# Gun control revisited

Gun control is always a hot topic and I have written about it in the past (here and here). I find the topic fascinating and I do not try to hide the fact that the analyses in those previous two posts were somewhat inadequate. There are many ways to look at the data and this post will use a novel way. Instead of sophisticated econometric analysis, however, expect only some elementary but very informative mathematics.

My earlier posts had slight anti-gun control conclusions but there were, as always, uncertainties. In this post, I will try to compare crime data internationally to see if homicide by firearm rates in the U.S. can in some way be explained by higher gun ownership rates. I will also discuss some of the problems with my earlier models and with any regression you see with gun ownership rates.

Here is my simple but powerful hypothesis: let us look at crimes that involve a firearm and crimes that do not. Suppose the U.S. crime rate without firearms is at the average of the set of countries in my data. Then, if the U.S. firearm crime rate is considerably above the average of the same data for other countries’, then this would seem to imply that higher gun ownership rates lead to higher firearm crime rate. Well, this is a simplified description, but I invite you to see this argument through with me in much more detail.

First though, let us see why it is essential to be very critical about my earlier findings on guns. The fact is that the classical normal linear regression model that I used rests – among others – on the following assumption:

There must be sufficient variability in the values taken by the regressors.

Gujarati: Basic Econometrics, p.335

That is the independent variables (the X’s) need to have sufficient variability. One independent variable in my regressions was the gun ownership rate. However, there is just simply no sufficient variability in gun ownership around the world. If we ignore developing countries, then all countries but the U.S. have between 0 and 45 guns per 100 inhabitants (the overwhelming majority is actually between 0 and 30). Then we have the U.S. at roughly 90 guns per 100 inhabitants. Beween 45 and 90, there is no country. Not one. In other words, we have no observations whatsoever for any of those values. We have no idea what a country with 60, 70 or 80 guns per 100 inhabitants would look like.

Even if we include developing countries, the second country is Yemen with only 55 guns per 100 inhabitants. The third one is again a developed country (Switzerland) with 45 guns per 100 inhabitants. This makes any (linear) regression with gun ownership as the independent variable highly susceptible to errors. Such regressions and inferences made based on them should thus be treated with utmost caution.

What is a way to go around running these regressions then? What if I were to tell you that on average U.S. crime rates not involving firearms (including homicide without firearm, assault, rape, robbery, theft, motor vehicle theft and burglary) are roughly around or slightly above the average of the same rates for all other developed nations. Where would you then expect homicide by firearm rates to be relative to the average of developed countries?

Given that only the U.S. has extraordinarily high gun ownership rates, one could hypothesize that:

• If guns increase crime, the U.S. homicide by firearm rate should be much more above the average of other countries.
• If guns do not increase crime, the U.S. homicide by firearm rate should be relative to the average where all other U.S. crime rates are relative to the average. Namely, roughly at the average or slightly above it.

Matter of fact, make my assumption above stronger. I said “on average U.S. crime rates not involving firearms are roughly around or slightly above the average”. But actually, this is not only true on average. This is true individually for all non-firearm crime rates. In other words U.S. homicide not by firearm, assault, rape, robbery, theft, motor vehicle theft and burglarly rates are all roughly at or slightly above the average.

So what does the data say? It’s shocking:

Blue columns are made using only the most recent year’s data for each country, red columns use the average of the last eight years. The average of other countries does not include the U.S. data. Finally, doing a similar exercise but using the median of other countries instead of their average paints the same picture.

To sum up, it doesn’t matter if we use the most recent data or almost decade-long averages, or whether we use the average or median of other countries’ crime rates, the picture above does not change.

So how to interpret this chart? Homicide by firearm rates in the U.S. are 12 times higher than homicide by firearm rates in other developed countries on average. All other (non-firearm) crime rates in the U.S., however, are only 1 to 2 times above other developed countries.

There remains at least one important question regarding this analysis: don’t other countries exhibit similar patterns? To answer this, consider this: on average U.S. non-firearm crime rates were 1.3 times above the average of other countries (that is the average height of the seven columns on the right is 1.3), whereas – as can be seen on the chart above – homicide by firearm rates were 12.1 times above the average. Relatively speaking thus, crimes involving firearms are 12.1/1.3 = 9.3 times more abundant in the U.S. than they could predicted to be based on the other crime rates. This 9.3 basically represents how much taller the “homicide by firearm” column is in the chart above compared to the average height of the other columns. So by looking at this statistic for all countries, we could see if they show a similar pattern or if the U.S. is an exception.

Out of a sample of 28 developed countries, the U.S.’s value is around 8-9 (depending on whether we use averages or medians and most recent or decade-long crime rates). There are three countries between 3 and 5 (Croatia, Italy and Switzerland). And the other 24 countries are below 2, with 20 being below or roughly at 1.

This seems to indicate that indeed the above graph looks the way it looks only for the U.S. In other countries, homicides by firearm are not much more abundant than other crimes. Somewhat of an exception are the three countries (Croatia, Italy and Switzerland) that have their scores between 3 and 5. But these scores are not that drastic. Using only the most recent data (equivalent of the blue column in the chart above), this is what these three countries look like:

Clearly, the U.S. figures dwarf even these countries. But note also that in Switzerland and Croatia the burglary rate and in Italy motor vehicle theft rate are about as much above the average as the homicide by firearm rate is. This indicates perhaps that the firearm crime rate is not so far from these countries’ average performance. In the U.S., however, the highest non-firearm crime rate is rape, but even rape is six times lower than homicide by firearm.

Also, note that the appearance of Switzerland in this list should not even come as a complete surprise as that country has the second highest gun ownership in the sample (after the U.S.) and the third largest gun ownership rate in the world.

As a final illustration, let us plot the relative abundance of homicides by firearm by country (which was 8-9 for the U.S., 3-5 for the three countries mentioned above, and less than 2 for the rest of the sample) vs. gun ownership rate:

This time I’m using the median data that is why the U.S. score is not 9.3 but 8.2. But the implications are clear. Again, a regression could be run on this but notice that there are virtually no countries beyond ~30 guns per 100 inhabitants (only 3), and literally none between 45 and 85 guns per 100 inhabitants making any regression result highly unreliable.

Strictly speaking what we established with this analysis is that U.S. homicide rates are “unnaturally” high compared to other crime rates in the U.S., and that this is due to the frequent occurence of homicides by firearms. Does this mean that the high number of firearms in the U.S. are responsible for the elevated homicide rate? The answer is possibly yes, but based on this data one cannot say for sure.

Therefore, after two articles (see here and here) establishing that perhaps guns are not to blame for anything, this one indicates that they are. Which one is more accurate? I would say this one (and my reasons are pointed out above). But note that, this article does not necessarily conclude that it is higher gun ownership rates that are to blame, maybe it’s just the inadequate regulation of those guns.

The next step would be to dig myself deep into how guns are regulated in several countries (the United States, Switzerland and Finland come to mind). Will I ever do this? We’ll see, I cannot promise. But if I do, you can definitely read about my findings here.

Sources: UNODC for crime data, Washington Post for gun ownership data.