In the second regression with all variables, we see a significant negative effect of these laws on violence with a beta of -0.368 Since we have a log dependent variable, we can think of this as a 36% decrease in violence, which has practical significance from a policy perspective.
The model with the just one variable has a larger coefficient than when we include excoriates. Both are statistically significant at high level. In terms of ‘real-world’ significance, this is a difference of almost 10%, whihc would make a substantial impact in a policy setting
There are numerous variables that would vary across states but not vary much over time. For example, if people believe there state is safe or has/does not have a lot of crime. This would vary only a little over time, but significantly between states.
In the state fixed effects model, we still see a statistically significant decrease in violence from shall-carry laws. But there are two important features. First, it is statistically significant at a lower level, suggesting we may have a wider confidence interval which is even more consequential because second, a decrease of less 5 percent is much less compelling than in the simple regression models. The second set is more credible since it controls for some of the omitted variable bias from unobserved state effects.
When we include time effects in the model, we see an even larger decrease in the impact, down below 3% with a coefficient of -.028. It also fails to be significant in this final model, suggesting that we cannot conclude any impact from the laws. This is the most reliable of the models because it controls for steady-state features of state and time, reducing the error term by an even greater degree.
| Dependent variable: | ||||
| lnvio | ||||
| OLS | panel | |||
| linear | ||||
| (1) | (2) | (3) | (4) | |
| shall | -0.443*** | -0.368*** | -0.046** | -0.028 |
| (0.042) | (0.033) | (0.019) | (0.017) | |
| incarc_rate | 0.002*** | -0.0001 | 0.0001 | |
| (0.0001) | (0.0001) | (0.0001) | ||
| density | 0.027** | -0.172** | -0.092 | |
| (0.013) | (0.085) | (0.076) | ||
| avginc | 0.001 | -0.009 | 0.001 | |
| (0.008) | (0.006) | (0.006) | ||
| pop | 0.043*** | 0.012 | -0.005 | |
| (0.003) | (0.009) | (0.008) | ||
| pb1064 | 0.081*** | 0.104*** | 0.029 | |
| (0.017) | (0.018) | (0.023) | ||
| pw1064 | 0.031*** | 0.041*** | 0.009 | |
| (0.008) | (0.005) | (0.008) | ||
| pm1029 | 0.009 | -0.050*** | 0.073*** | |
| (0.011) | (0.006) | (0.016) | ||
| Constant | 6.135*** | 2.982*** | ||
| (0.021) | (0.543) | |||
| Observations | 1,173 | 1,173 | 1,173 | 1,173 |
| R2 | 0.087 | 0.564 | 0.218 | 0.056 |
| Adjusted R2 | 0.086 | 0.561 | 0.177 | -0.013 |
| Residual Std. Error | 0.617 (df = 1171) | 0.428 (df = 1164) | ||
| F Statistic | 111.079*** (df = 1; 1171) | 188.411*** (df = 8; 1164) | 38.771*** (df = 8; 1114) | 8.151*** (df = 8; 1092) |
| Note: | p<0.1; p<0.05; p<0.01 | |||
| Dependent variable: | ||||
| lnrob | ||||
| OLS | panel | |||
| linear | ||||
| (1) | (2) | (3) | (4) | |
| shall | -0.773*** | -0.529*** | -0.008 | 0.027 |
| (0.061) | (0.046) | (0.025) | (0.024) | |
| incarc_rate | 0.001*** | -0.0001 | 0.00003 | |
| (0.0002) | (0.0001) | (0.0001) | ||
| density | 0.091*** | -0.186 | -0.045 | |
| (0.019) | (0.114) | (0.105) | ||
| avginc | 0.041*** | -0.018** | 0.014 | |
| (0.011) | (0.008) | (0.009) | ||
| pop | 0.078*** | 0.016 | 0.00002 | |
| (0.004) | (0.012) | (0.011) | ||
| pb1064 | 0.102*** | 0.112*** | 0.014 | |
| (0.024) | (0.024) | (0.031) | ||
| pw1064 | 0.028** | 0.027*** | -0.013 | |
| (0.012) | (0.007) | (0.011) | ||
| pm1029 | 0.027* | 0.011 | 0.105*** | |
| (0.015) | (0.009) | (0.022) | ||
| Constant | 4.873*** | 0.904 | ||
| (0.030) | (0.773) | |||
| Observations | 1,173 | 1,173 | 1,173 | 1,173 |
| R2 | 0.121 | 0.596 | 0.037 | 0.049 |
| Adjusted R2 | 0.120 | 0.593 | -0.014 | -0.021 |
| Residual Std. Error | 0.895 (df = 1171) | 0.609 (df = 1164) | ||
| F Statistic | 160.904*** (df = 1; 1171) | 214.832*** (df = 8; 1164) | 5.293*** (df = 8; 1114) | 7.048*** (df = 8; 1092) |
| Note: | p<0.1; p<0.05; p<0.01 | |||
| Dependent variable: | ||||
| lnmur | ||||
| OLS | panel | |||
| linear | ||||
| (1) | (2) | (3) | (4) | |
| shall | -0.473*** | -0.313*** | -0.061** | -0.015 |
| (0.046) | (0.034) | (0.026) | (0.025) | |
| incarc_rate | 0.002*** | -0.0004*** | -0.0001 | |
| (0.0001) | (0.0001) | (0.0001) | ||
| density | 0.040*** | -0.671*** | -0.544*** | |
| (0.014) | (0.116) | (0.110) | ||
| avginc | -0.077*** | 0.024*** | 0.057*** | |
| (0.008) | (0.008) | (0.009) | ||
| pop | 0.042*** | -0.026** | -0.032*** | |
| (0.003) | (0.012) | (0.011) | ||
| pb1064 | 0.131*** | 0.031 | 0.022 | |
| (0.017) | (0.024) | (0.033) | ||
| pw1064 | 0.047*** | 0.010 | -0.0005 | |
| (0.009) | (0.007) | (0.011) | ||
| pm1029 | 0.066*** | 0.039*** | 0.069*** | |
| (0.011) | (0.009) | (0.023) | ||
| Constant | 1.898*** | -2.486*** | ||
| (0.023) | (0.563) | |||
| Observations | 1,173 | 1,173 | 1,173 | 1,173 |
| R2 | 0.083 | 0.606 | 0.153 | 0.116 |
| Adjusted R2 | 0.083 | 0.603 | 0.109 | 0.051 |
| Residual Std. Error | 0.674 (df = 1171) | 0.443 (df = 1164) | ||
| F Statistic | 106.506*** (df = 1; 1171) | 223.663*** (df = 8; 1164) | 25.123*** (df = 8; 1114) | 17.845*** (df = 8; 1092) |
| Note: | p<0.1; p<0.05; p<0.01 | |||
The largest threat to internal validity are the potential relationship between our variable of interest (shall) and violent crime in a state. For example, if crime is higher in a particular place, people may desire these laws (or be more skeptical of guns, so we could see the reverse.) But this potential confoundedness risks the validity of the model.
Based on these models, we can conclude that there is no statistically significant effect from carry laws on crime rates. If we consider the confidence interval, it spans zero effect, so we can assume no impact. If we consider a hypothesis testing perspective, we cannot fully reject an impact since our confidence interval is small. That said, we do not have enough analysis to conclude a causal impact so additional OVB may exist.