Gun Control: An Extensive Analysis

[Content Warnings: suicide, homicide, gun violence]

Gun Violence

First, some background.

Guns were used in about 69% homicides in 2013. However, this is not particularly strong evidence that we should have stricter gun control regulations. To determine the extent to which we should regulate guns, we have to look at the empirical effects of gun control.

According to the Centers for Disease Control and Prevention, 33,636 people died due to firearms in 2013. Of these, 63.0% were due to suicide, and 33.3% were due to homicide (the remaining 3.7% were either accidental or with unknown intent). We will talk about both of these, but first I want to talk about where I’m coming from.

The way I see it, there are generally two types of analysis of the effects gun control.

The first type of analysis uses deductive reasoning. For instance, you could look at things like the lethality rate of guns versus other weapons and look at gun-use in crimes between areas with different laws and use probability theory to compute the expected number of lives lost due to guns under some set of (hopefully true) assumptions.

The second type of analysis uses inductive reasoning. For example, you could look at how different countries, states, or cities vary in terms of homicide and gun laws and how these differences have changed over time (e.g. after a new law has been enacted). They try to control for a whole bunch of confounding variables (like income, police enforcement, education, ethnicity, etc.), before finding a connection with the homicide rate.

Both these methods have their strengths and weakness. Deductive reasoning is problematic, because the jumps between steps are usually not air-tight, forcing us to make simplifying assumptions. There is no generalized, widely accepted method of these kind of inferences. The problem with inductive reasoning is that you usually can’t do experiments in the social sciences, so we’re trying to tease causal relationships from correlation, which is hard. In an ideal world, both deductive and inductive reasoning would lead us to the same conclusions. Sadly, we do not live in the ideal world…

Archetypal Homicides

This section is basically a summary of this widely cited paper, which examined 1967 homicides in Chicago. The authors’ goal was to analyze the statistics of homicides to shed light on whether reducing gun ownership would lead to fewer homicides.

First, the study revealed that, contrary to how they’re portrayed in popular culture, a supermajority of homicides are not the acts of hardened criminals committing crimes, but of people simply angry with each other:

  • 74% of homicides happen between people who know each other
  • 82% of homicides were due to “altercations” (e.g. arguments, disputes, etc.) rather than gang disputes or robberies
  • 54% of homicides occur after the offender or victim were drinking

Given that the vast majority of homicides happen in the heat of some dispute rather than as premeditated crimes, we have some evidence that gun control might be effective. Assuming that guns make altercations more likely to end in homicide, it would make sense that reducing guns could reduce crime.

The same paper then discusses the “most dangerous probable substitute weapon”. First, they find that firearms were used in 52% of homicides, followed by knives (30%) and no weapon at all (10%).

The question, then, is whether knives or firearms are more dangerous. They found that even though “serious knife attacks” are reported to the police 2.3 times as often as gun attacks, knives “accounted for less than half the number of homicides than guns did.” I’m not really sure how they square this away with their early data showing that 52% of homicides were conducted using firearms versus 30% with guns, but the two conclusions aren’t too far off: guns are about 4-5 times as deadly as knives.

If the only difference between an assault and a homicide is that the victim is much less lucky in the second, then this line of reasoning makes sense. If, however, you believe that the chief difference between assaults and homicides is that the offender actually has a greater desire to kill in the latter, then this analysis makes less sense. Obviously, the question isn’t which is true, but to what degree one or the other is true.

If you generally believe in this desire-to-kill hypothesis, though, the authors have an interesting observation for you. When you look at the data, altercations with different motives (money, sex, children, etc.) the ratio of homicides-to-assults for gun killings and knife killings remain more-or-less constant. This is exactly what you’d expect to happen if the difference between assaults and homicides were chance, but exactly what you wouldn’t expect, if you thought that more important altercations would make people have a greater desire to kill and therefore have a greater homicide-to-assault rate.

