I’m not sure why housing and fuel were juxtaposed; most “core” inflation indexes I’m familiar with remove fuel and FOOD, because the short term volatility for those two are very high.

[A national estimate of] housing generally is included.

I don’t agree with the root poster of this thread, though, because real wages are generally indexed to national consumption, whereas housing specifically (and to a lesser extent, food and services) are local markets, so you can have real wage growth but if you live in a high COL area, you really do have to look at real income and deflate (slightly! People often do COL deflation on gross salary, which is silly) for COL.