December 27, 2012

Death by firearm, gun possession and the GINI coefficient

The recent tragic events in Newtown rekindled the debate on gun control and the interest in the correlation between gun ownership and gun-related deaths. The issue is clearly very complicated, and a single variable will not explain much, but it would still be interesting to plot the interdependence of the various parameters. Of course, I claim no causality relation between them.

The most obvious variable couple to plot is the number of gun-related deaths vs. the number of guns per capita (both retrieved from Wikipedia). When I was halfway through the data treatment I noticed that a similar graph was made by Mark Reid. The plot is below, in log-log representation, since both the x and y axes cover more than two decades:

The three-letter country code is retrieved from here. The data seems to follow a linear tendency (dashed line), but even in a log-log plot some deviations are clearly visible, such as the cluster of values at top center (dashed frame).

I decided to consider some additional (economical) parameters, and the results are quite interesting.  Another variable that could be correlated with gun violence is the economical inequality, quantified for instance by the GINI index. Plotting the number of firearm casualties versus this variable (I used the coefficient defined by the World Bank, fourth column in the table) yields the following graph:
The "anomalous" points in the first graph now follow more or less the same tendency as the other countries (the dashed line is a guide for the eyes). The gun ownership is used as color code (see the legend), but values between 2 and 20 are difficult to distinguish in this log scale. A nice feature is that the countries with low gun ownership (in blue) which were at the bottom left in the first graph also follow the tendency in the second one.

Visually, I would say that the GINI coefficient explains the data better than gun possession. What other variables might be correlated with gun-related deaths ? For instance, below is the GDP dependence (data from here):
For the USA, the relation between firearm deaths and gun ownership can be seen, for instance, here. How about the economical indicators ? I retrieved GINI values for the US states in 2010 and the number of firearm murders in 2011.

[29/03/2018: I had used the wrong data for the graphs, as pointed out by an anonymous comment (see below). This is now corrected, but the general conclusions still hold.]

The graph is below, in lin-log representation:
The GINI range (41-50) is much smaller than the global scale (12-65 percentage points) but there is a clear correlation. This may not be all that surprising, since firearm murders are extremely well correlated with the total number of murders (and the correlation between inequality and violence seems intuitively plausible). What I find more interesting is that there is almost no dependence on the GDP per capita:
In both graphs I left out DC, which is far to the right of the other points in both inequality (53.2)  and GDP (174500) with a y value of 77, as well as HI, which has a very low murder rate.

It would therefore seem that the inequality is strongly correlated to firearm casualties, both for the US states and for world nations.


  1. This comment has been removed by a blog administrator.

  2. Could you please use gun homicides instead of gun deaths? The latter includes many suicides, which skews the data. Also see here for data sources and discussion of suicides/homicides:

  3. The graph showing gun homicide rate vs. GINI is wrong. According to the linked table, California does not have the highest rate of gun homicide in the country, and its rate is not 200 times Vermont's. I would guess that the graph shows total gun homicides (NY is also way too high, as is PA), but there are some entries like Texas that don't fit that pattern either. Bottom line I'm not sure what it is showing, but it's not right.

    1. You're right, I mixed up rates and total numbers. I'll redo the graphs with the correct data.