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Scientific American’s gun error

December 22nd, 2012, 10:43pm by Sam Wang

Update: A reader has pointed out that a substantial fraction of gun deaths are suicides (homicide data are here), raising a complication. However, this point is well-established in peer-reviewed literature (PDF): gun ownership increases death rates across the board: suicides, homicides, accidents… For more discussion of the relationship between guns and homicide, see the work of Harvard’s David Hemenway and collaborators (via Adam Gopnik). Also see Mark Duggan, who shows that changes in gun ownership are linked with changes in homicide rate; the relationship is stronger than for other forms of crime, as expected for a causal link.

Given the strength of US gun culture and the enormous number of guns, legislation will likely focus on secondary regulation (background checks, ammunition control, regulation of private sales, limits on magazine capacity) as detailed below. More research on gun safety would be welcome, but…

My last posting on guns made a simple point: in 1994-2004, restrictions on assault-style weapons probably reduced the number of people targeted in mass killings. However, a rash of comments nominated other “main” causes: violent video games, increasing population density, mental illness, lack of Christianity…it was an impressive array of alternative explanations.

Scientific American’s John Horgan enters the fray with a contrarian headline: More Guns Have Not Produced More Killings, But We Still Need Gun Control. However, the argument supporting the headline has a .45-sized hole in it.

First, let me give a general framework. A relatively simple (and obvious) way to examine the data is as follows:

  • Individuals’ baseline tendencies toward violence are variable. People from all groups are prone to it, some more than others.
  • Technology amplifies human intentions.
  • Guns are a cheap, widely available, and powerful technology for killing.

Based on this, framework, one model for the per-capita gun death rate D would be D = V * G * k, where V is the average tendency toward violence and G is availability of guns, with killing power k factored in. One could get fancier by through stratification: different groups have a different rate of V, and different guns have different effects, and so on. But the core idea is the same.

Previously, I showed evidence that regulating assault weapons (k) reduces D. What about the other variables?

Horgan points out that since 1993, the number of gun homicides has decreased, despite the fact that there are more guns than ever. Therefore, he asserts, more guns (G) do not lead to more killing.

The logical hole here is that the parameter V has declined over time, as part of an overall decrease in crime:

A similar decline in property crime occurred too (click the image for more data). Nobody knows the reason for this decline, though a very plausible explanation is reduction in environmental lead (not the Freakonomical idea, please).

A fairer comparison would be to compare gun deaths in different places at the same time. States are laboratories for democracy, culture, and social policy. For example, my home state of New Jersey is #49 out of 50 in per-capita gun ownership. Only Hawaii is lower. And we are ranked #47 out of 50 in the rate of gun death. (These are good things – I am not enthusiastic at the thought of the cast of Jersey Shore packing heat.)

Based on statistics on gun ownership and deaths, the overall tendency is clear:

The three states with the highest rate of gun ownership (MT, AK, WY) have a gun death rate of 17.8 per 100,000, over 4 times that of the three lowest-ownership states (HI, NJ, MA; 4.0 gun deaths per 100,000). The relationship is a near-perfect linear proportion: on average, as G goes up, D goes up (r=+0.63). These data suggest that whether or not our society finds it desirable, gun safety/control is a plausible means of reducing gun deaths.

A striking aspect of this graph is that the rate of gun ownership varies by almost tenfold across states. Residents of different states are in very different environments, gunwise. When opponents of regulation, who are usually in gun-rich states, say that a sufficiently-determined evildoer could get a gun even under a heavy regulatory regime, that could be correct. Think of this measure as an index of “gun culture.”

At its heart, this is not a surprising result. In gun deaths, the direct cause of death is a gun. In most cases, the death occurs as an intentional act of one person against another person. The strength of the correlation suggests that other factors of undoubted interest – socioeconomic factors, background screening – are secondary. Many of those variables go together: hunters, preppers/survivalists, and urban dwellers are different groups. For example, it would be interesting to see what is so special about South Dakota (unusually low gun death rate) or Arizona (unusually high).

An example of a secondary factor is mental illness. Much has been made of the mental illness of shooters like Adam Lanza and Jared Loughner. Violence is higher among the mentally ill (see here and here). In one study, about 1 in 5 imprisoned violent offenders were identified as mentally ill. Therefore even near-perfect detection of violent tendencies in this population would lead to at most a 20% reduction in violence. For this and other reasons, one could ask (NYTimes) whether mental health screening should be the principal approach to gun violence.

It has been suggested that action video games might incite violence. However, the evidence for this is surprisingly scanty. Indeed, such games can also reduce stress hormone secretion and act as a safety valve. So this is a mixed bag at best.

