As a follow-up to
last week's post on the subject, here are U.S. housing prices discounted by the "untrustworthy" U.S. government measure of inflation (the CPI-U-Research Series, to be specific). Note the fairly obvious housing bubble that begins to form in 1998.
I have reproduced Shadow Stats' proprietary annual inflation numbers. Here's what historical housing prices look like when discounted by the Shadow Stats
SGS Alternate measure of inflation:

When housing prices outpace inflation, real (i.e. inflation-adjusted) home prices rise. When inflation outpaces housing prices, real home prices fall.
Shadow Stats claims some pretty high inflation numbers, so it's hard for housing prices to keep up—even in good times. That's why we see the long-term decline in real housing prices shown in the second graph.
Now you can believe there was a housing bubble, or you can believe that Shadow Stats is trustworthy, but if you believe both you're delusional. Personally, I believe there was a housing bubble and Shadow Stats is full of B.S.