Do we really have a housing deficit? If you look at prices they indeed go up because nobody wants to sell and too many people have been wrongly convinced that buying is always a good idea.
If you look at rent on the other hand it has stabilized in most location. I was even able to negotiate a rent decrease last summer.
I'm not convinced we have a housing deficit. But I'm convinced that too many people are blindly buying at whatever prices, driving the prices irrationally up.