On the other hand, we have evidence against this hypothesis. Using Berkley data, we can compute the homicide-to-assault-ratio in different states. However, we find that there is no correlation between this and the percent of households in each state that own guns, even though you’d strongly suspect there would be if the only difference between homicides and assaults was weapons and chance.

The other potential issues are that (1) there might be a bias in which attacks are reported to police and (2) 1967-Chicago might not be representative of 2016-America.

For the first issue to discredit this analysis, you have to believe that gun-assaults are less likely than knife assaults to be reported to the police. I see no reason to believe this, and it seems intuitively more likely to me that the reverse would be true.

I have no real comment on the second issue. 1967-Chicago may or not be representative of 2016-America. I will point out that some changes:

  1. In 1967-Chicago, 52% of homicides used firearms, compared to 68% of murders in 2011-America. Knives, on the other hand, have fallen as much as gun-use has increased.
  2. About 23% of homicides occurred between people who didn’t know each other in 1967-Chicago, and that number has decreased to about 12% in 2011-America. However, these statistics are really incomparable, because the number of “unknown” relationships is 4% in the first dataset and 44% in the second.

I’d like to add one comments of my own. If we suppose that all altercations that took place with guns took place with knives, it looks like this would have saved 259 lives in 1967-Chicago – that’s roughly 40% of all homicides turned into assaults. This is, of course, merely a very rough estimate, but recklessly extrapolating to the US today implies that guns increase homicides by roughly 5,000 per year (out of 11,000).

Empirical Analysis

Unfortunately, this conclusion was not beared out in this study, which examined data from 1980 of 170 large US cities and compared how crimes between cities varied (i.e. cross-sectional).

They mention that the ceteris paribus criteria (all else being equal) is the only real problem of cross-sectional studies, but that it turns out not to be a huge concern, because “none of the known causes of variation in violence rates are strongly correlated with gun laws.” I’ll have to take their word on that.

This analysis of prior research is decidedly negative. They find that “most of the 29 studies found no impact of gun laws on total violence rates” and that of the 12 that did find favorable or mixed results, 3 were time series (a technique they spend a page debunking, though I’m not completely convinced) and most of the others were “seriously flawed.”

For their own part, they propose the following model:

For a more detailed look at their analysis, I’ll have to make you read the actual study, but their conclusion is that gun prevalence “may increase total suicide rates but [has] no effect on total rates of homicide, robbery, aggravated assault, rape, or fatal gun accidents.” (emphasis, theirs)

More Analysis

On the other hand, this study found that a 10% increase in gun ownership corresponds with an increase in the homicide rate by 0.2-0.3%. The author looked at how gun ownership changes predicted future murder rate changes versus future murder rate changes predicting gun ownership changes, thereby addressing the issue cited by the previous study that it’s difficult to determine whether increased gun ownership causes more crime or whether increased crime causes more gun ownership.

It’s worth pointing out that if we follow the first study (the basis for Archetypal Homicides), then we’d predict that a 10% increase in gun ownership would increase homicides by 4%, so we may be seeing a reduction in homicides due to self-defense or deterrence, just not enough to completely outweigh the increased crime rates.

Extrapolating that 0.25% estimate to all guns, yields a 2.5% increase in homicides due to gun ownership. Given that there are 12,253 homicides per year in the US, this comes out to about 300 more deaths per year.

Probably the most well-known argument against gun control is that if more people carried guns, criminals would commit fewer crimes, as there would be an increased expected cost with each crime. I think it’s fair to say that guns deter crime and are used for self-defense (see previous tangent), though the extent to which these are true varies quite a bit depending on who you ask. However, I think that it’s quite obvious that this mixed evidence is completely dwarfed by the effect of gun-ownership on suicides. Because of this, the rest of our analysis focuses exclusively on suicide deaths.

Suicide

First of all, if you are contemplating suicide, please contact the national suicide prevention lifeline at 1-800-273-8255. Most people who survive attempting suicide are glad they did.

I discussed suicide quite thoroughly already (I actually only became interested it while researching for this post). Why am I discussing it in an article on gun control? Because 20,666 Americans committed suicide using firearms in 2012, outnumber the number of homicides committed with the devices.

