They aren't making any more land. New Zealand has very lax laws regarding property ownership compared to many countries. No capital gains tax. Very limited ownership restrictions.

To pick on a common scapegoat, Chinese citizens can buy a house in New Zealand, so as their economy improves it drives our housing prices up (same level of supply, greater demand), but I can not buy in theirs.

I think it probably only has a small impact on housing prices (a much bigger problem is the political impossibility of any measure that drops housing prices) but I don't think you can say it has none.

I would personally be in favour of introducing a capital gains tax (but, as a renter, I would say that).