Guns are (probably) not responsible for the high murder rates in the US: how to understand the stats

by Alan Cohen

As I stated in my last post, I support gun control, and I am really appalled by what happened in Newtown. But this is one (rare) case where I think the people on the right may understand the facts better than those in the center and the left. Two of my favorite columnists, Charles Blow at the NY Times and Fareed Zakaria at the Washington Post, had recent columns (here and here) on how the US is the clear exception in the developed world on both gun ownership and murder rates, and suggesting that solution is simple: limit guns, have less murders.

These are nice, well-argued columns. Unfortunately, they appear to be wrong. I’ve been digging in the data a bit, and I think both of these columnists have taken correlation to be causality. (Note: Correlation can sometimes imply causality, contrary to popular belief – one needs to know how to do the right analyses and have the right data. But this is not the case here.) So I will work you through the data, as an example of how to do a more thorough statistical analysis of a question like this. Don’t worry, I won’t get too technical, and I’ll keep it intuitive…

The first step is to decide what data to collect. We are comparing across countries here, specifically, the 31 OECD countries. So we need country-level data. We want to understand what influences total murder rates. This is the important number, since it doesn’t do us much good if people start murdering each other with knives instead of guns, but at the same rate. We need rates, not totals, because population sizes are different. It’s not really fair to compare 10,000 US murders with 70 in Estonia, since Estonia only has 1.3 million compared to 300 million in the US. Rates are expressed as the number of homicides per 100,000 people per year.

What we want to understand is the factors influencing total homicide rate. We will further break this down into gun homicides and non-gun homicides. We also need data on gun ownership. I got all these data from Charles Blow’s column, calculating non-gun homicides by subtracting them from the total (which is actually measured as assault deaths). However, gun ownership isn’t the only thing that might influence homicide rates across countries. Poorer countries appear to have more homicides, as do ones with more income inequality. So I looked up two measures of income inequality (the Gini coefficient and the income ratio of the 10% richest to the 10% poorest, from Wikipedia). I also looked up per capita GNI (Gross National Income, the new word for GDP, from the World Bank).

There are lots of other things that could affect murder rates – culture, detailed aspects of gun laws, alcohol consumption – but many of these are hard to measure or hard to get data for. They might be important and we shouldn’t forget them, but I’m not enough of an expert to be able to include them here. And I can show, with just the gun, crime, and economic data, that just reducing gun ownership in the US would be unlikely to solve our problems.

The first step is just to look at a histogram of each variable. This shows us where the US is relative to the other countries:

The height of each bar indicates the number of countries in that range. We clearly see that the US is an extreme outlier for the gun murder rate, the total murder rate, and gun ownership. This is what was shown by Zakaria and Blow in their columns, and from which they drew the conclusion that simply getting rid of guns would solve the problem. But look: The US is also at the extreme high end of income inequality. We have pretty much the largest gap between rich and poor of any developed country. Lots of poor people, especially marginalized poor people in ghettos, leads to crime. So it’s not clear if it’s the guns, the income inequality, or both.

For per capita GNI, the US is in the middle of the range, though not many countries are at the upper end. But the really interesting histogram is the non-gun murder rate: look, the US is still in second place (that’s Estonia up there in first), even for all the murders committed without guns. This is a pretty strong argument against the simplistic idea that getting rid of guns would pull our murder rates down to those of other OECD countries.

We can go deeper. Let’s look at how total murder rates correlate with non-gun murder rates:

This plot makes it clear just how much of an anomaly the US is. We are way outside the range of what’s happening in other countries. There, the correlation is almost perfect: the total murder rate allows us to predict with great accuracy the rate of non-gun murders, and vice-versa. So the question is, why is the US different? Is it because a lot of murders that would have been committed anyway are committed with guns (thus driving down the non-gun murder rate artificially), or because a lot more total murders happen because of guns (thus driving up the total murder rate):

In the former case, were we to dramatically reduce gun availability so as to fall in line with other countries, we would have little change in the total murder rate, but we would force up the non-gun murder rate (the vertical arrow above). In the latter case, dramatically reducing gun availability would drive down the total murder rate, while the non-gun murder rate stayed constant (the horizontal arrow). Or the truth could lie in between – these data alone don’t tell us.