At this point, legislation on gun safety is a distinct possibility. Possible legislative actions include limits on magazine capacity and regulation of ammunition sales. In all cases, the challenge will be in identifying which actions are likely to reduce gun deaths. To reach this goal, empirical evidence is our friend.

Tags: Politics

43 Comments so far ↓

  • Sam Wang

    I encourage commenters to cite evidence.

    • Josh

      Two questions:

      a.) What’s the correlation in the ownership vs. per-capita death rate above?

      b.) Couldn’t a right-winger easily argue that the causation is the other way — that states with more gun deaths (for whatever sociological reasons) logically imply that citizens in those states should carry guns more frequently in order to protect themselves? Just as cities with more crime require more cops (and cops don’t increase the amount of crime)?

    • Jackson

      How do we know that V does not vary across states. Could the per capita gun ownership be a function of the populations propensity for violent crime?

  • 1000 Yards

    Glad to see your posting.

  • Chris

    Might there not be other variables affecting the graph in this? The biggest one I can think of immediately is whether the states along the line tend to have similar groups of people in socioeconomic status.

    Essentially, are the “rich” states clustering near the bottom left and the “poor” states clustering near the top right? Because if you look at the demographics of *who* commits gun violence, I would think there would be a stronger correlation by SES to firearm deaths than the gun ownership by state to firearm deaths.

    In these states, at the bottom left, such as in New Jersey, just *who* is causing these gun deaths? In the US, according to the 2010 FBI Uniform Crime Report, black men account for ~55% of homicides according but make up only 6% of the US population according to Wikipedia, and historically they’ve been pushed to the bottom of the Socioeconomic pile.

    Might their situation not explain some of the states better than their lack of gun control legislation? And for the remaining “white” states like Wyoming and Alaska, which hold large amounts of rural poor whites as well, would a low SES for the victims be a better predictor?

    I’d like to see a chart showing average income of gun-crime-related criminals by state. Though that information is probably hard to find.

    • The Dude

      The three states you list are also in the bottom 1/5th of overall population per state even though they have more territory than your states on the bottom left.

      May or may not be influential from a public resources angle, but worth a thought.

    • Paul

      Nate Silver shared some interesting data on firearms ownership citing the rural vs urban component.
      New Jersey is an interesting case since it’s urban areas such as Camden and Newark I’d think would have high rates of firearms violence. As to the racial component always get highlighted. What seemingly contradicts this is that most of the mass events are committed by young White men.

  • Doc Holliday

    You use the Violent Crimes rate to justify the point, but I think you need to compare this to the total number of Violent Crimes that actually result in murder, as alluded to by Chris.

    Looking at the BSJ data, most violent crimes do not even make use of a weapon. For all crimes but robberies, there is a comparable use of knives and guns. Total V might have gone down over time, but what is V in relation to G.

    • Sam Wang

      The most direct comparison in this regard would be number of non-gun homicides as the y-variable. As I write, guns are an amplifying technology. It is highly unlikely that somehow the deaths shown would be “replaced” by an equal number of non-gun types.

      We’re a bit short on intern assistance this year, so by all means feel free to send the state-by-state data when you find it.

  • Daniel Pope

    Gun advocates (I’m definitely not one of them) frequently argue that restrictions on guns won’t stop murderers, since there are other murder weapons. Can you plot state overall murder rates on the vertical access and find a similar near-linear relationship? My guess is that the relationship would be almost as strong as the one with firearms deaths.

  • David Hood

    I have seen it argued, for example at as a cite, that the number of non-fatal shootings has been increasing and that the explanation for this is improvements in medical technology converting what would have been death statistics into injury statistics. So another independent variable in the mix, and one that has changed over time.

  • Olav Grinde

    I wonder about several other factors.

    First, to what extent does unsolvable frustration and stress play a role? Is there, for instance, a strong correlation between shootings and high unemployment, foreclosures, low average wages paired with high cost-of-living?

    Second, to what extent is there a statistical correlation between drug abuse and number of shootings?

    Third, to what extent is there a correlation between shootings and gang presence? (i.e. “competitive business interests”, which is not to be confused with the drug abuse factor per se)

    May I also suggest that any analysis of American populations/subpopulations be compared with Canadian “control groups”?

  • Steve McCluskey

    Sounds like a multivariate analysis of the factors (number of guns, median income, economic inequality, racial diversity…) contributing to firearm homicide, other firearm crimes, non-firearm homicide in each state is in order.

    One concern: With only 50 data points, how many factors can be meaningfully examined without overfitting?

  • Wheelers cat

    Actually there is less gunownership overtime. I think the comparison would show increased death rates due to technology. So its not just the number of guns per deaths but the kinds of guns per deaths.
    It would be interesting to correlate relative grey matter in the amygdala with massacre killers. The strongest correlate with being a gun killer is the Y-chromosome. Shooters nearly always male. In this graph gun ownership has declined, yet gun deaths have increased.
    Technology of weps in rapidity of fire and magazine capacity have radically increased death by gun.
    Single shot bolt action rifles and chambered rounds for handguns prevented the mass slaughters that seem to be increasing in frequency.
    We could just not let XYs have guns. That would fix it.

