ECON 562
Research Paper
Benjamin Coomer
The Effect of Gun Laws on Gun Murder Rate by State
1. Introduction
Over the past four decades, the topic of gun control in the US has been at the forefront of politics, especially in the current decade. This is largely due to a frightening number of school / mass shootings and subsequent calls to enact stronger gun control laws.
A number of interesting issues are worth focusing on here, specifically the culture of guns in the US. Throughout US history, guns have been at the center of our identity. Everyone knows that the American Revolution occurred as an armed resistance and succeeded because of it. The individualistic culture and history of the United States centers on visions of a grizzled man, staring deep to the West with his family and his country and his god weighing deep on his soul, slowly cleaning his rifle. It’s the picturesque vision of America’s past. As if these glorified portraits aren’t enough, there is the ever-present danger of firearm confiscation, underlined by the attempts in the WWII period in Europe to disarm civilians – not to mention the incredibly influential and powerful NRA [1]. There is much to unpack in the US gun conversation, but further discussion may be better served in a sociology paper rather than this one.
This question is interesting because there are so many different approaches towards solving the gun problem in the US, and each of them seems to be backed up by differing studies. Both sides cannot be right unless this is truly an unsolvable problem; there should be a statistically significant policy or practice that can be enacted or kept out of law to lower the amount of gun violence in the US. This paper intends to discover what could be a valid approach by observing gun death rates across each state in 2016 and comparing nine different policies between them while also controlling for a few other variables.
2. Data
This dataset is made up of firearm death rates for each state per 100,000 people in the year 2016. There are nine different policies or policy umbrellas which will be analyzed to see which ones are truly significant in increasing or decreasing death rates. Each of these policies are summarized from the site lawcenter.giffords.org. First are laws for universal background checks in the state. Next are laws involving preventing child access to guns, of which strong laws punish negligent storage and weak laws punish intentional or reckless storage. Then there are regulations on concealed carry, with strong laws gives authorities some discretion in issuing permits while weak laws give little discretion to authority. Laws concerning disarming dangerous people are strong if they allow people to petition to disarm a dangerous person, and weak if they require prohibited people to give up their guns but not require proof of it. Mental health laws involve reporting health records to the NICS, with strong laws requiring this and weak laws allow voluntary submission. Strong open carry laws allow no open carrying of guns, while weak laws allow only some guns or requires permits for some. Private sale background checks are strong if background checks are required for all private sales and weak if they are only required for handgun sales. Laws about stopping access to domestic abusers are strong if all domestically violent people are prohibited from having guns, and weak if ownership is prohibited for only certain types of these people.
Lastly, laws involving waiting periods are strong if transfers are delayed for all or some guns and weak if transfers are delayed only if more time is needed for background checks. For each of these policies, there is also the option of having no laws in place regarding that topic, in which case the binary variable for strong and weak are both zero [2].
The summary statistics of each variable are as follows. There are also nine additional variables: eight that are just the sum of the strong and weak policies (a state will have a 1 if it has any law regarding that policy, and a 0 if it has none) and then one called “total” that is just the sum of those eight variables as well as “background checks” to get a measure of the total number of policies that favor gun control. These variables might prove useful later in the analysis if some other models seem worthy of pursing.
I was somewhat worried about the size of data, as there are only 50 observations; however, the histogram of FMR2016 shows a pretty normal distribution, so I feel comfortable moving ahead with the regression. This is only meant to be an introductory snapshot to explore the effectiveness of gun control, and which specific policies are good or bad; while a comparative analysis of panel data may be more effective in this regard, obtaining that data for each state is incredibly difficult. Next, there is some worry that there was possibly one major shooting in a state that makes the FMR2016 number artificially high for that one year. After some more research, it seems that only a very small percentage of firearm deaths are the result of mass shootings, so this problem can be somewhat ignored [3]. Lastly, there may be differences in reporting methods between states, as well as biased reporting based on political aims. This will be unavoidable in almost any study however, so there’s not much to keep one from moving forward. These are really my only worries involving the data.
3. Methodology
The most encompassing form of the model being estimated is
Yi= β0+β1X1i+β2X2i+…+β18X18i+ui
where Yi is each state’s FMR2016 (the firearm mortality rater per 100,000 people), X1i is each state’s gun ownership rate of 2013 (most up to date estimates readily available), X2i is each state’s indicator variable for background checks, X3i is the indicator for strong child prevention laws, X4i is the indicator for weak child prevention laws, and so on in the order of variables summarized previously – i.e. X18i is the indicator for weak waiting period laws, and Ui is the error term. The model will be changed around a lot however as I explore the many different policies. The explanation of my methodology is explained below, with the actual regression results shown in section 4.
An initial simple regression is performed to get a feel for where to begin. Here, FMR2016 is regressed on backgroundchecks to see how important background checks are on the mortality rate. The results are statistically significant, but R-squared is about .36, so we can do better. Before beginning to add variables outright, I want to check for correlation to make sure there is no multicollinearity or risk of overspecifying, over-controlling, etc. Through this the only worrisome result we see is the correlation between backgroundchecks and private. In the future, I will avoid using these variables in the same model to avoid the consequences of multicollinearity, especially since more data can’t be obtained for this year.
Next I try a regression of FMR2016 on private, and obtain similar results to the original simple regression, with marginally higher F-value and R-squared. I think I will stick to private over backgroundchecks in future models – people may automatically go through private channels rather than trusting a more reputable seller.
