Monday, May 16, 2016

Do guns kill people or do people kill people? An economist's perspective

Marshall and I think a lot about the economics of violence, so when the debate about gun control started on House of Cards, I started considering the classic,
"Guns don't kill people, people kill people." 
I mulled over this a bit and got in a debate with my wife since it didn't seem immediately obvious to me what this statement meant and whether it was testable.

I think the economist's take on the statement is that guns are a "technology" used to "produce" murder. This framing made it easier for me to think about what people meant in a way that had some testable predictions.

If "people kill people," that means there are other technologies out there that are pretty similar to guns and can easily be used to produce murder. In econospeak: guns have substitutes. This could happen for two reasons. First, either there are other technologies that produce murder at similar cost, where costs include both the psychological burden of committing murder and the convenience of gun technology, in addition to actual dollar costs. Alternatively, there might be technologies out that that are much more costly than guns (think: committing murder with a knife probably has different psychological costs), but the "demand" for murder is so high that people are willing to use those much more costly technologies to get the job done, i.e. demand for murder is inelastic. If this is true, then raising the cost of gun technology (e.g. strengthening gun control measures) won't save lives since people will be so motivated to produce murder they'll just use the alternative technologies, regardless of whether they they have to pay a higher cost of doing so.

If "guns kill people," I think that means gun technology is so much better than the next closest substitute that simply the presence of guns affects the likelihood that murder is produced. In order for this to happen, it seems you need two conditions to hold. (1) People would have to be willing to commit murder if they can use a gun, but not if they can't (demand for murder would have to elastic) and (2) gun technology must substantially lower the cost of committing murder relative to the closest substitute (seems likely to me). If these conditions are true, then one could effectively reduce the total production of murder by raising the cost of using gun technology, forcing people to use costly alternative technologies. If demand for murder is elastic, then some marginal would-be-murderers will find it's not worth the trouble and lives will be saved.

This led me to an alternative framing of the original statement, which seemed much more tractable to me:
"Are guns and knives substitutes?"
My curiosity piqued, I stayed up late hunting down some data to see if there were any obvious patterns.

I found the FBI Uniform Crime Reports, which tabulate homicides by weapon used for each state in Table 20. I created a state-by-year panel for 2005-2014, converting homicide counts into rates with census data, which goes up until 2010. I needed a measure of the "cost" of gun technology, and after a little hunting around (there is amazingly little data on gun-related anything) found Okoro et al (Pediatrics, 2005) which estimated the fraction of homes with a loaded firearm present using a randomized survey.  Obviously, there is a lot of other stuff that goes into making gun use costly, but it seemed to me that having a loaded gun in the house would dramatically lower the cost of using the gun for murder compared to the alternative situation where a gun had to be located and obtained prior to the act. The data set I put together is posted here in case you want to mess around with it.  (I imagine an enterprising graduate student can analyze the time series variation in this data, but I ended up collapsing this to a cross-section for simplicity.)

The first thing I did was to plot the homicide rate (where a gun was the weapon used) for each state against the fraction of homes with a loaded weapon present. Maybe someone has done this before, but I was struck by the plot:

The slope of the fitted line is 0.18, implying that a 1% increase in homes with a loaded firearm is associated with and average 0.18 additional annual gun murders per 100,000 state residents. This might not be a causal relationship, it's just a correlation. But the the idea that "guns don't kill people, people kill people" has the testable prediction that "guns and knives are substitutes." If this is true, then we would expect that in the states where guns are less accessible, people simply commit murder with other weapons. If we assume for the moment that people in all different states have similar demand for murder, then the substitutability of guns and other weapons would lead us to expect to see this:

Basically, where people don't have guns, they don't kill with guns and instead kill using other weapons. In places where guns are widespread, they are a cheap technology and so they are used more relative to their substitutes.

The FBI data contains information on the weapon used in a homocide, so I just group together all non-gun technologies, which in the FBI data are coded as "knives or cutting instruments," "hands, fists, feet, etc," and "other weapons." When I plot these data (grey circles) I get:

This is not the result we'd expect to see if "people kill people." The murder rate with non-gun technologies is almost totally unrelated to the presence of guns, and if anything it increases with gun ownership rather than decreases as we would expect if demand for murder were totally inelastic and people just swapped knives for guns seamlessly. This would suggest that "guns and knives are not really effective substitutes," implying that "guns probably kill people."

Now, this is correlational evidence, it's isn't a careful quasi-experimental study. There are alternative explanations that could explain this pattern.  First, demand for murder could simply be much higher in the states where people have more loaded firearms. This seems plausible, would be consistent with the non-gun murder pattern, but is hard to test. Second, people could have loaded firearms hanging around specifically because they are afraid of high murder rates (reverse causality). This "armament" hypothesis is a story that I think a lot of people tell, and it probably plays some role. But the association here is such that people have to be really afraid of murder in the sense that a small number of additional murders causes a lot of people to go out and purchase guns that they leave loaded in their house. The slope of the red line is 0.18, so in order for the armament story to make sense, if 0.002% more of the population were murdered this would have to cause roughly 10% more of the population to start leaving a loaded gun in their home.  This is possible, but my intuition is that people aren't quite that skittish.


  1. Interesting approach! I don't think I have seen that before. But how does this fit with fact gun sales and public carry of firearms has gone up dramatically over the last 10 to 20 years yet the violent crime rate has gone down over the same time?

    As you mentioned your approach is somewhat simplistic and alternate explanations are possible. The one that comes to my mind is that a common cause results in both higher gun ownership rates and higher murder rates.

    Having studied (as a non-professional) this for many years my initial hypothesis would be that different cultures have a correlation with both high gun ownership and high violence rates. Read Thomas Sowell’s book Black Rednecks and White Liberals for example.

    This might explain why there is so much scatter in the data in your graphs. Some cultures have very high gun ownership rates (for example, more rural states with good hunting opportunities) with very low murder rates. While other cultures (for example those with high rates of organized crime or drug gangs) have high gun ownership with high murder rates.

  2. Common wisdom says that they are not substitutes. Gun enthusiasts are especially aware of the maxim "Never bring a knife to a gunfight."

    In "econospeak", there's a path dependency, and it's one-way. It's very difficult to remove guns from a population that is filled with them. Australia did it, but they don't have a national history that required an armed rebellion to achieve separation from their colonial masters.