Gun Control: An Overview

[Content Warnings: suicide, homicide, gun violence]

[The only thing left to do is fixing two broken pie charts.]

The evidence that guns increase the homicide rate is mixed, with estimates ranging from no effect to an increase of 9 homicides per year for every million guns owned.

Deductive Analysis

This section is basically a summary of one widely cited paper Zimring, which examined 1967 homicides in Chicago. The author’s 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
{ "type": "pie", "series": [ { "x": "motive", "y": "percent" } ], "title": "Homicide by Motive" }
Teen Gang Disputes3%
{ "type": "pie", "series": [ { "x": "relationship", "y": "percent" } ], "title": "Offender-Victim Relationship" }
Family or Lover27%
Friend, Acquaintance, or Neighbor44%

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.” This implies 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 data from the Department of Justice Crime - National or State Level, 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 Kalesan, 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.

I’d like to add one comment 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.

Inductive Analysis

The elasticity of homicide to guns is the percentage that homicides would increase if gun-ownership increased by 1%. For instance, if the elasticity is estimated at 0.13, then a 1% increase in gun-ownership can be expected to cause a 0.13% increase in the homicide rate.

My review of empirical analyses gave me four different estimates for the elasticity of gun control using cross-sectional and time-series analysis.

StudyYearStudy CitationsElasticity
Kleck, Patterson The impact of gun control and gun ownership on violence rates19932160
Duggan More guns, more crime20013670.025
Miller, et al. Rates of household firearm ownership and homicide across US regions and states, 1988–199720021520.25
Cook, Ludwig The social costs of gun ownership20061250.20

These are all significantly lower than the 0.4 estimte given by the Chicago study, which may be indicative of guns discouraging violence. Unfortunately, no one can agree on how many times guns are used in self-defense [show], let alone how much this reduces crime, so your guess is as good as mine. Fortunately, we only care about the net-change in homicide, so we can ignore this.

Given our lack of certainty on the preventative effect guns have on crime, I think it is reasonable to ignore the high 0.4 estimate for the gun-homicide elasticity and consider the elasticity estimates provided by the empirical studies. These estimates range from 0 to 0.25 [see above table].

Since there are 310 million guns in the United States Ingraham and roughly 11,200 people died due to firearms in 2013 Xu, this implies that at most 9 people are killed each year per million gun increase.

Ignored Research

I ignored the paper “Gun ownership as a risk factor for homicide in the home”, because it looks at individual households and finds that households with guns are more likely to include homicides by guns Kellermann. However, like the first study, this ignores the claimed deterrence effect, which could very well be important to the analysis.

I also ignored “Effects of Restrictive Licensing of Handguns on Homicide and Suicide in the District of Columbia” Loftin, because while the natural experiment it analyzes looks great, they don’t consider to what extent guns were actually reduced. Moreover, they look only at homicide-by-gun, not at homicides overall, so it’s possible that that the homicides shifted to other methods.

Gun Suicide

While the concept of an "externality" is very popular [at least to economists], it has a less wellknown cousin: the internality. An internality is when your actions have a positive/negative consequence for your future self. As with externalities, internalities should be taxed/subsidized to "internalize" them.

With this in mind, when deciding how much to tax gun ownership, it’s not enough to look at how much owning a gun increases the probability that other people are harmed by it. Instead, since humans don't tend to properly weigh future eventualities, we need to account for part of them.

To be more concrete, because guns increase the probability of self-harm, and because this is underappreciated, gun ownership has an internality that should be taxed. To perform this calculation, we will look at how gun ownership impacts suicide and injury.

The natural counterargument against considering suicide with guns as an internality/externality of guns 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 Harvard T.H. Chan School of Public Health. 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 Lost all hope. US methods of suicide, 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. In other words, for every million guns owned, suicides increase by about 61 Ingraham.

One retort to this analysis is that people who want to attempt suicide with a gun, will find one some other way to obtain a gun. I intuitively doubt this, and data from this study confirms my skepticism Kaplan. 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 of 1.

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 few 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, and aggregates data from these places 1990 United States Census Regional Variations in Suicide Rates, and is weighted by population 1990 United States Census.

Gun Injuries

Injuries caused by guns are less important than suicides and homicides, but still not negligible. The financial cost of firearm related injuries is around $4.3 billion per year (about $14 per gun Ingraham).

During the 6 years between 2010 and 2015, we averaged 79,845 reported nonfatal firearm-related injuries per year. Of these, roughly 16,050 were accidental, while 63,795 were intentional Nonfatal Injury Reports, 2000 - 2015. Comparing this to the 20,666 suicides that occur each year with firearms, we can see that injuries outnumbered suicides nearly 4-to-1.

Of these roughly 80,000 injuries each year, about 38,600 result in hospitalization, resulting in about $4.1 billion in health care costs and worker productivity lost Data & Statistics (WISQARS™): Cost of Injury Reports. Another 33,300 resulted in visits to the emergency department, costing a total of $0.2 billion.

Combined, this gives us the estimated cost ($4.3 billion per year) in gun-related injuries. This, is, of course an underestimate, because there is human suffering as well. However, these costs are almost certainly dwarfed by the social costs of suicide.


However, these internalities (suicide and self-injury) should only be taxed by 70%, because people do care somewhat for their future-selves already, so this brings down our estimated internality from 61 deaths per million guns to 43 deaths per million guns.

From this we can conclude that every million guns owned has an externality/interanlity of deaths between 43 and 52 per year. Using this in conjunction with the age of homicide, suicide victims, and estimates of the value of human life, we can determine the amount guns should be taxed for increasing deaths among a population. Then, all we need to do is add the $14/gun that injuries cause for the upper bound and 70% of that for the lower bound. This implies guns should be taxed somewhere between $83 and $454 per year [show].

However, we need to make some adjustments. First, not all guns are equally likely to end in suicide or homicide, so we should adjust this tax rate by the type of gun [show].

Gun TypeKill Ext.Suicide Int.Tax
Handgun0 - 24 138$249 - $1342
Rifle 0 - 1 25 $53 - $217
Shotgun0 - 2 11 $29 - $111

The ranges in the last column exist because of (1) uncertainty over how much guns increase homicides and (2) how much we’re valuing human life.

Second, because of different levels of income and the individualistic nature of internalities, typical taxes will have a suboptimal impact on individual’s behavior. While our analysis above works for typical people, we need to adjust for their incomes.

Finally, it's suboptimal that everyone should pay the same tax, because certain people are more likely to commit homicide/suicide/injury than others. Ideally, we'd just prevent such people from getting guns in the first place, but that seems infeasible. My friend Dan Gold brought up an ingenious solution to this problem: instead of having the government tax guns, require gun owners to purchase gun-insurance. If their gun is used to kill someone (including suicide), some amount of money would be owed to the government by the insurance company. Because a competitive free market is reasonably efficient, this should result in accurate "taxing" of gun ownership - or at least, as accurate as our society can reasonably achieve.

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