There are also other interesting clues in the data:

If we put all the countries together, there is a relatively strong correlation between gun ownership and total murder rate, concordant with Blow and Zakaria’s argument and suggesting but not proving a relationship. But if we take the US out, there is absolutely no relationship whatsoever. And as we know, the US is anomalous in a bunch of ways, so we probably should not include it. The evidence from the other countries alone would suggest that gun ownership has no relationship whatsoever to homicide rates. Any correlation that depends on one data point is not really a correlation, just an anecdote.

The next step in a thorough analysis is a regression model. This allows us to see if the correlations we see above are mediated by some of the other variables. For example, if murder rates are lower in rich countries and gun ownership is low in rich countries, maybe gun ownership has no effect of its own – it just appears to have one because it is associated with per capita GNI. Regression models help us answer this kind of question.

I won’t bore you with the details, but the results are pretty clear: when we include the US in the model, total murder rates are predicted by gun ownership AND income inequality AND per capita GNI – each one of these things appears to play a role, even when controlling for the others. But when we exclude the US, the overall model performs poorly and only per capita GNI appears to have a (weak) association with total murder rates.

So this is telling us the same thing again: when the US is included, all these things seem important, but when it’s not they don’t. The US is anomalous in many ways: in addition to those listed above, there is more racial tension, more intergenerational poverty in ghettos and in some rural areas, more a culture of mistrusting government, more a culture of violence than in the other OECD countries. Based only on the lessons we can learn from the other countries without the US, there is no reason to suspect that limiting gun ownership would decrease overall murder rates.

But what the data are really telling us is that we don’t know: for the things that are relevant to murder rates, the other countries don’t provide much guidance because the US is too different. (I’m not an American exceptionalist, and it’s rare that I would utter that phrase!) It’s possible that by limiting guns we would change the culture of violence and drive down both gun and non-gun murder rates. It’s possible that we would increase paranoia and gun hoarding and drive up mass shootings without decreasing normal murders. My best guess? Limiting guns would make a small dent in murder rates, but would not come anywhere close to bringing us down to the level of other countries. If it were that simple, US non-gun murder rates would not be so abnormally high.

Is gun control still a good idea? Yup. Why not save some lives if we can. But let’s not pretend that we can get the US down to several hundred homicides per year just by passing a few gun laws. Instead, let’s invest in health care, education, and anti-poverty initiatives, the long-term solutions to poverty and crime.

Thoughts? Comments? Disagree?  Let me know in the comments… Here are the raw data, in case you want them.

Country	Firearm homicide rate	Assault death rate	Guns per 100	Gini coefficient Late 2000s Wikipedia	UN RP 10% Wiki	per capita GNI 2010 (world bank)
Australia	0.1	1	15	336	12.5	46200
Austria	0.2	0.5	30.4	261	6.9	46920
Belgium	0.7	1.4	17.2	259	8.2	45780
Canada	0.5	1.6	30.8	324	9.4	43250
Czech Republic	0.2	0.8	16.3	256	5.2	18490
Denmark	0.3	0.7	12	248	8.1	59410
Estonia	0.2	4.5	9.2	315	10.8	14180
Finland	0.4	1.9	45.3	259	5.6	47460
France	0.1	0.8	31.2	293	9.1	42190
Germany	0.2	0.6	30.3	295	6.9	42970
Greece	0.3	1.4	22.5	307	10.2	26890
Hungary	0.1	1.4	5.5	272	5.5	12860
Iceland	0	0.3	30.3	301	NA	33890
Ireland	0.5	0.8	8.6	293	9.4	41720
Israel	0.1	2.1	7.3	371	13.4	27270
Italy	0.7	0.8	11.9	337	11.6	35530
Japan	0	0.3	0.6	329	4.5	42050
Luxembourg	0.6	1.8	15.3	288	NA	76820
Netherlands	0.3	0.9	3.9	294	9.2	48920
New Zealand	0.2	1.3	22.6	330	12.4	29350
Norway	0.1	0.7	31.3	250	6.1	86390
Poland	0.1	0.9	1.3	305	8.8	12450
Portugal	0.4	1.2	8.5	353	15	21830
Slovakia	0.2	1.2	8.3	257	6.7	16030
Slovenia	0.1	0.4	13.5	236	2.9	23910
South Korea	0	1.2	1.1	315	7.8	19720
Spain	0.2	0.7	10.4	317	10.3	31460
Sweden	0.4	1	31.6	259	6.2	50580
Switzerland	0.8	0.6	45.7	303	9	71590
United Kingdom	0.1	0.3	6	345	13.8	38140
United States	3.2	5.7	88.8	378	15.9	47350