Chicago Law and Economics Working Paper during any year before passage of the law. 16 Table 3 also presents data on a narrower sample consisting of multiple shootings that appeared in the first section of the New york Times at the time the shootings took place We use this sample as an estimate of more serious or, at least, more notorious multiple shootings. Similar to the data on all multiple shootings, the New York Times data show a decline of 91 percent in the rate of multiple shootings after a state adopted a shall issue law. Finally, we consider the possibility that shall issue laws lead criminals to substitute bombings for shootings Data on bombings (from the Bureau of Alcohol, Tobacco and Firearms annual publication Arson and Explosives: Incidents eport) suggest no systematic impact on the number of bombings After the passage of shall issue laws, actual and attempted bombings increased slightly, incendiary bombings fell and other bomb-related incidents(involving stolen explosives, threats to treasury facilities and hoax devices) declined compared to the before law period ll. Accounting for Other Factors Although the above tables suggest that shall issue laws reduce mass shootings, other factors may explain these changes. To take account of this possibility, we estimated regression equations with the following state specific variables: the arrest rate for murder; real per capita personal income; real per capita government payments for income maintenance, unemployment insurance and retirement; the unemployment rate; the poverty rate; state population and population squared; and a set of demographic variables that subdivide a state's population into 36 different race, sex, and age groups. We also include year and state specific dummy variables in the regression analysis. Table 5 lists the variables included in the regression analysis Thus our results hold constant both the effects of any national trends and state-specific effects on multiple shootings which may coincide with the adoption of shall issue laws. So, for example, if the multiple shooting rate declines nationally between two years, the regression coefficient on the law variable tests for whether the decline is relatively greater in states that adopted shall issue laws 16 Of course, there were zero mass shootings in individual states in particular years before the passage of concealed handgun laws
Chicago Law and Economics Working Paper 10 during any year before passage of the law.16 Table 3 also presents data on a narrower sample consisting of multiple shootings that appeared in the first section of the New York Times at the time the shootings took place. We use this sample as an estimate of more serious or, at least, more notorious multiple shootings. Similar to the data on all multiple shootings, the New York Times data show a decline of 91 percent in the rate of multiple shootings after a state adopted a shall issue law. Finally, we consider the possibility that shall issue laws lead criminals to substitute bombings for shootings. Data on bombings (from the Bureau of Alcohol, Tobacco and Firearms annual publication Arson and Explosives: Incidents Report) suggest no systematic impact on the number of bombings. After the passage of shall issue laws, actual and attempted bombings increased slightly, incendiary bombings fell and other bomb-related incidents (involving stolen explosives, threats to treasury facilities, and hoax devices) declined compared to the before law period. III. Accounting for Other Factors Although the above tables suggest that shall issue laws reduce mass shootings, other factors may explain these changes. To take account of this possibility, we estimated regression equations with the following state specific variables: the arrest rate for murder; real per capita personal income; real per capita government payments for income maintenance, unemployment insurance and retirement; the unemployment rate; the poverty rate; state population and population squared; and a set of demographic variables that subdivide a state’s population into 36 different race, sex, and age groups. We also include year and state specific dummy variables in the regression analysis. Table 5 lists the variables included in the regression analysis. Thus our results hold constant both the effects of any national trends and state-specific effects on multiple shootings which may coincide with the adoption of shall issue laws. So, for example, if the multiple shooting rate declines nationally between two years, the regression coefficient on the law variable tests for whether the decline is relatively greater in states that adopted shall issue laws 16 Of course, there were zero mass shootings in individual states in particular years before the passage of concealed handgun laws
