I was reading about this in Vancouver and Toronto. From what I read, the foreign buyer taxes did indeed massively decrease foreign real estate investment, but it's not at all clear that it actually lowered home prices, or even slowed down home price growth. Not what I expected or hoped to see (as I live in SF and would advocate for something similar here if it worked).
I'd say that's true. The reasons being that the housing economy is an enormously complex system and so while addressing certain problems fixed those problems, there still remained others which still continued to induce high prices.
(using Vancouver as an example, after the foreign buyer tax the city still has an incredibly low near 0% rental vacancy, which makes secondary home investment enormously profitable and continues to keep prices lofty)
This doesn't mean that it wasn't a good idea to address the foreign buyer problem, but it was clear that the system instantly shifted to compensate for the lack of foreign buyers, and new buyers appeared. There was plenty of local buyers, many of which had existing properties with inflated land values they could borrow against and the ultra low interest rates from the pandemic that aided them in bidding up properties to buy. Good for local buyers to have less foreign competition, no real change for local renters.
The most real direct outcome of the foreign buyer tax was the nature of the housing product that was made changed. Previously there were companies that were building "luxury" condos explicitly marketed as pied a terres to a foreign audience (largely from major cities in asia). Overnight this sort of thing went away and the same companies that were previously pushing these products instantly pivoted into building purpose built rental buildings for locals.
Ultimately I think the foreign buyer tax is good for local renters, but further work needs to be done.
It didn't lower housing prices because foreign buyers were single digit percentage of all transactions. Canadian real estate is mostly propped up by Canadian buyers buying multiple properties by leveraging existing equity.
It's not unusual for someone to use their HELOC to buy and 2nd or 3rd property and rent it out.
Of course with rising interest rates (and mostly variable mortgages) that's all coming home to roost now, al la USA in 2008.
If you spread the area widely enough (ie. entirely of Metro Van) yea it was single digits, but if you looked at a narrower amount of municipalities and neighbourhoods (ie. where there were new builds, burnaby and richmond) there were places where it was high teens closer to 20% than 10%. This is why the government ended up acting.
The fact that there was significant amounts of foreign buying is not in contention. You can google Globe and Mail articles from ~2016 that cite these figures.