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working paper, 1997.

5. A second change was also made. Because of the large number of observations noting no deaths or injuries from mass public shootings in a given year, I used a statistical technique known as Tobit that is particularly well suited to this situation.

6. The results shown below provide the estimates for the simple linear time trends before and after the adoption of the law. They demonstrate that for each year leading up to the passage of the law, total deaths or injuries from mass public shootings rose by 1.5 more per 10 million people and that after the passage of the law, total deaths or injuries fell by 4 more per 10 million people. The difference in these two trends is statistically significant at the 1 percent level for a two-tailed t-test. It is interesting to note that higher murder arrest rates, although they deter murderers, do not seem to deter perpetrators of mass public shootings.

Linear time trends for deaths and injuries from mass public shootings before and after adoption of concealed-handgun law

Total deaths and injuries per 100,000 population

Average annual change for years after adoption

of the law -0.04*

Average annual change for years before adoption

of the law 0.015*

Arrest rate for Murder —0.0003

*Statistically significant at least at the 10 percent level for a two-tailed t-test Note: numbers are negative; years furthest beyond adoption are the largest

7. See appendix 4 for the means and standard deviations of the variables used in these regressions.

8. Again, this is stating that a one-standard-deviation change in arrest rates explains more than 15 percent of a one-standard-deviation change in crime rates.

9. Running the regressions for all Pennsylvania counties (not just those with more than 200,000 people) produced similar signs for the coefficient for the change in concealed-handgun permits, though the coefficients were no longer statistically significant for violent crimes, rape, and aggravated assault. Alan Krug, who provided us with the Pennsylvania handgun-permit data, told us that one reason for the large increase in concealed-handgun permits in some rural counties was that people used the guns for

NOTES TOPAGES 106-117/285

hunting. He told us that the number of permits issued in these low-population, rural counties tended to increase most sharply in the fall around hunting season. If people were in fact getting large numbers of permits in low-population counties (which already have extremely low crime rates) for some reason other than crime, it would be more difficult to pick up the deterrent effect of concealed handguns on crime that was occurring in the larger counties.

10. A one-standard-deviation change in conviction rates explains 4 to 20 percent of a one-standard-deviation change in the corresponding crime rates.

11. I reran these regressions using the natural logs of the arrest and conviction rates, and I consistently found statistically larger and even economically more important effects for the arrest rates than for the conviction rates.

12. For example, see Dan M. Kahan, "What Do Alternative Sanctions Mean?" University of Chicago Law Review 63 (1996): 591-653.

13. See John R. Lott, Jr., "The Effect of Conviction on the Legitimate Income of Criminals," Economics Letters 34 (Dec. 1990): 381—85; John R. Lott, Jr., "An Attempt at Measuring the Total Monetary Penalty from Drug Convictions: The Importance of an Individual's Reputation," Journal of Legal Studies 21 (Jan. 1992): 159-87; John R. Lott, Jr., "Do We Punish High-Income Criminals Too Heavily?" Economic Inquiry 30 (Oct. 1992): 583-608.

14. Put differently, six of the specifications imply that a one-standard-deviation change in the number of concealed-handgun permits explains at least 8 percent of a one-standard-deviation change in the corresponding crime rates.

15. Philip Heymann, a former deputy attorney general in the Clinton administration and currently a law professor at Harvard University, wrote, "None of this [the drop in crime rates] is the result of... the Brady Act (for most guns were never bought by youth from licensed gun dealers)." See "The Limits of Federal Crime-Fighting," Washington Post, Jan. 5, 1997, p. C7.

16. For a discussion of externalities (both benefits and costs) from crime, see Kermit Daniel and John R. Lott, Jr., "Should Criminal Penalties Include Third-Party Avoidance Costs?" Journal of Legal Studies 24 (June 1995): 523-34.

17. Alix M. Freedman, "Tinier, Deadlier Pocket Pistols Are in Vogue," Wall Street Journal, Sept. 12, 1996, pp. Bl, B16.

18. One hundred and eighty-two million people lived in states without these laws in 1991, so the regressions would have also implied nine more accidental deaths from handguns in that year.

19. Given the very small number of accidental deaths from handguns in the United States, the rate of such deaths in the vast majority of counties is zero, and the last two columns of table 5.6 again use Tobit regressions to deal with this problem. Limitations in statistical packages, however, prevented me from being able to control for all the county dummies, and I opted to rerun these regressions with only state dummy variables.

20. For example, see Nicholas D. Kristof, "Guns: One Nation Bars, the Other Requires," New York Times, Mar. 10, 1996, sec. 4, p. 3. For some evidence on international gun ownership rates see Munday and Stevenson, Guns and Violence (1996): 30.

21. See Ian Ayres and Steven Levitt, "Measuring Positive Externalities from Unobserv-able Victim Precaution: An Empirical Analysis of Lojack," NBER working paper 5928 (1997); and John Donohue and Peter Siegelman, "Is the United States at the Optimal Rate of Crime?" Journal of Legal Studies 27 (Jan. 1998).

22. See notes 12 and 13 above.

CHAPTERSIX

1. Isaac Ehrlich, "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy

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