Evidence that foreign buyers drove up prices

Withe the recent rumors that the federal ban on foreigners purchasing real estate, I'm constantly throwing in "do you have proof this actually was meaningful?" to any post about this, only be to be met by insults.

I'm on the hunt for non-partisan statistics that show that foreign buyers contributed towards significant price increases, that would have not existed if the buyers had not been present.

What is not proof :
- Statistics showing that a certain % of homes were purchased by foreigners. This does not show a direct contribution towards price increases.
- "But prices went down" - there can be dozens of reasons why prices go up, and dozens of reasons why prices go down. Some of them significant, some of them not.

Why I'm skeptical :
- Any policy that paints "foreigners" as bad or blames an "other" is pretty much guaranteed to be pure politics. This is one of the oldest plays in the book - along with "divide and conquer" (think "boomer vs young" "owner vs non-owner".
- Unbiased statistics are very hard to come by, particularly for a "hot" topic like real estate.