The natural counterargument is that people who attempt suicide will do so with or without guns. However, it’s extremely important to note that while “only” 4% of non-gun suicides are fatal, 85% of suicides by firearm are fatal. Hence, the use of guns to attempt suicide results (from a consequentialist perspective) in an expected 0.81 deaths (0.85-0.04 = 0.81). Since 85% of attempted suicides with firearems are fatal, and there were 20,666 suicides with firearms, we can estimate there were 24,300 attempts with firearms. So, it would appear that removing guns from general access would prevent about 19,700 suicides each year (0.81 * 24,300).

This is probably a slight overestimate, because of those who attempt but don’t commit suicide, 3% do eventually die by suicide. However, correcting for this (0.85-0.04-0.03 = 0.78) still implies that removing guns altogether would prevent around 19,000 suicides per year.

One retort to this analysis is that people who want to attempt suicide with a gun, will find one some other way. I intuitively doubt this, and data from this study confirms my skepticism. A simple analysis shows that the slope between % of households that own guns in a region and the % of suicides that use guns in that region is more-or-less 1. Indeed, it looks like the evidence actually points to it being greater than 1, so if anything our deductive analysis underestimated the number of suicide deaths caused by guns. However, for the rest of this analysis, I will continue going with the lower, deductive estimate.

I should also add, that this slope is maintained even after accounting for suicide rate, median income, and urban-ness. More precisely, it is maintained if we account for any two of those three variables - after that, we run into the issue of having too many degrees of freedom and two little data points to use meaningful statistical analysis. If you're interested in running the analysis yourself, here is the csv file. The data is all from the 1990s, aggregates from these places, and is weighted by population.

Net Analysis

Each suicide causes (on average) 34.6 years of lost life. Even the lowest dollar value placed on human life (in America) is $50,000/year. We'll use this estimate for the following, but if you disagree and think that (e.g.) the average year of human life is $150,000 per year, just multiply all the later figures by 3.

Anyway, using the $50,000 figure, we can estimate the annual social cost of gun ownership in suicides at $32.9 billion. Dividing this by the roughly 300 million guns implies that the average gun causes about $110 of social harm per year in suicides.

Given that the evidence is stronger for suicides than for homicides and since gun-suicides outnumber homicides 1.9-1, it is extremely generous to proponents for gun control to suggest that the overall cost of gun-related deaths is around $167 per gun per year, so this gives us an estimate of $110 per year per gun in social cost, with a strong upper bound at $167 per year. I’ll ignore a minimum bound, because I’m not really sure how to determine that.

Types of Guns

Okay, so we can estimate that the total externality of gun-ownership is probably between $32.9 billion and $50.2 billion per year, but we can do better. It turns out that some guns are much more likely to be used for suicide and homicide than others:

Gun Typemill. in US% of gun-kills% of gun-suicides
Handgun11071.3%80%
Rifle1144.0%15%
Shotgun864.4%5%
Sourcehereherehere

This, in turn, implies that we have

Gun Typekills per 100,000 gunssuicides per 100,000 gunsexternality per gun per year
Handgun6.513.8$239 - $352
Rifle0.42.5$43 - $50
Shotgun0.31.1$19 - $24

Note, the ranges in the last column indicate whether we’re being just counting suicide or being extremely pessimistic (counting suicide and presuming that gun-control is equally effective in preventing homicides).

I’m sure that if we instituted such a tax policy, the number of handguns owned would dive, because people would conveniently “lose” them - $202 bucks a year isn’t cheap. This isn’t just my opinion: this study estimates that the elasticity of demand for handguns was between 2 and 3 between 1961 and 1994. If we increased the price of handguns by the proposed $239 dollars, this is about a 45% increase in price in just the first year, meaning (according to our economic model), we’d see at least a 90% reduction in handgun ownership. When we take into account the fact that gun owners will have to pay this every year, the expected drop becomes even worse. Now, this is almost certainly pessimistic (overextrapolation at its finest), but it indicates that we’re talking about a severe reduction in handgun ownership.

