The math here seems straightforward enough. What fraction of immigrants build houses? Of those that do, how many houses do they build? And how many people live

The math here seems straightforward enough. What fraction of immigrants build houses? Of those that do, how many houses do they build? And how many people live in a house? You should be able to estimate whether current policies contribute more to the demand side or to the supply side. And, policy tweaks could have effects on any of those factors.