Firearm laws and the network of firearm movement among US states

This is an analysis of state-level data from 2010 to 2017. The study was determined to be exempt from Institutional Review Board regulation at the University of California, Los Angeles because it uses de-identified, publicly available, state-level data.

We constructed the network of firearm movement between 50 states using publicly available firearm trace data (2010–2017) from the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) at the time this study was conducted. The ATF maintains a database of firearms used in crimes which are successfully traced to their original point of purchase [14]. The ATF conducts firearm tracing at the request of law enforcement agencies engaged in a criminal investigation in which a firearm has been used or is suspected to have been used, with the intent to link a suspect to a firearm and identify trends and pattens in the movement of illegal firearms. Using these data, we defined a network tie between two states when there was movement of 100 or more firearms in a given year from the state where the firearm is purchased (“source state”) to the state where the firearm is recovered (“destination state”). A state could serve as both a source state and a destination state for another state if it was both a source and destination for 100 or more firearms in a given year. A network of firearm movement was constructed for each year, for a total of 8 networks. For each state, we calculated the number of states for which it served as source state (outdegree) and the number of states for which it served as destination state (indegree). Sensitivity analyses were conducted by constructing the network of firearm movement using cut-offs of 50, 60, 70, 80, and 90 or more firearms.

The primary dependent variables were the number of states for which the index state was the source of 100 or more crime-related firearms in a given year (outdegree) and the number of states for which the index state was the destination of 100 or more crime-related firearms in a given year (indegree), which were calculated based on the networks described above.

Following other studies [1, 11, 15], the independent variable was the firearm law strength score, an unweighted count of state-level firearm laws. This variable was obtained from the State Firearm Laws Database, which compiles data on state-level laws in all 50 states since 1991 and codes them into fourteen categories of laws that regulate and deregulate firearms [16]. Laws regulating firearms include those regulating dealers and buyers, those regulating possession of firearms, those regulating purchase or possession of assault weapons, and those preventing individuals with a history of crime, domestic violence, and mental health conditions from possessing firearms. Laws deregulating firearms include laws providing blanket immunity to firearm manufacturers and Stand-Your-Ground laws that allow individuals to use firearms with immunity from the law when they can claim a self-defined need to protect their property. A higher firearm-law strength score denotes more laws regulating firearms and fewer laws deregulating firearms. This variable was scaled to have a mean of 0 and a standard deviation of 1.

We examined all state-level firearm laws rather than limiting the focus to those that specifically prohibit firearm trafficking by regulating the purchase of firearms. Prior studies have found that numerous categories of state-level firearm laws, ranging from those that regulate purchase or registration of firearms, those that regulate concealed carry permits, to those that allow municipalities and cites to regulate firearms, were associated with less interstate movement of crime-related firearms [9, 10, 17, 18]. Further, studies interviewing persons incarcerated for firearm-related offenses showed that the majority of firearms were acquired through their friends, acquaintances, family members, and other members of their social network [19, 20]. Such transactions in the secondary firearm market were unreported and remained unregulated by laws targeting firearm trafficking, especially as many laws exempt the transfer or sale of the firearm to relatives.

We used the following state-level data to adjust for characteristics previously associated with firearm-related violence: poverty rate [21‐23], a validated proxy measure for state-level firearm ownership [24], and county-weighted state density as a proxy for the average urbanicity of the state (the sum across all counties in the state of [county population / county land area] * [county population / state population]) [21, 23, 25]. The proxy measure of state-level firearm ownership developed by Siegel and colleagues [24] uses the proportion of firearm suicides in a state and per capita number of hunting licenses [26], and is highly correlated with survey-measured, household firearm ownership at 0.95. We also adjusted for state area and census division [23] to account for differences in firearm movement by state size and geographic location. These variables were scaled to have a mean of 0 and a standard deviation of 1.

The distribution of the number of states for which the index state serves as the source or destination of 100 or more crime-related firearms is skewed to the right and contains a large proportion of zeros (Additional file 1: Figure S1). Therefore, we fitted zero-inflated negative-binomial models, which is designed to address overdispersion and excess zeros when analyzing count data. A Poisson model assumes that the conditional mean is equal to the conditional variance. Negative binomial models are modified Poisson models that relax this assumption, allowing the conditional mean and variance to be estimated separately, and is used for modeling over-dispersed count variables. Zero-inflated models assume that there are two latent groups: observations that necessarily have a high probability of a zero outcome (excess zeros) because of some underlying attributes, and observations that might have a zero, but might have a positive count with nonzero probability [27, 28]. In the context of this analysis, firearm movement, say, from Alaska to Florida is likely to be an excess zero because of the distance involved, while movement from Georgia to Florida is likely to be driven by policy. Zero-inflated models consist of two parts, a binary model and count model (in our case, negative binomial model) to account for excess zeros [28, 29]. We fitted a fixed-effects zero-inflated negative-binomial model to estimate the association between the number of firearm laws and the number of states for which the index state serves as the source of 100 or more crime-related firearms in a given year, adjusting for the covariates listed above. We subsequently fitted a zero-inflated negative-binomial model to estimate the association between the number of states for which the index state is the destination of 100 or more crime-related firearms in a given year, adjusting for covariates.

To test the sensitivity of our results against the choices for our methodologic approaches, sensitivity analyses were conducted. First, we fitted similar zero-inflated negative binomial regression models using the cut-offs of 50, 60, 70, 80, and 90 or more firearms. Second, we fitted similar negative binomial regression models without the zero inflation. Finally, in order to account for the serial autocorrelation between data, we fitted linear regression models with a Prais-Winsten estimator to model the association between the number of firearm laws and the log-transformed non-zero counts of states for which the index state serves as the source of 100 or more crime-related firearms or as the destination of 100 or more crime-related firearms, adjusting for covariates [30]. The networks were constructed and analyzed using igraph version 1.2.4.1 and sna version 2.4 packages, and linear regression with Prais-Winsten estimator was conducted using prais version 1.1.1 package for R. Zero-inflated negative-binomial regression with robust confidence intervals and negative binomial regression analyses were conducted using Stata version 16.

Interpretation of our findings are subject to limitations. This is an associative study, and as such we are unable to establish causality between firearm laws and movement of crime-related firearms. Our gun ownership variable was a proxy measure and we did not have detailed data on actual gun ownership at the state level. As an ecological analysis, the study cannot make any causal claims at the individual level, but instead points to policy factors associated with state-level firearm movement. The firearm trace data used in our analysis only included firearms used in crimes that were recovered by law enforcement, not all firearms or all firearms used in crimes. Finally, this study did not assess the impact of interstate firearm movement on negating the effects of stricter firearm laws, nor how such a relationship could affect overall state rates of firearm-related violence. Strengths of the study include using longitudinal data over an eight-year period and including all 50 states to give a more complete picture of how firearms are shared among states.

Taken together, these results suggest that the effectiveness of firearm-restricting policies at the state level is complicated by a network of firearm movement among states. These results suggest that firearms travel in complicated webs among states, and therefore, state-level firearm policies may not sufficiently address firearm availability within states. This may in part explain why certain firearm laws have not been found to have the intended effects on firearm-related violence: a recent systematic review showed that state-level laws that aim to curb firearm trafficking through regulating firearm dealers and mandating theft reporting showed conflicting and inconclusive results on the state’s firearm-related violence [7]. Our study suggests the need for federal or regional firearm laws that may better regulate crime-related firearms that move across states.