Seeing as we don’t just want millions of illegal and untracked firearms, I’d suggest a massive and generous buy-back program, which would probably amount to between $60 and $170 billion dollars ($525 per gun times 110 million handguns versus 310 million guns).

Of course, the standard response is that “the power to tax involves the power to destroy”, however my re-response is that I don’t want to eliminate gun ownership, I just want to

  1. Encourage people to get rid of guns they don’t really want, but are too distracted by daily life to get rid of.
  2. Encourage people to shift from handguns to rifles and shotguns, both of which are much more difficult to hide, and (in my non-expert opinion) are purchased for a more utility-specific purpose in mind (hunting and shooting).

Seeing as I’m coming to the end, I should probably mention a couple brief points that didn’t find their way into the main post:

  1. Policies (like gun-safes or training) might improve gun safety. I don’t really have the motivation to examine each and every policy that claims to reduce fire-arm deaths, so I simplified my analysis. You’ll note, it’s still wicked long. Moreover, I think it’s worth pointing out that looking at the proper tax to place on guns, still gives you a general sense of the restrictions that should be placed on them. The good news is that if your favorite regulation gets passed and it reduces deaths, then the optimal tax will go down, so if we implemented empirical-based externality taxes on guns, conservative’s twin goals of reducing gun deaths while protecting/expanding the right to bear arms become one: reducing gun deaths reduces the tax on guns, allowing greater and cheaper ownership.
  2. We should probably tax the rich more than the poor for owning guns, because each additional dollar has less marginal value for the right. We should probably also tax less for the 8th gun someone owns than the 1st, because I suspect owning multiple guns has diminishing returns in terms of deaths due to guns.
  3. The second amendment was a law implemented to (presumably) try and achieve a better society. Discussions about whether extensively taxing gun ownership is constitution is completely independent to whether taxing gun ownership is right.
  4. It’s quite possible that assault rifles, high-magazine guns, or whatever your favorite category is should be banned outright. Or not. I don’t know. I don’t have the data.
  5. I would say the main argument against what I’ve said is that I assume the utility of people who attempt suicide equals the utility of people who don’t. However, as I’ve addressed before, the vast majority of people who attempt suicide regret it and don’t do so again. So, although it is probably true that the average person who attempts suicide has lower utility-per-year than someone who hasn’t, the effect of this on the outcome of our analysis is probably not huge. The utility lost from suicide will still dwarf the utility lost from homicide, and even if people who attempt suicide have half the utility of the general population, it still doesn’t change the qualitative results: hand-guns should be extensively taxed while rifle and shotguns should be moderately taxed. Moreover, recall that I used the lowest estimate for the value of life; every other estimate I found was over twice as high.
  6. The only evidence I've seen to oppose my take on the suicide data is that a raw correlation between gun-ownership rates and suicide rates reveals no correlation between the two. However, lack-of-correlation does not imply lack-of-causation. The most likely explanation is simply that states with high gun-ownership tend to have lower suicide-attempt-rates for some as-yet-unknown cultural reasons.

Bonus

I’m not sure this study adds much to this analysis, but given that its widely cited, I figure I’d add it for completeness. It examined suicide and homicide rates between “11 European countries, Australia, Canada and the United States”. Here’s the part of the abstract:

Positive correlations were obtained between the rates of household gun ownership and the national rates of homicide and suicide as well as the proportions of homicides and suicides committed with a gun. There was no negative correlation between the rates of ownership and the rates of homicide and suicide committed by other means; this indicated that the other means were not used to "compensate" for the absence of guns in countries with a lower rate of gun ownership

Larger studies are needed to examine more closely possible confounding factors such as the national tendency toward violent solutions, and more information on the type and availability of guns will be helpful in future studies. Nevertheless, the correlations detected in this study suggest that the presence of a gun in the home increases the likelihood of homicide or suicide