11 Multiple victim Public Shootings during the two year period. This approach may actually understate the impact of shall issue laws since the year dummy variables may also pick up some of the changes attributed to the increasing number of states that passed these laws Table 6 presents regressions for twelve different dependent variables(six for multiple shootings and six for bombings)using the simplest specifications of the shall issue law variable-a dummy law variable which equals one if a state has a concealed handgun or"shall issue'law and zero otherwise. The regression analysis contains 953 observations (50 states and the District of Columbia for 19 years minus 16 observations for various states and years in which we lacked data on the arrest rate). 7 To simplify the table, we only present the regression coefficients(and t-statistics)on the dummy law variable The results of Table 6 indicate that concealed handguns laws significantly reduce multiple shootings in public places(but have no systematic effects on bombings). For example, shall issue laws appear to lower the combined number of killings and injuries(equation(3)) in a state by 11. 1 per 10 million people per year, or by more than 80 percent of a one standard deviation change in the murder and injury rate from multiple shootings. Equations(4)and(5)imply that the average state passing these laws reduces the number of murders and injuries by 6.9 and 6.5 persons respectively. Indeed these estimated fects are so large that they often exceed the annual average number of murders and injuries from public shootings in a state(either absolutely or per 100,000 persons). To be sure, we expect large deterrent effects from these laws because of the high probability that one or more potential victim or bystander will be harmed. Still th drop in murders and injuries is surprisingly large. and as we shall see, do not seem to reduce the magnitude of the laws effec rol variables Turning to the other variables in the regressions in table 6, we find that states with larger populations have more multiple shooting 17 The states and years of the missing observations are as follows: Florida (1988): Illinois(1993-95); lowa(1991): Kansas(1993-95): Kentucky (1988) Montana(1994-95): New Hampshire( 1984 and 1995): Pennsylvania (1995) nd vermont(1978-79). As a further check on our results, we reestimated the regressions in Tables 6 and 7 deleting the arrest variable and adding the 16 missing observations. The coefficients and levels of significance on the shall issue law variable were virtually unchanged
11 Multiple Victim Public Shootings during the two year period. This approach may actually understate the impact of shall issue laws since the year dummy variables may also pick up some of the changes attributed to the increasing number of states that passed these laws. Table 6 presents regressions for twelve different dependent variables (six for multiple shootings and six for bombings) using the simplest specifications of the shall issue law variable—a dummy law variable which equals one if a state has a concealed handgun or “shall issue’ law and zero otherwise. The regression analysis contains 953 observations (50 states and the District of Columbia for 19 years minus 16 observations for various states and years in which we lacked data on the arrest rate).17 To simplify the table, we only present the regression coefficients (and t-statistics) on the dummy law variable. The results of Table 6 indicate that concealed handguns laws significantly reduce multiple shootings in public places (but have no systematic effects on bombings). For example, shall issue laws appear to lower the combined number of killings and injuries (equation (3)) in a state by 11.1 per 10 million people per year, or by more than 80 percent of a one standard deviation change in the murder and injury rate from multiple shootings. Equations (4) and (5) imply that the average state passing these laws reduces the number of murders and injuries by 6.9 and 6.5 persons respectively. Indeed these estimated effects are so large that they often exceed the annual average number of murders and injuries from public shootings in a state (either absolutely or per 100,000 persons). To be sure, we expect large deterrent effects from these laws because of the high probability that one or more potential victim or bystander will be harmed. Still the drop in murders and injuries is surprisingly large. And as we shall see, alternative measures of shootings and adding other control variables do not seem to reduce the magnitude of the law’s effect. Turning to the other variables in the regressions in Table 6, we find that states with larger populations have more multiple shooting 17 The states and years of the missing observations are as follows: Florida (1988); Illinois (1993-95); Iowa (1991); Kansas (1993-95); Kentucky (1988); Montana (1994-95); New Hampshire (1984 and 1995); Pennsylvania (1995) and Vermont (1978-79). As a further check on our results, we reestimated the regressions in Tables 6 and 7 deleting the arrest variable and adding the 16 missing observations. The coefficients and levels of significance on the shall issue law variable were virtually unchanged
