> > I posit the "housing" part of the CSI is almost completely inelastic and only reflects what people pay in rent/mortgage, not the cost of entry.
but the CPI covers both owners equivalent rent (if you owned your house) and rent (if you rent)?
> A longstanding criticism of the reported unemployment numbers is that it doesn't take into account those who have given up / dropped out of the labor force
You mean U1-6 that the BLS puts out? There's a good reason for why some are excluded. eg. if you count only the people that are working, then your numbers would be biased if the number of retirees is going up or if people are studying rather than working. Even if you count working age adults it's still problematic because it's affected by people transitioning from/to homemaking. Women entering the workforce would have halved that number, but I doubt people would hail that as some sort of massive victory in terms of unemployment.
Likewise just using raw home prices is problematic because it's tied to interest rates (since it's an asset). Raising mortgage rates will certainly drive down housing prices, but whether that's actually better for consumers is debatable. Your purchase price might be lower but your interest would be higher, making it a wash.