Next, I include a control variable gunownership. The thought here is that maybe the level of firearm prevalence may affect total violence levels, and that laws concerning private sales are intended to keep criminals from obtaining firearms, not lawful citizens. The results are promising, with both estimates significant and an R-squared around .56, so I will move ahead to see what other policies may be effective.
At his point, I add policies involving carrying restrictions. It seems that when opencarry and concarry are include individually and together, R-squared doesn’t significantly increase. Concarry is never significant, although policies restricting opencarry do seem to be significantly less than 0 at the 10% level (for one-sided, divide P>|t| by two if t is the same size as the predicted direction). While we can bet that opencarry may be somewhat effective in decreasing gun violence, I will exclude it from future models because of lack of contribution to R-squared.
Next, laws involving protecting children should be considered as these are decently outside the range of policies that we’ve included so far. In these, one can be legally liable if minors are able to or do get access to guns due to poor storage [2]. The results here don’t show significance for having any laws here, so maybe we should look more closely at the difference in strength. Strong child prevention laws are characterized as penalizing any negligent storage, whereas the weak laws only penalize intentional mis-storage [Gifford]. Because of the extremity in difference, only strong child prevention laws are included. This regression of FMR2016 on private, gunownership, and childaccesspreventions is promising – all three explanatory variables are significant at the 5% level, the F-stat is high at 28.93, and R-squared increases to .65.
Next, disdang is added, although the results cause both private and disdang to be insignificant at the 10% level while R-squared increases negligibly. A second regression with just the strong laws concerning disarming dangerous people is tried – this time private is significant while the new variable remains insignificant and R-squared nearly the same—so I will not include this variable. I try adding a few more variables, namely mental, prodom, and waiting, but none of these are close to significant and barely affect R-squared.
Lastly, I’m going to regress FMR2016 on all 18 explanatory variables from my original regression to see if I can gleam anything about what could be added. R-squared is up to .77, the F-value is a much lower 5.84, and the only estimates significant at the 10% level are gunownership, childaccesspreventionw, and privatesalebackgroundw. It’s a bit of a mess, but the overall p-value of 0 does yield promising results: that the overall effect of these policies together is statistically significant. The final model that I settle on is
Yi= β0+β1X1i+β2X2i+β3X3i+ui
where Yi is the firearm mortality rate in 2016 for state i, X1i is the gun ownership rate for that state, X2i is the binary variable indicating any laws on private sale background checks, X3i is the binary variable for strong child access prevention laws in that state, and ui is the error.
4. Results and Discussion
The results for the thirteen different regression models follows below, with the last one containing all 18 explanatory variables listed separately.
From the top two tables, we can see that in Model 7, all variables are significant and R-squared is decently high. I think that this is the most appropriate model to use without fear of overspecifying by adding too many variables. From Model 13, there’s not a lot that we can take away except that strong private background checks are significant at a 10% level and effective at decreasing firearm mortality rates. Weak child access prevention laws are somehow significant and cause firearm mortality rates to be higher than if there were no law whatsoever; I imagine something fishy is going on there that might be a result of not having more data, or strange interactions with the other variables.
Since Model 7 is the chosen model, now I will interpret the results. The constant estimate means that there is an expected firearm mortality rate intercept of 9.729 per 100,000 people. After controlling for the percentage of gun ownership by state, which says that increasing the ownership by 10 percentage points increases the mortality rate by 1.6 per 100,000 people, we can see the effects of policies that require background checks for private sales, and for strong policies that prevent access to firearms by children. Their estimated coefficients are, respectively, -2.52 and -3.65, meaning a state with both of these laws enacted can expect to see a decrease in their firearm mortality rate of over 6 per 100,000 people. This may not seem like a lot but, after controlling for ownership rates, a state without these laws can expect a firearm mortality rate of 9.7 per 100,000. If enacting these laws can cut that rate to nearly a third of what it was before the laws were enacted, then the magnitude of this is huge.
As one final regression, I created the variable totstrong, which is a sum of the total number of strong laws that a state has in place. I regressed FMR2016 on this and controlled for gun ownership. R-squared is still decently high and each variable is significantly significant. While it is harder to give an accurate interpretation of these estimated coefficients (you can’t really say that enacting 3 strong laws will decrease the mortality rate by 3), I do think it shows that there is a relationship between states with multiple strong gun control laws and lower firearm mortality rates.
5. Conclusion
From these results, I conclude that it appears strong gun control laws are generally effective in decreasing firearm mortality rates when the firearm ownership rate is controlled for. Specifically, having background checks for private sales of some or all guns is effective in decreasing the firearm mortality rate, as is having strong laws that place legal liability on people that negligently store their firearms. There are a few caveats, however. Principal among them is the limited amount of data that was used, which can be worrisome when performing analysis. Additionally, we can not be sure of an entirely causal effect of laws on mortality rates in the context of this study. Maybe specific laws were put in place or repealed because of currently high mortality rates, or maybe they were put in place only recently and haven’t had a chance to have an effect yet. A more rigorous study would make use of panel data and prove that after a law had been enacted in one state, it experienced significant changes relative to a similar state that didn’t pass a law.
As a closing thought – having seen the effect of these regressions controlling for gun ownership rates, I think that in the future, gun buyback programs would be worth looking into as an effective method of decreasing firearm mortality rates. The question remains: do places with high rates have those high rates because of the greater number of firearm owners, or do people choose to equip themselves more often in more dangerous places? A rigorous study on this relationship in the future may help reveal more about the most effective ways of decreasing firearm mortality rates.