Chicago Law and Economics Working Paper deaths and injuries per 100,000 persons though the rate increases at a decreasing rate. We also find that personal income, poverty and population density are insignificant while retirement payments and unemployment have positive and significant (or marginally significant) effects on the murder rate. Higher arrest rates for murder are associated with fewer multiple murders and killings but hese results are never statistically significant8(The full regressions are available from the authors on request. Finally, notice that the number of bombings in Table 6 (with the exception of"other bombing incidents"in eq. 12 )are not related to shall issue laws. Some types of bombings appear to rise and others fall after the passage of a law, the signs often depend on whether bombings are expressed as a rate or an absolute number, and five of the six coefficients are not statistically significant. In short, there does not appear any significant substitution between shootings and bombings in states enacting" shall issue"laws. (In the remaining tables we do not report the results for the bombing regressions because, in almost all cases, bombings are not significantly related to shall issue laws.) Table 7 replaces the simple dummy law variable with two time trend law variables for those states that passed laws between 1985 ( the first year a state passed a law during the 1977 to 1995 sample eriod) and 1995. The first is a time trend variable before passage of the law that takes the value 0 in the year the law is passed (and all years following passage),-1 in the year before passage, -2 in the second year before passage and so forth. The second is a post law variable that takes the value 0 in the year the law is passed (and 0 in all years before passage), 1 in the first year after passage and so on The main reason for this specification is that we expect the impact of shall issue laws to increase over time as more peopl ple obtain ermits. It may take many years after enacting a handgun law for states to reach their long run level of permits. For states in which 18 We note that the arrest rate variable understates the actual (or expecte arrest rate of individuals who go on shooting sprees. More than 90 percent of these offenders are either arrested or killed, which is slightly greater than the overall arrest rate for murder. The 90 percent figure (which comes from a Nexis search) represents perpetrators who were immediately captured or killed. We do not know whether those who escaped were apprehended later
Chicago Law and Economics Working Paper 12 deaths and injuries per 100,000 persons though the rate increases at a decreasing rate. We also find that personal income, poverty and population density are insignificant while retirement payments and unemployment have positive and significant (or marginally significant) effects on the murder rate. Higher arrest rates for murder are associated with fewer multiple murders and killings but these results are never statistically significant18 (The full regressions are available from the authors on request.) Finally, notice that the number of bombings in Table 6 (with the exception of “other bombing incidents” in eq. 12) are not related to shall issue laws. Some types of bombings appear to rise and others fall after the passage of a law, the signs often depend on whether bombings are expressed as a rate or an absolute number, and five of the six coefficients are not statistically significant. In short, there does not appear any significant substitution between shootings and bombings in states enacting “shall issue” laws. (In the remaining tables we do not report the results for the bombing regressions because, in almost all cases, bombings are not significantly related to shall issue laws.) Table 7 replaces the simple dummy law variable with two time trend law variables for those states that passed laws between 1985 (the first year a state passed a law during the 1977 to 1995 sample period) and 1995. The first is a time trend variable before passage of the law that takes the value 0 in the year the law is passed (and all years following passage), -1 in the year before passage, -2 in the second year before passage and so forth. The second is a post law variable that takes the value 0 in the year the law is passed (and 0 in all years before passage), 1 in the first year after passage and so on. The main reason for this specification is that we expect the impact of shall issue laws to increase over time as more people obtain permits. It may take many years after enacting a handgun law for states to reach their long run level of permits. For states in which 18 We note that the arrest rate variable understates the actual (or expected) arrest rate of individuals who go on shooting sprees. More than 90 percent of these offenders are either arrested or killed, which is slightly greater than the overall arrest rate for murder. The 90 percent figure (which comes from a Nexis search) represents perpetrators who were immediately captured or killed. We do not know whether those who escaped were apprehended later
