Earlier quoted context omitted.
Wait. Aren't rent, healthcare, AND education all included in the eight components of CPI? Isn't that how the government measures inflation? I think one of the big things left off is housing prices. But I'm pretty sure rent, healthcare, and education are part of it: https://www.bls.gov/cpi/factsheets/medical-care.htm http://webapps.dol.gov/dolfaq/go-dol-faq.asp?faqid=94
Rent is not in the CPI. That's what made Shiller's work useful (comparing housing costs and CPI). Edit: Shiller was wrong (I asked him about this point after a lecture about his work on historical housing prices).
Housing prices go into much bigger bubbles than rent. If interest rates go up or down, it doesn't very much affect the average person's ability to pay rent. But it has a huge impact on how much the average person can borrow.
My understanding for the reason that housing prices aren't included in CPI is because nobody buys houses in cash. So including mortgage payments in theory makes sense -- but it' tricky -- because everyone's mortgage originated at different times and under different circumstances.