Most academic studies including this one from the U of A show immigration has a nominal effect on housing prices:
journals.library.ualberta.ca
While the impacts of immigration on rents are anecdotally greater, the industry itself is quite efficient and particularly responsible to supply and demand. Interestingly enough, jurisdictions that meddle in that - ie rent controls - often experience reductions in supply and higher rents over the long term.
Interesting read thanks for the share. That 2-way fixed model they built is....interesting. Being 10 years removed from 300 level econ courses I'm not sure I properly understand wtf they're doing lol. But it got published and uses great sources, so I'll trust it.
The issue of high housing costs is a bit more complicated than just one factor I will give you that; but immigration and migrating Canadians do play a role in it and I would be much more interested in a paper that looked at more regional phenomena than trying to eye the issue Nationally from a macro lens.
Every city faces different issues, but ultimately every city faces a mixture of the following factors: inelastic supply-side issues, population growth, foreign investment/laundering, speculative investing, shifts in perceptions of homes as an investment rather than a home, easy financing, NIMBYS, zoning restrictions, materials/labour costs, a lack of government home building programs, broader inflationary pressures, dwindling rental stock, international capital flows and global trends, etc.
It's complicated, a mixed bag of all the above things for each individual region with no single easy answer. I keep hearing from people that the coming boom in housing starts we are expecting to see across the country with federal policy changes will solve the problem; but how do you build a million homes and not expect raw and engineered materials to face inflationary pressures? Thus driving up the costs of said starts? Are people prepared to spend 800 dollars per square foot on a home? Can they? Is that plan economic?
Or, should we be rubber stamping mining projects, subsidizing mills, and encouraging the development of engineered goods manufacturing in the country thus driving prices down and making it easier to build?
I honestly don't know the answer.