  • James Allworth

    We have correlation established here, but is it causality? What happens if its the other way around – more gun deaths results in higher gun ownership? To see the process in action, see here:

    It would suggest that the lower rates of ownership are not causing less deaths, but rather, vice versa – that lower rates of gun deaths are leading to fewer gun purchases. The states that have the best grip on violent crime get a virtuous cycle; the others are stuck in a violence/gun cycle.

    Gun controls are obviously still valuable in such a circumstance – as part of a circuit breaker in making people feel safe. The Australian experience backs this up.

  • Michael Sweeney

    Please tell me the “gun deaths” stat doesn’t include firearm suicides. These obviously occur more in states with greater gun ownership but I think it’d be tough to correlate overall suicides with guns (look at Japan). It’s an easy inference to make that suicides by firearms would be replaced mostly by suicides by other methods in gun averse jurisdictions.

    I bet if you remove suicides from the sample the gun death/ownership correlation is much weaker.

  • Paul H. Rosenberg

    This is a great little piece of work. Of course it’s only a correlation, and others have pointed out potential problems–some of which I know enough about to know they’re not fatal. But two quick comments, one supportive, the other cautionary.

    First, the supportive one: there’s at least one individual-level study that DOES establish such a link, and it’s pretty hard to see how it could be other than causal: “Investigating the Link Between Gun Possession and Gun Assault”

    From the abstract: “Results. After adjustment, individuals in possession of a gun were 4.46 (P < .05) times more likely to be shot in an assault than those not in possession. Among gun assaults where the victim had at least some chance to resist, this adjusted odds ratio increased to 5.45 (P < .05)."

    This, to me, is pretty conclusive. But I still want to raise a note of caution, because conclusive doesn't mean it explains everything. And that is the issue of common causation. Right of the bat, for example, the 10 most gun-owning states are all Red States, the 10 least gun-owning are all Blue.

  • David Hood

    For those interested in what the broader correlations to gun homicides are, it seems the Gini measure of social inequality within a group is one of the few things that produces a consistent correlation between counttries or within U.S. states

    Based on that, any attempt to measure the effectiveness of gun control measures probably needs to adjust for Gini (so the question becomes are gun homicides within a similar Gini cohort influenced by gun control measures).

  • Mel Snyder

    Does it really matter whether firearm deaths are suicides or assaults? Your graph is still very relevant.

    The states with the highest gun ownership and firearm deaths have practically no black populations, to speak of. Wayne Lapierre would argue that its not gun ownership that accounts for their murder/suicide rates – it’s their abysmal mental patient care. He’d argue they have a higher percentage of deranged citizens responsible for the high gun death rate in the upper right quadrant of your graph – no connection with gun ownership.

    Having listened to political debate from Sarah Palin and her recent command to Congress – “Don’t retreat – reload” – I would not quibble with Lapierre’s judgment in at least a few of those upper-right-quadrant states DO have at least a few seriously deficient people running around with guns.

    There’s one flaw in Lapierre’s argument that your graph exposes – the states with the lowest gun ownership and gun fatalities have the lowest percentages of mentally challenged citizens.
    The notably liberal states in the lower left quadrant have the lowest percentage of crypto-zombies among their populations, waiting to invade an elementary schools.

  • David Lovas

    I fundamentally disagree with your analysis of the information presented, however, it was an Interesting read nonetheless. – also I find it important to point out that the shooter was not Ryan Lanza, but his younger brother Adam. (Disregard if someone else has already made this correction).

    Anyway, thanks for the article.


  • Kevin

    Sorry if I overlooked it, but do you break out how many of these crimes were committed with ‘assault-style’ weapons vs revolvers/semi-automatic pistols? I’m going to guess a high percentage will be pistols, and not the much hyped rifles. On an aside, if the data is available it would be interesting to break that out and compare the trend against the last assault gun ban that was in place and see if there is any statistical difference.

    • Don

      I think the “semi-automatic” and high capacity parts are key. It doesn’t really matter if it’s a pistol or rifle and what it looks like. Again, function and capacity are the key. A rifle or pistol with a high capacity magazine that can be quickly changed out, that can fire as fast as one can squeeze the trigger, is the problem.

  • Rajen S

    Is it possible to obtain replication data for this analysis? I’m intrigued by some of the plausible yet testable alternative hypotheses.

  • Amitabh Lath

    About the suicide issue: I remember from my undergraduate days at an institution where the suicide rate among students was (is?) horrific.

