Death by firearm and its relation to health expenditure

An argument that often appears in the discussion of gun casualties is that adequate care for the mentally ill can reduce crime to a certain extent (see e.g. Joe Nocera's column in the New York Times.) This sounds intuitively reasonable, but the importance of the effect is less clear.

It is also difficult to find a relevant quantitative measure of health care quality, but I assume that health expenditure (per capita) is a reasonable proxy. Below, I plot the number of casualties (same data as in the previous post) as a function of expenditure, as a total amount and as GDP percentage (data from Wikipedia.)

There might be a very slight descending trend as a function of total expenditure, but scarcely any effect of the GDP percentage. The healthcare argument is mainly invoked with respect to the USA, but the graph tells a different story: high expenditure and high casualty rate. It is of course possible that the expenditure on mental healthcare is disproportionately low in the US, but indiscriminately throwing money at the problem will not make it go away.

Another interesting region is the lower left corner of the first graph: it is populated by Eastern European countries and former Soviet republics where the number of casualties and the health budget are both low. Are the mentally ill better taken care of in Azerbaijan than in the US ? I would not bet on it. What these countries have in common, however, is that they have fewer guns and lower inequality (see the previous post).

It is tempting to find a causality relation between two social problems, if only because solving one would automatically get rid of the other, but in the present case I have not seen a solid, data-based  argument.