Following Friday’s events, the attached image went viral. The figures (if correct) are certainly suggestive, but obviously, the population at risk varies widely between countries. What we need is the gun-related homicide *rate for a sample of comparable countries*. I headed over to the Brady Campaign, which had created the image, but could not easily find comparative data. Next, I tried the very useful Gun Policy Project. Their website features very detailed country profiles, but unfortunately no ready made tables, and so I spent a lazy hour keying in gun-related and total homicide numbers as well as possession rates (guns per 100 people) for 34 OECD countries.

Looking at the data, I decided to remove Mexico from the sample: The civil war like situation in the North means that relatively few guns are enough to kill about 11,000 people each year in a population of just over 112 million people. Put differently, about one in 10,000 Mexicans is shot dead each year. Thankfully, no other OECD member is in a comparable predicament.

Next, I created boxplots for the distribution of possession rates, gun-related and total homicide rates.

Possession, total homicide and gun-related homicide rates for OECD members

The US of A is clearly an outlier in every respect. I was somewhat surprised by Estonia’s high homicide rate. While the country’s population is small at 1.3 million people so that random fluctuation could have an impact, a rate that is roughly six times the median seems excessively high.

Next, I specified a Negative-Binomial model of gun homicide counts as a function of the gun possession rate, controlling for the population at risk of being shot dead. Yes, I know this is dodgy with a small, non-random sample:

Negative binomial regression Number of obs = 33
LR chi2(1) = 8.17
Dispersion = mean Prob > chi2 = 0.0043
Log likelihood = -162.78208 Pseudo R2 = 0.0245
------------------------------------------------------------------------------
gunhomicides | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
possrate | .0209951 .0083522 2.51 0.012 .004625 .0373652
_cons | -12.85624 .2292694 -56.07 0.000 -13.30559 -12.40688
ln(popula~n) | 1 (exposure)
-------------+----------------------------------------------------------------
/lnalpha | -.1823302 .228441 -.6300664 .265406
-------------+----------------------------------------------------------------
alpha | .8333261 .1903659 .5325565 1.30396
------------------------------------------------------------------------------
Likelihood-ratio test of alpha=0: chibar2(01) = 2361.65 Prob>=chibar2 = 0.000

As expected, gun possession raises the risk of being shot dead significantly. According to the model, each additional gun per 100 citizens increases the *relative risk* by exp(0.021) = two per cent (careful: If the initial risk is very low, that means that you are still quite safe).

These findings are, however, largely driven by the US with their very high possession and homicide rates. If they are excluded from the sample, the effect of gun possession is much less pronounced:

Negative binomial regression Number of obs = 32
LR chi2(1) = 0.09
Dispersion = mean Prob > chi2 = 0.7660
Log likelihood = -151.9413 Pseudo R2 = 0.0003
------------------------------------------------------------------------------
gunhomicides | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
possrate | .0043764 .0148325 0.30 0.768 -.0246948 .0334475
_cons | -12.61879 .298236 -42.31 0.000 -13.20332 -12.03426
ln(popula~n) | 1 (exposure)
-------------+----------------------------------------------------------------
/lnalpha | -.1926419 .2319586 -.6472725 .2619886
-------------+----------------------------------------------------------------
alpha | .8247772 .1913142 .5234716 1.299512
------------------------------------------------------------------------------
Likelihood-ratio test of alpha=0: chibar2(01) = 2318.53 Prob>=chibar2 = 0.000
And yet, given the countries the number of gun homicides in the US is massively underestimated
by the model:

Negative binomial models for gun possession/gun homicides w and w/o US

Gun possession is easily comparable across countries but a less than perfect measure of the underlying regime. As a ratio, it does not capture the actual distribution/accessibility of guns, nor does it pick up differences in licensing laws or the availability of automatic weapons. As can be seen from the dashed line, outside the US more guns still mean more killings, but there is a lot of noise in that relationship. There are, however, three countries with very low possession rates of less than 1.5. Unsurprisingly, they also have extremely low gun homicide rates. A final, nonparametric plot picks up this relationship:

Nonparametric model for gun possession / gun homicide

So what’s the implication for the US? If the model was true and the US would bring down its possession ratio to the OECD median of 13.5 per 100 citizens, the model predicts 1071 gun homicides, as opposed to 9,146 actual cases (2009). That would be 8,075 lives saved.

But the model does not fit very well, and we might be better off with a very naive, non-parametric estimate. If the US became less like the US and more like the rest of the OECD, its gun homicide rate might come down to the OECD median. That would amount to 846 people murdered using a gun, less than 10 per cent of the current figure. Of course, some of those people who would be spared the bullet might be killed by other means, but that is arguably more difficult. And this is just homicides. If you add manslaughter, suicides and accidents, it seems safe to assume that the NRA/Second Amendment culture costs at least 8,000 lives a year.