Index clearly factors in inflation in housing rental prices but has only a poor equivalent called the "owners equivalent" factor for measuring increasing owner occupied housing prices.
In order to prevent “inappropriate results for goods [housing] that are purchased largely for investment reasons” the CPI had to drop its use of an asset price method for measuring change in owner-occupied housing in the early 1980s in favor of a calculated equivalent method.
The owners’ equivalent “measures the change in the implicit rent, which is the amount a homeowner would pay to rent, or would earn from renting, his or her home in a competitive market.”
Clearly, it cant be trivial to estimate rental price equivalents for owner-occupied housing and given how far out of whack housing prices are with respect to rents in many areas, it seems reasonable to conclude that during the housing boom years it may have been even more difficult to estimate the price inflation associated to owned housing by equating it to a competitive rental market.
This may have skewed the perception of inflation (the CPI itself) during the real estate boom years during which home ownership rose to its highest levels, keeping rental prices in check and thus keeping the housing rental and the owners’ rental equivalent components of the CPI low.
Use of the owners’ equivalent may have grossly under represented real home price inflation during this period by trying to equate two prices that are seemingly no longer associated.
Now that the housing market is reversing, rental demand and rental prices are increasing causing the CPI to show a significant increase in its housing component.
This would seem to create a possible viscous cycle whereby the Fed would attempt to control inflation (as partly perceived by the CPI) by raising interest rate, which would in turn depress the housing market, resulting in higher demand and prices in the rental market, thus causing more housing rental cost related price inflation to register in the CPI.
It seems the guys at the Fed must be sharp enough to recognize this catch 22 but it is an interesting conundrum.
The CPI seems to be a well regarded inflation indicator (arguably one of the most watched and anticipated) and it may have been distorting inflation throughout the last 10 year run-up in housing prices.
It would seem that in order to effectively “factor out” current inflation in house rental prices (so as to prohibit rental housing price inflation from creating a cause to increase interest rates) you would need to somehow readjust the CPI numbers to account for all the owner occupied housing price inflation during the real estate boom years.