Taking guns to the data

Gun control receives a lot of attention in the media nowadays. I decided to look at some data to see whether guns are to blame for anything.

First, I regressed the homicide rate in OECD countries on the gun ownership rate, the poverty rate and the poverty gap. The reason I chose these variables is because (as the pro-gun crowd often points out) homicide rates can be large not only because of the abundance of guns but also because of poverty in general. Poverty generates crime, which at first may be petty crime, but as lawlessness perpetuates, it may very well turn into a higher homicide rate.

The measures of poverty I chose are the poverty rate and gap. The former is the proportion of the population that lives below the poverty line, which is defined as 50% of the median household income in the given country. So this is a measure of the extent of poverty. The latter tells us by how much the mean income of the poor falls below the poverty line. So this is a measure of the magnitude of poverty.

The reason for choosing these measures is because they are comparable across countries, and they are available for all developed (OECD) countries, which are the countries that I’m mainly interested in.

As I plotted out the data, it seemed that the best fit would be a log-linear model (see detailed regression results at the end of the post):

$ln HOM_i = \beta_0 + \beta_1 ln GUN_i + \beta_2 ln POVR_i + \beta_3 ln POVG_i$

As the log-log plots look like this:

One result of the regression was that the influence of gun ownership is not statistically significant. Therefore, there appears to be no discernible relationship between gun ownership and the homicide rate.

Interestigly, the poverty rate’s effect is statistically significant (p=0.00604) while the poverty gap’s isn’t. This may be interpreted as follows: while the extent of poverty does have positive effect on the homicide rate (more poverty, more homicides), the magnitude of poverty doesn’t seem to matter. That is to say: once a certain amount of people falls below the poverty line, it doesn’t matter how much below the poverty line they are. At least from the perspective of the homicide rate. You can find the detailed regression results at the end of this post.

After this I also took a quick look at the number of mass killings per country (1980-2013) and gun ownership. Here the sample was a lot larger. I regressed the number of mass killings on gun ownership, but found no clear relatonship when looking at the plots. It was a quick analysis in Excel:

When the U.S. is included in the sample (top picture) there appears to be a relationship between the two variables. But this relationship is entirely driven by the U.S. The moment the U.S. is taken out of the sample (bottom picture), this relationship disappears and the conclusion one can quickly reach is that there is no discernible relationship between the number of mass shootings and gun ownership.

It seems clear from these statistics that the U.S. is not doing so badly in these areas (homicides, mass shootings) because of its high gun ownership rates. The problems lie elsewhere. This is not to say that gun control wouldn’t help. It most certainly would help if mentally ill people couldn’t get their hands on guns, but a simple brute force reduction of guns would probably not make any difference. It appears thus that it is not the guns that need to be targeted, but the individuals who misuse them.

Sources: Wikipedia for gun statistics, homicide rates, and data on mass killings; (religious, political, racial, domestic, vehicular, grenade and uncategorized killings not included; period is 1980-2013) OECD for poverty stats.

Regression results:

Residuals: Min 1Q Median 3Q Max -1.06468 -0.41431 -0.06713 0.32161 2.01417

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.5041 3.5480 1.551 0.13291
log(GUN) 0.1980 0.1260 1.571 0.12829
log(POVR) 1.4876 0.4977 2.989 0.00604 **
log(POVG) -0.7144 0.8128 -0.879 0.38750

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6892 on 26 degrees of freedom
Multiple R-squared: 0.3339, Adjusted R-squared: 0.2571
F-statistic: 4.345 on 3 and 26 DF, p-value: 0.0131