Do Gun Buybacks Save Lives? Evidence from Panel Data

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1 IZA DP No. 4995 Do Gun Buybacks Save Lives? Evidence from Panel Data Andrew Leigh Christine Neill June 2010 DISCUSSION PAPER SERIES Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor

2 Do Gun Buybacks Save Lives? Evidence from Panel Data Andrew Leigh Australian National University and IZA Christine Neill Wilfrid Laurier University Discussion Paper No. 4995 June 2010 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: [email protected] Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the inst itute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author.

3 IZA Discussion Paper No. 4995 June 2010 ABSTRACT * Evidence from Panel Data Do Gun Buybacks Save Lives? that reduced the stock of firearms by In 1997, Australia implemented a gun buyback program the number of firearms withdrawn, we around one-fifth. Using differences across states in test whether the reduction in firearms availa bility affected firearm homicide and suicide rates. We find that the buyback led to a drop in the firearm suicide rates of almost 80 per cent, with death rates. The estimated effect on firearm no statistically significant effect on non-firearm homicides is of similar magnitude, but is less precise. The results are robust to a variety of specification checks, and to instrumenting the state-level buyback rate. JEL Classification: I12, K14 Keywords: firearms ownership, homicide, suicide, panel data Corresponding author: Andrew Leigh Research School of Economics Australian National University Canberra ACT 0200 Australia E-mail: [email protected] * We are grateful to Juan Baron, Philip Cook, Jean Eid, Azim Essaji, Ana Ferrer, Francisco Gonzalez, Jens Ludwig, Alex Tabarrok, Justin Wolfers, editor John Donohue, an anonymous referee, and seminar participants at the Australian National Un iversity, the Research Institute of Industrial Economics, the University of Calgary, the University of California-Berkeley, the University of Melbourne, the University of Michigan, the University of Wisconsin-Madison, and the Association for Public Policy Analysis and Management 2008 Fall Conference for valuable advice and comments on this paper, and to Jenny Chesters, Susanne Schmidt and Elena Varganova for outstanding research assistance. All errors are ours.

4 1. Introduction Arthur, Tasmania, the Australian federal Following the 1996 massacre of 35 people in Port plement tough new gun control laws. Under government persuaded all states and territories to im ms legislation was tight ened and made more the National Firearms Agreement (NFA), firear consistent across all states and territories. As part of the NFA, it became illegal to hold particular no longer legal were subject to a types of firearms, in particular certain long guns. Guns that were government buyback, with owners being compensated for their newly illegal firearms at market 1 In terms of the absolute ralia’s gun buyback ranks as the numbers of guns destroyed, Aust prices. any country over the period 1991-2006 (Small Arms largest destruction of civilian firearms in Survey 2007, Table 2.10). Its eff ect was to reduce Australia’s fi rearms stock by around one-fifth, more than 650,000 firearms. In United States terms, this would be equivalent to a reduction in the firearms stock of 40 million firearms (Reuter and Mouzos 2003). Although so me of the firearms that were handed in came from households with mu ltiple firearms, survey evidence suggests that 2 the buyback reduced the share of Australian households with one or more firearms. Previous studies of gun buybacks have typically found that they have little effect on death et al. rates or violent crime (Rosenfeld, 1995; Callahan , 1994). Compared with these studies, an investigation of the Australian gun buyback has three major adva ntages. First, its scale is significantly larger than most other gun buybacks. In absolute numbers, five times as many guns were handed in under the 1997 Australian buyback as were bought back in the United Kingdom’s 1 We use the term ‘buyback’ here ed in Australia. The program , since that is the terminology us differed from what have been called buyback programs in the US, however, where buyback programs have typically not been accompanied by a ban on the firearms ‘bought back’. 2 We have been unable to locate reliable evidence on the share of Australi an households that owned a gun in 1996, immediately prior to the buyback. Th e best data appear to come from the International Crime Victim Surveys (ICVS), wh ich indicate that 15 percent of Australian ed with just 8 percent in 2000. households owned a firearm in 1992, compar 2

