How do researchers know that excessive regulation is causing high housing prices? Using the process of elimination. It isn’t rising demand, as the U.S. population rose even faster back when housing prices were roughly stable. It isn’t because of higher construction costs — those, adjusted for inflation, have been almost flat for decades.
On the other hand, there is good evidence that heavy-handed housing regulation is boosting home prices by restricting supply. Strictly regulated urban areas like New York City and the Bay Area have high prices and low construction, while more lightly regulated areas like Houston and Dallas have much lower prices and much more construction.

We need to build housing (supply) in places people want to live (demand).

Otherwise, the only people who will be able to afford the supply are wealthy, or willing to live with a bunch of roommates.

The only reliable way to lower housing costs is to build more housing.

Here is the archive link.