It is interesting to compare US vs Canadian suicide rates to see what impact gun ownership could have.
https://journals.plos.org/plosone/article?id=10.1371/journal...
https://journals.plos.org/plosone/article?id=10.1371/journal...
> we did not have the ability to control for differences between the two countries including poverty, unemployment, health systems, cultural, or other differences
The authors go on to suggest that they may in fact be underestimating the amount of suicides that could be averted with reduced gun ownership, but there are an awful lot of confounding factors that are simply not addressed in this paper.