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

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.