    We had to take some basic seminars in this.
    Basic tenet: a suicide attempt is a plea for help.

    Women are more likely to use pills and if found in time can be helped, given therapy. Men are more likely to use guns.

    Bottom line is if men did not have access to guns, more of them would be alive.

  • Jacob H

    Assault rates seem like a better proxy for V than property crime. One suggestion would be to regress homicide rate on gun ownership rate, as you did, but controlling for assault rate. That might disentangle some of the omitted variable bias.

    • Amitabh Lath

      This suggestion makes sense. If there is a large population of gun violence of the “jilted boyfriend/husband” variety, then there will be a correlation with violent crimes.

      Maybe there is a correlation with states that take domestic violence seriously and lock guys up, vs ones that don’t and it escalates to guns.

  • Sam Wang

    Here is another study, from Mark Duggan, demonstrating a close relationship between gun ownership and homicide – closer than for other forms of crime. This is the expected result for a causative link.

    As I have written before, cite evidence please, or at least ask questions that take evidence into account.

  • Craig

    How do the deaths break down by type, homicide, suicide, accident, by state? Do rates compare between states and cities or counties of comparable population, or population density? Do cities of similar density and population have similar rates? States like Alaska and Wyoming have smaller populations than a number of cities, and states have widely varying areas of population density. California’s population is concentrated in urban areas and there are perhaps, as marked differences between the various counties/cities as there are when looked at on a “state” basis.

    • Anon

      I checked a few sources and I see that if you draw your circle around cities the rate goes way beyond 20 per 100,000. those cities are “Blue” areas

      Cities have substantially higher rates of murder by gun, as Moroz points out. New Orleans has the highest rate, 62.1 per 100,000, more than twice its metro rate. Detroit has the second highest rate with 35.9, nearly four times its metro rate, followed by Baltimore (29.7), Oakland (26.6), and Newark (25.4). St. Louis, Miami, Richmond, Philadelphia, and Washington, D.C., round out the top 10. All of these rates are considerably higher than their metro rates — in most cases more than double or triple, or in the case of Newark, nearly eight times its metro rate. On the other side of the ledger, Austin has the lowest rate of gun-related homicides (1.5), followed by San Jose (1.9), Portland (2.2), Virginia Beach (2.7), and San Diego (2.8).

  • Concealed carrying liberal

    Funny Part is, handguns are the weapon of choice for crime–Most now carrying 9-17 rounds , self-feeding ‘semi-automatic’ . For crime it used to be the ’38 special’, about what cops used to use. This is roughly an 8 shot revolver. One has to dump the shells and add new bullets (usually via quick load) before firing. Now cops usually carry Tech 9mm, holding 12 rounds in the magazine and one in the chamber. They often carry a backup glock-17–(17 more rounds ) These are the Standards in police and crime, and they allow for a much faster firing rate (as Semi autos vs revolvers) and with an increased capacity of 4-8 rounds. ‘Assault rifles’ ‘ are almost lame by comparison, when talking about most deaths.

  • Jonathan Marvin

    Curious as to why the District of Columbia was left off the graph. Perhaps because it is a remarkable outlier?
    DC ownership: 3.8% (lowest)
    DC firearms death rate: 31.2 (highest)

  • Andrew

    Any chance a cluster analysis identifying similar states might clarify these results? At the least it looks like the Northeastern states and HI (bottom left) would be in their own cluster. Clustered groups might reduce some noise in future analyses, just a thought.

  • franky

    Something that has been largely ignored in these numbers is ethnic geography, probably in the name of political correctness. The per/ 100,000 ratios are entirely misleading. In order to get to the truth, it is necessary to acknowledge the truth.

  • coolstar

    A point I raised before here is that a critical factor in mass deaths seems to be the rate of fire This is related to magazine size, obviously, but not totally dependent upon it. David Brin has suggested legislature to limit ROF directly. Who, outside of law enforcement and the military, really needs to get off more than one round for every two seconds? (ok, bird hunters, I suppose). Let the cr**kers keep their huge magazines, if the ROF is limited to 0.5 hz!

  • Andrew

    Thanks for the great article and the graphic representation of firearm deaths to gun ownership. .63 is an incredibly strong correlation.

    For outliers like AZ and SD, I am wondering if the rate of gun violence in AZ is higher due to the nature of their laws versus the nature of SD’s laws? In AZ, you can get a gun easily and can conceal and carry, whereas in SD they cannot get a conceal and carry permit as easily. Also, the level of organized criminal activity in AZ is much higher than SD, leading me to suspect more guns are owned for hunting and recreation in SD than for self protection.

    Sorry I have no sources to cite, but maybe this could be the next study you conduct on the subject? It sure would go a long way towards explaining some of the antecedents to gun violence.