I'm not sure why you're being downvoted. This is the theoretical prediction based on simple microeconomics. By example, I believe NY rent controls were ineffe

I'm not sure why you're being downvoted. This is the theoretical prediction based on simple microeconomics. By example, I believe NY rent controls were ineffective to the point where rents outside of controlled areas went higher than they otherwise would have and within rent control areas there was (and is) scarcity of housing.