5 much-touted gun buyback in the same year. Since d eath rate data are typical ly quite variable, the able to be distingu effects of smaller scale buybacks are unlikely to be ished from random noise. plied across the nation meant that gun owners could not simply Second, the fact that the policy ap firearm, as can occur in the case of the more travel across jurisdictions to purchase a replacement limited buybacks typical in the United States. And thir d, the ability of an island nation to restrict illegal gun imports, coupled with the absence of any domestic gun manufacturers producing for the retail market, meant that legal restrictions on gun ownership were more likely to ‘bite’ in Australia 3 than would be the case in c ountries with porous land borders. Although researchers have studied the Australian firearms buyback, most of these studies have looked only at time series va riation. This approach suffers fr om the problem that the control group must be inferred from past time trends. If a time-specific shock affected homicide and suicide rates at the same point as the firearms buyback, it will be impossible for time series approaches to disentangle the policy ch ange from the shock. By contrast, our approach in this paper exploi ts variation both across states and over time. tes of firearm buyback The cross-state variation arises from different ra in different states. Specifically, we ask the question: did firearms death rates decrease more substantially in states where more guns were bought back? nd that the with drawal of 3500 To preview our results, we fi guns per 100,000 individuals reduced the firearm suic ide rate by close to 80 per cent, and had no statistically significant effect on non-firearm death rates. Estimat es of the effect on firearm homicides are less precise, but point estimates sugge st the firearm homicide rate also dropped by a substantial proportion. These results are robust to the incl usion of state-specific controls and time trends, to allowing for breaks in the state-specific time trends, to flexible modeling of the dynamic 3 Reuter and Mouzos (2003) raise this point, and provide an extensive discussion of the background as a preliminary evaluation of its effects. to and details of Australia’s NFA, as well 3

6 impact of the NFA, and to using instrumental variables techniques to allow for potential This paper therefore provides evidence that endogeneity in the state-level gun buyback rate. rates, and may also lowe r overall death by suicide reduced access to firearms lowers firearm death and homicide. The remainder of this paper is structured as follows. In Section 2, we briefly discuss the international evidence on firearm availability and violent deaths, as well as some of the estimating this relationship. Sec tion 3 outlines the institutional methodological issues involved in s national-level trends. details of the Australian firearms buyback, and show Section 4 presents our sults. The final section concludes. cross-state empirical strategy and re 2. Evidence on the e bility on violent deaths ffects of firearm availa 2.1 Firearm possession and deaths The relationship between firearms ownership rates and violent de ath rates is one of the most hotly-contested issues in the ec onomics of crime. From a theore gun control could tical standpoint, the particular circumstances (Marceau 1998). One either increase or reduce violence, depending on set of hypotheses suggests that the relationship should be positive: more guns in the hands of criminals increases the probability that an assault wi ll end in death, while the presence of guns in a home raises the chance that a suicide attempt will be successful. But another set of hypotheses suggests a negative relationship: more guns in th e hands of law-abiding citizens may have a 4 Cook and Ludwig deterrent effect, which might in turn re duce the overall incidence of violence. (2006) provide a comprehensive review of the empi rical literature regard ing the mechanisms by which firearm ownership ma y affect death rates. 4 Duggan (2001) cites various estimates on the numb er of US gun owners who successfully defend themselves from criminals each year: ranging from 75,000 to more than 1 million. 4

7 There are a number of studies that have found a positive re lationship between firearms ss countries or across regions within a country ownership and firearms deaths using variation acro (e.g. Killias 1993). However, it is possible that th is does not reflect a causal pattern (Duggan 2001). nomic factors in particular juri sdictions could explain both high Cultural, legislative, or socio-eco gun ownership rates and high firearm death rates. A more compelling empirical approach is to use panel data. Under this approach, any factors that differ across jurisdictions and remain fixed over time can be cont rolled for by including jurisdictional-specific fixed effects in a multiple regression model. Similarly, any time-varying factors that affect all jurisdictions in the same way can be controlled for using time-specific fixed effects. Again, such approaches have been used at the sub-national and cross-national levels. Miller et al. (2005) find that reductions in firearm owners hip rates across US st ates are associated with declines in firearm suicide rates. Across a panel of 13 countries, Ajdacic-Gross et al. (2006) estimate a random effects model, and similarly fi nd a negative relationshi p between the share of on of suicides committed with a gun. firearms-owning households and the proporti While these models can control for differences in death rates that are fixed geographically or in time, without a fuller causal model of death ra tes they cannot ac count for correlati ons that arise between firearm availability and death rates that are caused by a third factor. For instance, a drought may lead to both increased firearm purchases to deal with wildlife encroaching on farmland and higher suicide rates of farmers due to increased bankruptc y. Or an exogenous rise in drug trafficking could lead to increased purchases of firearms by worried householders and increased homicides due to gang-related conflict. Beyond this, many other socio-economic variables have nd it is quite plausible that these same factors also been found to affect suicide and homicide, a 5

