I'm a millenial.  I live in Toronto.  I grew up in the suburbs of Toronto.  And I have a very different view than a lot of those posting.  It may be interesting for some of the posters to see there are alternative view points on the housing market:

The reason many people my age come to a big city is higher incomes; there are costs associated with this, housing included.  We do what we can, and if we want more space we'll 'cash out' and move to an area with lower incomes.  We're not fixed to one city, or necessarily even one country.  We often compare other cities COL (plus flights) to income opportunities there.

A prop purchase to me is an investment (either in saving rent, or renting out)

Do I think there are foreign buyers?  Yes lots.

Should we tax purchases?  No, its should be free mkt.

I am, however all for municiple taxes on vacant properties, higher than income taxes on rental income.  These are taxes that will uniformly ensure properties actually used, regardless of origin.