If suicides and gun ownership were being driven by a third factor we would expect gun ownership to be correlated with all suicides not just gun-suicide. What we find, however, is that an increase in gun ownership decrease non-gun suicide. From an economics perspective this makes perfect sense. As gun ownership increases, the cost of gun-suicide falls because guns are easier to access and as the cost of gun-suicide falls there is substitution away from non-gun suicide.
Put differently, when gun ownership decreases other methods of suicide increase. Substitution among methods is not perfect, however, so when gun ownership decreases we see a big decrease in gun-suicide and a substantial but less than fully compensating increase in non-gun suicide so a net decrease in the number of suicides.
- See more at: http://marginalrevolution.com/marginalrevolution/2013/11/firearms-and-suicides-in-us-states.html#sthash.eq0Uf9z1.dpuf