Table 1 presents the results of descriptive characteristics. States had an average of 26 (SD 25.2) firearm laws, ranging from two laws (Idaho, Mississippi and Missouri in 2017) to 106 laws (California in 2017) (Figure 1). On average, a state was the source of 100 or more crime-related firearms for 2.2 (SD 2.7) states. This ranged from Texas in 2017, which was the source of 100 or more crime-related firearms to 15 states, to 142 observations over eight years (36%) in which a state was the source of 100 or more crime-related firearms to zero other states that year. On average, a state was the destination of 100 or more crime-related firearms for 2.2 (SD 3.4) states. This ranged from California in 2017, which was the destination for 100 or more crime-related firearms from 22 states, to 181 observations (45%) over eight years in which a state was the destination of 100 or more crime-related firearms from zero states that year.
Table 1. Descriptive statistics of state-level characteristics (2010 – 2017)
Variable
|
|
Mean (SD) or N
|
Poverty rate (%)
|
|
17.9 (4.3)
|
County-weighted density
|
|
1.08 (2.24)
|
Area (km2)
|
|
196667 (249856)
|
Firearm ownership
|
|
16.22 (21.94)
|
Number of firearm laws
|
|
25.99 (25.23)
|
|
0 – 9
|
98
|
|
10 – 19
|
115
|
|
20 – 29
|
77
|
|
30 – 39
|
31
|
|
40 – 49
|
14
|
|
50 – 59
|
4
|
|
60 – 69
|
23
|
|
70 or more
|
38
|
States that serve as origin for 100 or more firearms to
|
0 states
|
142
|
|
1 state
|
76
|
|
2 states
|
60
|
|
3 states
|
34
|
|
4 states
|
21
|
|
5 or more
|
67
|
States that serve as destination for 100 or more firearms to
|
0 states
|
181
|
|
1 state
|
66
|
|
2 states
|
52
|
|
3 states
|
17
|
|
4 states
|
18
|
|
5 or more
|
66
|
The network of interstate firearm movement is depicted in Figure 2, which shows the average movement of firearms across states over 8 years, when the average is 100 or more firearms. The width of the arrow between two states is proportional to the average number of firearm movement between those states. States that do not have an average of 100 or more firearms move across its borders are excluded from this figure, as are New Hampshire and Massachusetts, which are connected to each other but not to other states. The highest volume of firearm movement occur between neighboring states: Arizona to California (1332 firearms); Indiana to Illinois (1173 firearms); Nevada to California (850 firearms); Virginia to Maryland (581 firearms); Georgia to Florida (499); South Carolina to North Carolina (474), Pennsylvania to New York (382 firearms) and New Jersey (356 firearms); Oregon to California (355 firearms). The exceptions are the movement from Texas to California (523 firearms), Virginia to New York (451 firearms), Georgia to New York (391 firearms), and Florida to New York (360 firearms). In addition, there is movement across long distances, going north from Georgia to New Jersey (181 firearms) and Texas to New York (106 firearms), and west from Louisiana to California (123 firearms) and Ohio to California (120 firearms). The general pattern evoked by Figure 2 is of gun flows from low-regulation states in the south and southwest to high-regulation states.
Table 2 presents the results of the multivariable zero-inflated negative binomial analysis estimating the relationship between firearm laws in a state and the number of states for which it serves as the source of 100 or more crime-related firearms. Each additional standard deviation in the number of firearm laws was associated with 33% fewer states to which a given state is the source of 100 or more crime-related firearms incidence rate ratio (IRR) = 0.67 (b = -0.40, 95% confidence interval [CI] -0.53, -0.27, p <0.001), adjusting for covariates. In addition, each additional standard deviation in the number of firearm laws was associated with higher odds of not being the source of 100 or more crime-related firearms to any state (adjusted odds ratio (aOR) = 1.56; b = 1.06, 95% CI 0.54, 1.58, p < 0.001). Each additional standard deviation in the firearm ownership was associated with 38% fewer states to which it is the source of 100 or more crime-related firearms (IRR = 0.62; b = -0.47, 95% CI -0.59, -0.35, p<0.001). Each additional standard-deviation in the firearm ownership was associated with higher odds of not being the source of 100 or more crime-related firearms to any state (aOR = 2.88; b = 0.44, 95% CI -0.02, 0.90, p = 0.059), although this did not reach statistical significance. The Vuong test of zero-inflated negative binomial model versus negative binomial showed that V = 6.31 (p<0.001), rejecting the negative-binomial model in favor of the zero-inflated negative-binomial model.
