Zero correlation between state homicide rate and state gun laws

There's been much talk recently—including from President Obama—about there being a substantial correlation between state-level gun death rates and state gun laws. Now correlation obviously doesn't equal causation; there may be lots of other factors that are the true causes of both of the things that are being measured. But if we do look for now at correlation, it seems to me that the key question should focus on state total homicide rates, or perhaps (for reasons I describe below) total intentional homicide plus accidental gun death rates. And it turns out that there is essentially zero correlation between these numbers and state gun laws.

To begin with, here's why I focus on total homicide, rather than gun homicide or all gun deaths. First, few people care much about whether they are stabbed to death or shot to death. And even if gun restrictions do decrease gun homicides, that effect may well be offset (or more than offset) by an increase in other homicides:

1. Some killers would kill with knives or other weapons instead of guns.
2. To the extent that today some attempted killings are stopped by defenders who have guns, those attempts might succeed if the guns become harder enough for defenders to get.
3. To the extent that today some potential killings (or attempted robberies, rapes, or burglaries that lead to killings) are deterred by attackers' fear of running into a gun, it might be that fewer will be deterred if guns become harder enough for defenders to get.

If—put together—these effects mean that tighter gun laws will mean 100 fewer gun homicides in a state but 100 more homicides with knives or other weapons, the net result would hardly be a gun law success.

Now of course you might think this won't happen, and the 100 fewer gun homicides will be only slightly offset by, say, 20 extra knife homicides. But to determine whether that's true (to the extent that correlations can determine such things), you'd want to see how gun laws are correlated with total homicides, not with gun homicides. If you're right that the stronger gun laws will yield this net 80-homicide decline, that should show up in stronger gun laws being correlated with total homicide rates.

Second, suicides are quite different from homicides. Morally speaking, restraining people's liberty, and in particular their ability to defend themselves, to prevent murder of unwilling victims deaths is quite different from restraining that liberty to prevent others from willingly killing themselves. It is no accident, I think, that the calls for gun restriction are usually specifically tied to murders—whether mass killings or the aggregate of individual killings—and not to suicides.

Suicide is also likely to be driven by many factors related to culture and the person's living situation, factors very different from those involved in homicide. The age-adjusted suicide rate among blacks in the U.S., for instance, is less than 40% of the suicide rate among whites, while the homicide rate is much higher for blacks than for whites—and that's just one of many examples.

Beyond that, if you really want to commit suicide (and there's good reason to think that people who use a gun to try to commit suicide—as opposed to, say, pills—really do want to commit suicide) but can't get a gun, it's not hard to find alternate reliable means of killing yourself. (On the latter point, see the National Academies' Firearms and Violence report, which concludes, as of 2004, that "Some gun control policies may reduce the number of gun suicides, but they have not yet been shown to reduce the overall risk of suicide in any population.") And, finally, even if some gun laws could decrease suicide, those would often be very different gun laws than those intended to decrease homicides. For instance, even total handgun bans or sharp restrictions on handgun purchases, which have been urged as means of reducing homicides, would be highly unlikely to affect suicides, which could just as well be committed with shotguns (a la Kurt Cobain or Ernest Hemingway). Same for bans on so-called "assault weapons," bans on large capacity magazines, restrictions on carrying guns in public, and more.

The careful reader might be asking, "What about accidents?" The substitution effects I describe above (e.g., reduction in gun homicides might be offset by increase in knife homicides) are indeed highly unlikely for accidents, so it makes sense to look at total intentional homicides plus fatal gun accidents. Indeed, that's what my counts of "homicides" below will refer to below. But if you want to exclude fatal gun accidents, and focus only on intentional homicides, the results are virtually identical, since fatal gun accidents are so much rarer than homicides—for instance, in 2012, there were 548 fatal gun accidents but 16,688 homicides, according to CDC's WISQARS database. (Note that I used an average of three years' worth of accident data, 2011 to 2013, because there are very few gun accidents in any given year in most states.)

So, given this, let's look at how jurisdiction-level homicide rates (i.e., homicides per 100,000 people) correlate with jurisdiction-level gun laws, counting the 50 states and D.C. (I use 2012 Justice Department homicide data, from the Proquest Statistical Abstract of the United States, 2015. I use the 2013 gun law scores and grades from the Brady Campaign, with low scores meaning a low level of gun restrictions and high scores being a high level. And I use an estimate of my own for D.C. based on the Brady Campaign's criteria, since the Brady list didn't include D.C.; I think my estimate is if anything an underestimate of D.C.'s tight gun laws, at least as of 2012-13.) I have also run the analysis using the data from the National Journal article that has recently been in the news, and the result is virtually identical.

First, the ten lowest-homicide jurisdictions, again including both intentional homicide and accidental gun deaths:

Jurisdiction Homicide rate Brady score Brady grade New Hampshire 1.1 5.5 D‐ Vermont 1.3 -4.0 F Iowa 1.6 14.0 C‐ Massachusetts 1.8 60.5 B+ Utah 1.8 -2.0 F Minnesota 1.9 19.5 C Maine 1.9 3.0 F Hawaii 2.1 58.5 B+ Idaho 2.2 0.0 F Wyoming 2.4 -5.0 F

Now the ten highest-homicide ones:

Jurisdiction Homicide rate Brady score Brady grade Arkansas 6.3 1.0 F Maryland 6.4 66.5 A‐ Tennessee 6.4 2.0 F Missouri 6.8 -0.5 F Michigan 7.1 15.0 C South Carolina 7.3 1.0 F Alabama 7.5 3.5 D‐ Mississippi 8.1 -4.0 F Louisiana 11.6 -2.0 F D.C. 13.9 50.0 B

And a scatter-plot:

The correlation between the homicide rate and Brady score in all 51 jurisdictions is +.032 (on a scale of -1 to +1), which means that states with more gun restrictions on average have very slightly higher homicide rates, though the tendency is so small as to be essentially zero. (If you omit the fatal gun accident rates, then the correlation would be +.065, which would make the more gun-restricting states look slightly worse; but again, the correlation would be small enough to be essentially zero, given all the other possible sources of variation.) If we use the National Journal data (adding the columns for each state, counting 1 for each dark blue, which refers to broad restrictions, 0.5 for each light blue, which refers to medium restrictions, and 0 for each grey, which refers to no or light restrictions), the results are similar: +0.017 or +0.051 if one omits the fatal gun accident rates. You can also run the correlation yourself on my Excel spreadsheet.

Now of course this doesn't prove that gun laws have no effect on total homicide rates. Correlation, especially between just two variables, doesn't show causation.

Perhaps there are other confounding factors (such as demographics, economics, and so on). Perhaps even controlling for those factors, there will be other missing factors that are hard to control for—for instance, maybe as the crime rate increases, calls for gun controls increase, so high crime causes more gun restrictions, or maybe calls for more freedom to defend oneself increase, so high crime causes fewer gun restrictions (e.g., liberalized concealed-carry licensing rules). And of course when small changes in the model yield substantial changes in results (e.g., if you calculate the state gun scores differently, the results will likely be different), you know how little you should credit the output. Figuring out the actual effect of government actions, whether gun laws, changed policing rules, drug laws, or anything else, is devilishly difficult.

But since people have been talking about simple two-variable correlations between gun laws and crime, I thought it would be helpful to note this correlation—or, rather, absence of correlation.