Econometrics Problem Set 5

Tarun Singh Worked With: Alexander Marcus and Alex Sloan Economics 1123, Problem Set 5

1) a) The coefficient on shall in regression (ii) seems to show that the

presence of a shall-carry law decreases the amount of violent crime by 36.83%. This number is large in the “real world” sense because it seems to suggest that 36.83% of violent crime can be prevented by allowing people to carry concealed weapons. b) Adding the control variables in regression (ii) does not change our conclusion about the effect of shall-carry laws. Although adding the control variables did reduce the coefficient on shall by .0746, the coefficient was still very large and still statistically significant, so it does not change our conclusion. c) A variable which may vary from state to state but varies little over time could be the marriage rate. The marriage rate may lead to OVB as there may be a correlation between gun ownership and marriage rate that may be left out. Another variable that may lead to OVB could be income inequality in a state. This income inequality would differ from state to state but most likely differ little over time, and if there is a correlation between income inequality and certain types of crime this could also lead to OVB.

2) Table 1 The Effect of Concealed Handgun Laws on Violent Crime: Regression Results Dependent variable: ln(vio) Coefficient on shall

State characteristic control variablesa? State fixed effects? Year fixed effects? F-statistic testing the hypothesis that the state fixed effects are zero F-statistic testing the hypothesis that the year fixed effects are zero HAC (clustered) SEs? N

(1) -.4429646 (.0475283 )

(3) -.046141 5 (.019943 3) Yes

(4) -.027993 5 (.019373 3) Yes

(5) -.02799 (.04163 86)

No

(2) -.368386 9 (.034787 9) Yes

No No –

No No –

Yes No 210.38 (0.000)

Yes Yes 291.42 (0.000)

Yes Yes –

–

–

–

14.63 (0.000)

20.67 (0.000)

No 1173

No 1173

No 1173

No 1173

Yes 1173

Yes

Notes: All regressions include an intercept. For regressions (1) – (4), heteroskedasticity-robust standard errors appear in parentheses below estimated coefficients; for regression (5), the standard errors are heteroskedasticity-robust and clustered at the state level, so as to allow for serial correlation in the error within a state. p-values appear in parentheses beneath heteroskedasticity-robust F-statistics (or, for regression (5), heteroskedasticity-robust-clustered F-statistic). a Regressions with “state characteristic control variables” include the following regressors: incarc_rate, density, avginc, pop, pb1064, pw1064, pm1029. Table 2 The Effect of Concealed Handgun Laws on Robberies: Regression results Dependent variable: ln(rob) Coefficient on shall

(1) -.773320 7 (.069262 3) No

State characteristic control variablesa? State fixed effects? No Year fixed effects? No F-statistic testing the – hypothesis that the state fixed effects are zero F-statistic testing the – hypothesis that the year fixed effects are zero HAC (clustered) SEs? No N 1173 Notes: See the notes to Table 1.

(2) -.528820 2 (.051002 1) Yes

(3) -.007818 9 (.026442 8) Yes

(4) .0268298 (.025240 6)

No No –

Yes No 190.47 (0.000)

Yes Yes 247.55 (0.000)

Yes Yes –

–

–

12.32 (0.000)

24.73 ( 0.000)

No 1173

No 1173

No 1173

Yes 1173

Yes

(5) .026829 8 (.05335 64) Yes

Table 3 The Effect of Concealed Handgun Laws on Murders: Regression results Dependent variable: ln(mur) Coefficient on shall

State characteristic control variablesa?

(1) -.47337 25 (.04853 6) No

(2) -.313173 5 (.035701 9) yes

(3) -.06081 (.027213 8) yes

(4) -.014952 4 (.027224 7) Yes

(5) -.01495 (.03910 6) Yes

State fixed effects? No No Yes Yes Yes Year fixed effects? No No No Yes Yes F-statistic testing the – – 88.22 106.12 – hypothesis that the (0.0000) ( 0.000 ) state fixed effects are zero F-statistic testing the – – – 12.62 18.75 hypothesis that the ( (0.000) year fixed effects are 0.0000 ) zero HAC (clustered) SEs? No No No No Yes N 1173 1173 1173 1173 1173 Notes: See the notes to Table 1. 3) As seen in the tables above, adding fixed state effects changes the conclusions we had reached. In all three tables adding fixed state effects decreased the coefficient on shall, meaning when we account for fixed state effects, shall carry laws have less of an effect reducing violent crime rates. Similarly, when adding fixed time effects the coefficient on shall changes in all three tables, however, this change is much smaller than the change seen by adding fixed state effects and the change caused by fixed time effects causes the coefficient to either increase or decrease depending on which table we are looking at. Looking at the F-statistic testing the null hypothesis that the fixed year effects are zero, we see that we reject the null hypothesis in all three tables. This leads me to believe that the best regression is either regression 4 or regression 5 as both would capture the OVB that would be present if we omitted fixed state effects and fixed time effects. The clustered standard errors are larger than the conventional heteroskedasticity-robust errors, however our conclusions are not sensitive to the use of clustered standard errors since the coefficient on shall was not significant in any of the regressions when adding fixed state effects and fixed time effects. The regression data shows us that allowing for shall carry laws slightly reduces violent crime and murder rates but also slightly increases robberies. However, the data also shows that allowing for shall carry laws has no statistically significant effect on violent crimes, robberies or murders. The differences in these estimates across crime rates are consistent with the differences in the natures of these crimes. For example, violent crimes and murders tend to be crimes of passion so if there are more relaxed gun carrying laws victims will be better able to defend themselves, and this may dissuade their assailants, thus the slight negative coefficients for shall when looking at violent crimes and murder make sense. Robberies on the other hand are often pre-meditated, and if people can carry guns easier they have a greater ability to use the guns to rob a store which may be what is leading to the slight positive coefficient for shall when looking at robberies. The possibility of OVB due to a correlation between income inequality and certain violent acts still remains. It would be interesting to look at data that

accounts for income inequality. I would also like to look at data in a quadratic form or to include interaction terms between population density and income inequality to see if there is any functional form misspecification. The conclusions, furthermore, may be affected by functional form misspecification.

Using the data from regressions 4 and 5 we observe that there is no significant relationship between concealed weapons laws and the crime rates we studied.