Correlation != causation. The lack of factoring these locality inputs means they lose the broader context of their conclusion and that’s what makes it incomplete to me
No no, you're misunderstanding. The study did factor locality-specific inputs like the ones you're describing. In fact they included all of them by measuring the actual realized supply production for each locale.
They do matter a lot. I disagree with their conclusion that they don’t matter.
There is plenty of available evidence that when zoning laws are less restrictive and buildings get faster approval the overall cost of housing comes down over time in significant ways.
The way income factors into this tends to be driven by the fact that the weather the neighborhood the more time that is spent at city hall by residents lobbying for regulations to preserve their market values in their neighborhoods in order to achieve artificial local scarcity which drives the home values up.
One is in regards to the lasting effects of Houston's 1998 zoning reforms[0]
Another looks more broadly at patterns of regulations and how they affect the market[1]
Bloomberg also did some nice reporting in this space[2] as well which goes over many cases of attempted land use / zoning reform and various outcomes, most notably that trying to only single out 1-2 regulations is at best token reforms and more meaningful comprehensive reforms are needed to zoning and land use laws.
This is simply what I have easy access to at the moment, but there is more out there that studies housing as an ecosystem and they all seem to be converging on similar conclusions: the real estate market (housing in particular) is functionally broken around the country
