Canadians pay quite a bit more for alcohol than Americans. Our alcoholic consumptions are very similar.
There is a fair amount of illegal (ie bootleg) alcohol here but not as bad as when they tried to use taxes to get ppl to stop smoking. There was lots of smuggling then, and the associated violence. So to have any effect the taxes have to be high enough to discourage ppl but that level of taxation leads people to find ways to avoid the taxes and creates criminal enterprises.