Dec 162012
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

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

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

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.


How many people die each year because of the "Second Amendment"? My estimate is 8000+ 1
Nov 142011
Unless you spent the last couple of days under a rock, you will have heard about the terrible series of (at least) ten neo-Nazi murders that has stunned Germany. In my view, three things are particularly remarkable about this crime.

First, the mainstream media including the public broadcasters and the left-liberal press refer to the series as ‘Dönermorde’, i.e. ‘Kebab Killings’, because most of the victims were small businessmen of Turkish origin. This is impious at any rate, and not exactly sensitive in the context of ethnically motivated violence.

Second, for most of the media the victims are ‘foreigners’ (‘Ausländer’), although they spent much of their lives in Germany. The BBC and other English-speaking media refer to ‘ethnic Turks’ or ‘persons of Turkish origin’. Much food for thought here.

Third, Germany has seventeen offices for the protection of the constitution (one in each state as well as a federal institution), effectively secret services that are given the task to observe extremists. Add to that the same number of federal and state criminal investigation offices, plus seventeen crime prosecution services, plus countless special branches and task forces who are supposed to keep an eye on Neo-Nazis.

These agencies are not understaffed or underfunded, and their employees are not lazy: In 2003, an attempt to ban the NPD collapsed because the party leadership had been infiltrated by so many undercover agents that some of the judges sitting on the Federal Constitutional Court were not sure the NPD had any political life of its own. How could the killers possibly escape this machine?


Three possible answers spring to mind:

  • Parts of the left claim that the state still turns a blind eye when it comes to right-wing extremism. That may or may not have been true in the past but is certainly not a correct description of the situation today. The various agencies’ performance has much improved over the last decade, and much of the increase in the number of reported hate-crimes is due to the fact that officers are now trained to look very carefully for extremist motives, and that the rules for collecting statistics have been harmonised.
  • Quite predictably, the right (and many politicians who specialise in Home Affairs) argue that coordination and communication between the various agencies need to be improved. While this may seem reasonable, this is a perennial and very delicate issue in Germany. For historical reasons, the constitution puts strict limits on the cooperation between secret services and the regular police. Moreover, policing is generally the domain of the states, which jealously guard their rights.
  • Finally, many observers just begin to wonder if one or more agencies were involved much closer with the killers than they let on at the moment. Nobody really seems to know how many Neo-Nazis are moonlighting as undercover agents for whom. Is it possible that agencies did not share their information with other institutions in order to protect their sources? Given the scale of the NPD disaster in 2003, it seems quite possible. I strongly
    suspect this is how the story will pan out over months to come.
Random thoughts on right-wing terrorism in Germany 2
Mar 192009
Radio 4 never fails to amaze me. This morning, just three minutes before the 9 o’clock news, they interviewed David Spigelhalter. Spiegelhalter is obviously the man who gave us BUGS. But he  is also Winton Professor of the Public Understanding of risk at the University of Cambridge, and a man who can (within the 90 seconds they allocated him) explain to a lay public why a spade in knife-crime (last summer, four people were killed in the space of just one day) is not totally unlikely and does not necessarily indicate an increase in the murder rate, illustrating the idea of clustered risks in passing. He even convinced the anchor that stats is actually fun, even if you look at 170 murders per year in a population of just 7 million Londoners. I was duly impressed (you can listen here to the interview with Spiegelhalter). In fact, I was so impressed that I googled him once I reached the office and came across his website, which has full coverage of the London murder mystery (that is solved by modelling a Poisson distribution of the incidents).


David Spiegelhalter on Risk, Knife-Crime and the Probability of Being Killed in London 3