However, I disagree with your assertion that inflation must show up in higher wages.
As I wrote before, historically, before the global labor market, price inflation led to wage inflation. People used to say that houses rose with inflation. Inflation has been higher than the gov’t statistics, so housing has been rising less than inflation for many years. People just said it rose with inflation, bec. they believed inflation was 2-3%, and housing rose 2-3%.
I would say that housing price increases have lagged inflation by 1-3%.
Wages are no longer rising as quickly as they did, in the global labor market.
I would not expect housing prices to rise with inflation, whether the 2% CPI or the 5-8% actual figure which includes housing/food/energy/tuition/health care and all the other stuff which is either left out or minimized. (For example, while health care takes up about 5% of a family’s budget, it only makes up 1/10% of the CPI, or something like that…)