[andrepd]

If your thesis is true then increases with immigration should be correlated with increases in housing prices, right? But this is not at all what is empirically verified.

It's not a supply-side problem (or not only or even majorly a supply-side problem). We can see this because the housing bubble is occurring in widely different places with widely different construction rules: both very restrictive and very lax. This is fundamentally a finance bubble.