I am not convinced. The attribution to the simple zoning system is surely not a complete proof, if any. Consider a counter-example: South Korea that has a very similar zoning system. Yet the housing price around Seoul soared roughly by 60% the past 3 years---so did rents (to a smaller but still significant rate). All the while the apartments supply has been at record high in 10 years. That zoning policy may be a factor but clearly not sufficient.