Multiple victim Public Shootings data on permits are available the share of the population with permits is still increasing a decade after the passage of the law (Lott, 998b,p.75) In Table 7, we find that deaths or injuries from mass shootings are rising before the passage of the law and falling afterwards (though the before law trend is only marginally significant in most cases). The F-test for the differences in these time trends is always significant at least at the. 02 level. As expected, therefore, the more years a shall issue law has been in effect in the 14 states that passed laws starting in 1985, the greater the decline in murders and injuries (both absolutely and per 100,000 )from mass public shootings Because of the relatively large number of shootings that occurred in the year prior to enactment of the laws and the possibility that our results might be picking up a simple regression to the mean, we reestimated the regressions in Tables 6 and 7 after emoving the observations for that year. All of the shall issue coefficients in the shooting regressions remained statistically significant, with the single exception of the injury rate in Table 6 which was negative but no longer statistically significant. 20 19 We note three other points related to Table 7 (1)Eight states in our sample had shall issue laws during the entire period. All eight passed their laws before 1960 and so should have reached their equilibrium level of permits before 1977(the first year in our sample These value assigned to two time trend variables for these states and states that never enacted laws is zere (2)A second reason for the split time trend specification is that if (relative to other states) shootings in states that pass shall issue laws are rising befor the law goes into effect and falling thereafter, a dummy law variable would underestimate the law's impact (even though the regression contains year ummy variables). For example, imagine that the increase in shootings before the law is symmetrical with the decline after the law. a simple dummy variable for the presence or absence of the law would indicate that the law had no effect yet the law might well have caused a change in the trend from positive to (3)We also estimated regressions adding two time-squared variables for the law variables. Here we find the same pattern of declining murders and injuries after passage of the law with the decline flattening out by the sixth year after enactment of the law 20 Because of the relatively large number of shootings that occurred in the year prior to enactment of the laws and the possibility that our results might be picking up a simple regression to the mean, we reestimated the regressions in
13 Multiple Victim Public Shootings data on permits are available the share of the population with permits is still increasing a decade after the passage of the law (Lott, 1998b, p. 75).19 In Table 7, we find that deaths or injuries from mass shootings are rising before the passage of the law and falling afterwards (though the before law trend is only marginally significant in most cases). The F-test for the differences in these time trends is always significant at least at the .02 level. As expected, therefore, the more years a shall issue law has been in effect in the 14 states that passed laws starting in 1985, the greater the decline in murders and injuries (both absolutely and per 100,000) from mass public shootings. Because of the relatively large number of shootings that occurred in the year prior to enactment of the laws and the possibility that our results might be picking up a simple regression to the mean, we reestimated the regressions in Tables 6 and 7 after removing the observations for that year. All of the shall issue coefficients in the shooting regressions remained statistically significant, with the single exception of the injury rate in Table 6 which was negative but no longer statistically significant.20 19 We note three other points related to Table 7. (1) Eight states in our sample had shall issue laws during the entire period. All eight passed their laws before 1960 and so should have reached their equilibrium level of permits before 1977 (the first year in our sample). These value assigned to two time trend variables for these states and states that never enacted laws is zero. (2) A second reason for the split time trend specification is that if (relative to other states) shootings in states that pass shall issue laws are rising before the law goes into effect and falling thereafter, a dummy law variable would underestimate the law’s impact (even though the regression contains year dummy variables). For example, imagine that the increase in shootings before the law is symmetrical with the decline after the law. A simple dummy variable for the presence or absence of the law would indicate that the law had no effect yet the law might well have caused a change in the trend from positive to negative. (3) We also estimated regressions adding two time-squared variables for the law variables. Here we find the same pattern of declining murders and injuries after passage of the law with the decline flattening out by the sixth year after enactment of the law. 20 Because of the relatively large number of shootings that occurred in the year prior to enactment of the laws and the possibility that our results might be picking up a simple regression to the mean, we reestimated the regressions in