Table 2: Zero‐inflated negative binomial model describing the relationship between a state’s total number of firearm laws and number of states to which it is the source 100 or more crime-related firearms in a given year, adjusting for state‐level characteristics, 2010-2017
Negative binomial model
|
|
|
Variable
|
b (95% CI)
|
Incidence Rate Ratio
|
Intercept
|
‐1.10 (-1.59, -0.60)***
|
0.33
|
Year
|
0.10 (0.08, 0.13)***
|
1.11
|
Poverty rate
|
0.10 (0.01, 0.18)*
|
1.10
|
Density
|
‐0.07 (-0.34, -0.21)
|
0.94
|
Area
|
0.77 (0.58, 0.96)***
|
2.16
|
Firearm ownership
|
‐0.47 (-0.59, -0.35)***
|
0.62
|
Number of laws
|
‐0.40 (-0.53, -0.27)***
|
0.67
|
Census Division
|
|
|
|
New England
|
ref
|
|
|
Mid‐Atlantic
|
2.50 (1.97, 3.02)***
|
12.13
|
|
East North Central
|
1.83 (1.31, 2.36)***
|
6.26
|
|
West North Central
|
0.39 (-0.21, 0.98)
|
1.47
|
|
South Atlantic
|
2.41 (1.92, 2.91)***
|
11.16
|
|
East South Central
|
1.77 (1.25, 2.28)***
|
5.85
|
|
West South Central
|
0.85 (0.26, 1.43)**
|
2.33
|
|
Mountain
|
0.30 (-0.22, 0.82)
|
1.35
|
|
Pacific
|
1.74 (1.24, 2.23)***
|
5.69
|
|
|
|
|
Zero‐inflation model
|
|
|
Variable
|
b (95% CI)
|
Adjusted Odds Ratio
|
Intercept
|
‐1.87 (-2.32, -1.42)***
|
0.15
|
Firearm ownership
|
0.44 (-0.02, 0.90)
|
2.88
|
Number of laws
|
1.06 (0.54, 1.58)***
|
1.56
|
Vuong Non-Nested Hypothesis Test-Statistic: 6.31, p<0.000
Multivariable zero-inflated negative-binomial analysis estimating the relationship between firearm laws and the number of states to which a state is the destination of 100 or more crime-related firearms is shown in Table 3. Each additional standard deviation in the number of firearm laws in a state is associated with 83% more states for which it is the destination of 100 or more crime-related firearms (IRR = 1.83; b = -0.60, 95% CI 0.47, 0.74, p <0.001), adjusting for covariates. The Vuong test of zero-inflated negative binomial model versus negative binomial showed that V = 4.78 (p<0.001), rejecting the negative binomial model in favor of the zero-inflated negative-binomial model.
Table 3: Zero‐inflated negative binomial model describing the relationship between a state’s total number of firearm laws and number of other states for which it is the destination of 100 or more crime-related firearms in a given year, adjusting for state‐level characteristics, 2010 – 2017
Negative binomial model
|
|
|
Variable
|
b (95% CI)
|
Incidence Rate Ratio
|
Intercept
|
-2.00 (-2.58, -1.42)***
|
0.14
|
Year
|
0.10 (0.07, 0.14)***
|
1.11
|
Poverty rate
|
0.22 (0.08, 0.36)**
|
1.24
|
Density
|
-0.01 (-0.06, 0.04)
|
0.99
|
Area
|
1.02 (0.76, 1.29)***
|
2.78
|
Firearm ownership
|
-0.37 (-0.78, 0.03)
|
0.69
|
Number of laws
|
0.60 (0.47, 0.74)***
|
1.83
|
Census Division
|
|
|
|
New England
|
ref
|
|
|
Mid‐Atlantic
|
2.80 (2.24, 3.35)***
|
16.39
|
|
East North Central
|
2.99 (2.44, 3.54)***
|
19.90
|
|
West North Central
|
1.66 (0.96, 2.36)***
|
5.27
|
|
South Atlantic
|
3.15 (2.61, 3.68)***
|
23.24
|
|
East South Central
|
2.56 (1.92, 3.21)***
|
12.99
|
|
West South Central
|
1.24 (0.37, 2.10)**
|
3.44
|
|
Mountain
|
1.02 (0.35, 1.69)**
|
2.78
|
|
Pacific
|
1.31 (0.67, 1.94)***
|
3.70
|
|
|
|
|
Zero‐inflation model
|
|
|
Variable
|
b (95% CI)
|
Adjusted Odds Ratio
|
Intercept
|
-13.53 (-34.30, 7.24)
|
0.000
|
Firearm ownership
|
18.11 (-6.79, 43.01)
|
7.24 x 107
|
Number of laws
|
-4.12 (-13.66, 5.42)
|
0.02
|
Vuong Non-Nested Hypothesis Test-Statistic: 4.78, p<0.000
Sensitivity analyses using the cut-off of 50 firearms instead of 100 showed similar results (Appendix Tables 1 and 2). Each additional standard deviation in the number of firearm laws is associated with higher odds of not being the source of 50 or more crime-related firearms to any state (aOR = 1.95; b = 0.67, 95% CI 0.16, 1.17, p = 0.009), 48% more states for which it is the destination of 50 or more crime-related firearms (IRR = 1.48 ; b = 0.39, 95% CI 0.31, 0.47, p <0.000), and decreased odds of not being the destination of 50 or more crime-related firearms from any state (aOR = 1.44 x 10-11; b = -24.97, 95% CI -41.34, -8.60, p = 0.003), adjusting for covariates.