Chicago Law and Economics Working Paper Table 8 adds other law variables that may influence the number of mass shootings. The law variables include the following: a dummy variable if a state has a waiting period before an individual can obtain a gun and the length of this period in days and days squared (see Lott and Mustard for a discussion of this variable); the probability of execution (equal to the number of executions per murder in a given year); and a dummy variable for whether a state imposes additional penalties for using a gun in the commission of a crime. 21 Three conclusions emerge from Table 8. First, the statistically significant negative impact of shall issue laws on mass public shootings continues to hold. Second, the regression coefficients on the shall issues variables are of the same magnitude as in Table 7 Third, the other gun related law variables and the capital punishment variable have no significant impact on mass shootings The point estimates on the waiting period variables sometimes imply that longer waiting periods increase the risk of mass public shootings and other times they imply the reverse. In no case is the waiting period variable statistically significant. Although the execution rate has a negative coefficient in the six regressions, it is never statistically significant. The execution variable itself may be only weakly related to the probability that a mass murderer will be executed given the Tables 6 and 7 after removing the observations for that year. All of the shall issue coefficients in the shooting regressions remained statistically significant, with the single exception of the injury rate in Table 6 which was negative but cant. For example the t-statistics for the shall issue dummies in specifications 1 to 3 in Table 6 are.02,-1456, and-2.295 and the F-statistics for the before and after trends corresponding to specifications 1 to 3 in Table 7 are 20. 15, 6.67, and 13.99. Similar results were also obtained when the two years preceding a state's adoption of the law were deleted from the sample. The t-statistics for the shall issue dummies in specifications 1 to 3 in Table 6 are-2.732,-1.50, and.281; and the F statistics for the before and after trends corresponding to specifications 1 to 3 in Table7are20.96,7.92,and15.29 See the Tracy L. Snell, Prisoners executed under civil authority in the Statistics, May 14, 1997. For the nd jurisdiction, 1977-1995, Bureau of Justice United States, by year, region, source of penalties imposed for when a gun is used in a commission of a crime see Thomas B. Marvell and Carl E. Moody The Impact of Enhanced Priosn Terms for Felonies Committed with Guns, Criminology 33(May 1995): 247, 258-61
Chicago Law and Economics Working Paper 14 Table 8 adds other law variables that may influence the number of mass shootings. The law variables include the following: a dummy variable if a state has a waiting period before an individual can obtain a gun and the length of this period in days and dayssquared (see Lott and Mustard for a discussion of this variable); the probability of execution (equal to the number of executions per murder in a given year); and a dummy variable for whether a state imposes additional penalties for using a gun in the commission of a crime.21 Three conclusions emerge from Table 8. First, the statistically significant negative impact of shall issue laws on mass public shootings continues to hold. Second, the regression coefficients on the shall issues variables are of the same magnitude as in Table 7. Third, the other gun related law variables and the capital punishment variable have no significant impact on mass shootings. The point estimates on the waiting period variables sometimes imply that longer waiting periods increase the risk of mass public shootings and other times they imply the reverse. In no case is the waiting period variable statistically significant. Although the execution rate has a negative coefficient in the six regressions, it is never statistically significant. The execution variable itself may be only weakly related to the probability that a mass murderer will be executed given the Tables 6 and 7 after removing the observations for that year. All of the shall issue coefficients in the shooting regressions remained statistically significant, with the single exception of the injury rate in Table 6 which was negative but no longer statistically significant. For example, the t-statistics for the shall issue dummies in specifications 1 to 3 in Table 6 are -3.02, -1.456, and -2.295; and the F-statistics for the before and after trends corresponding to specifications 1 to 3 in Table 7 are 20.15, 6.67, and 13.99. Similar results were also obtained when the two years preceding a state’s adoption of the law were deleted from the sample. The t-statistics for the shall issue dummies in specifications 1 to 3 in Table 6 are -2.732, -1.50, and -2.281; and the Fstatistics for the before and after trends corresponding to specifications 1 to 3 in Table 7 are 20.96, 7.92, and 15.29. 21 See the Tracy L. Snell, Prisoners executed under civil authority in the United States, by year, region, and jurisdiction, 1977-1995, Bureau of Justice Statistics, May 14, 1997. For the source of penalties imposed for when a gun is used in a commission of a crime see Thomas B. Marvell and Carl E. Moody, The Impact of Enhanced Priosn Terms for Felonies Committed with Guns,” Criminology 33 (May 1995): 247, 258-61