8 5 might affect firearms purchases. vable to the econometrician. Such factors may be unobser t in the literature as to an appr opriate empirical model of either Moreover, there is little agreemen sure that all relevant socio-economic factors have homicide or suicide rates, making it difficult to be e effect of firearms av ailability on death rates been addressed, and therefore that estimates of th reflect a causal relationship. Further, it may be the case that places with both high firearm ownership and high firearm death rates have relatively low homicide and suic ide deaths by non-firearm methods. This suggests substitution between methods; in other words, firear ms are used in homicides and suicides in places with high firearm ownership rates simply because th e firearms are available. In the extreme case of complete method substitution, access to firearms has no impact on the number of violent deaths, merely the method by which those violent deaths occu r. From a policy standpoint, this is clearly an important question, yet pure cross-s ectional or time series methods are unable to separate out these effects. ccuracy of data on firearm availa Another concern is the a bility. Duggan ( 2001) notes that a lack of reliable data on gun ownership makes many of these studie s rather difficult to rely on. He shows are closely correlated with firearm uses subscriptions to gun magazines (which he ownership) as a proxy for firearm ownershi p. Cook and Ludwig (2006) and Bridges and e or accidental deaths th at are due to firearms Kunselman (2004) use the percentage of either suicid 5 Among the factors that have been found to affe ct suicide rates are New Deal spending (Fishback, Haines and Kantor 2007); the divorce rate (G ruber 2004); divorce laws (Stevenson and Wolfers 2006); the violent crime rate, and the Vietnam Wa r, and the share of the population aged 15-24 (Cebula and Zelenskaya 2006); business cycles (Varen 2004); alcohol us e (Carpenter 2004); unemployment rates and permanent income (Ham ermesh and Soss 1974); and urbanization rates (Neumayer 2003). Factors correlate d with homicide include inequa lity and poverty, percent of the population that is urban, resident in female headed households, or has recently moved (Cook and and average weekly earnings (Narayan and Ludwig 2006); and male youth unemployment rates Smyth 2004). 6

9 as a proxy for firearm availability. All three found that a m availability rate higher (estimated) firear was associated with higher firearm homicide rates. Finally, the results from such by the endogeneity of firearm studies may be contaminated ownership. For example, in juri sdictions with higher ra tes of violent crime, individuals may be more likely to own a firearm to protect themselves . In this case, firear ms ownership may merely reflect current crime rates or expect ations of future crime rates. In order to identify the causal effect of access to firearms on deaths, it is preferable to exploit some exogenous source of variation in firearms ownership rates. 2.2 Firearm regulation and deaths Perhaps one of the most promising avenues for identifying such exogenous changes in access to firearms is to examine the effects of cha nges to firearm legislation and regulations. Some caution is required in attributing changes in regulation to changes in access to firearms, since the degree of enforcement may be equally important. Inde ed, it is possible that stricter legislation may enforcement. Another issue is that legislative not in fact reduce firearm access in the absence of reforms often include a package of measures – whic h can make it difficult to separate, for example, regulations on ownership from rules gove rning the proper storage of firearms. There have been a very large number of studi es of tighter firearms legislation or other related policy changes on death ra tes. We cannot carry out a compre hensive review of the entire literature here. The majority of these, however , rely mostly on time series methods – including studies of the 1977 Canadian gun co ntrol legislation (Carrington 1999; Leenaars and Lester 1996) and of the 1994 US federal assa ult weapon ban (Koper and Roth 2001a; see also Kleck 2001; Koper and Roth 2001b). These studies tend to find some evidence of a decline in firearm related deaths gun control legislation. following the passage of tighter 7

10 Four existing papers study th e effects of Australia’s 1997 Na tional Firearms Agreement on et al. series approach to the Australian firearms deaths. Chapman (2006) take a purely time evidence of a decline in firearm suic question, arguing there is ides and perhaps in homicides after 1997. They also note that there were 13 mass s hootings in Australia during the period 1979-96, but none in the decade 1997-2006. Baker and McPhedra n (2006) also take a simple time series approach. Their empirical findings are similar to those of Chapman et al . (2006), although their interpretation of the results is markedly diffe rent. Lee and Suardi (2010) estimate an ARIMA model and attempt to find a struct ural break in the time-series pr ocess for firearm and non-firearm homicides and suicides at 1997, but find none. Ozanne-Smith et al. (2004) examine the effects of fir earms legislation in Australia on periods of policy change. The fi overall firearm deaths, using two rst was a tightening of firearms legislation in the state of Victoria, which occurred around 1988, preceding by almost a decade the tion that occurred in the rest more general tightening of legisla of Australia in 1997. Comparing rest of Australia, they find that such deaths fell more rapidly in firearm deaths in Victoria and the pidly in the rest of Australia from 1997-2000. Victoria during the period 1988-1995, and fell more ra They conclude that tighter gun controls led to a substantial reduction in firearm-related deaths overall, and in firearm suicides in particular. The results in that paper re ly on the assumption that the NFA had no effect on firearm availability in the state of Victoria, which is not consistent with the evidence that substantially more firearms were bought back in Victoria than in many other states. A problem with studies of nationa l gun control law changes that rely on time series variation is that it is impossible to distinguish between tw o factors, both of which may be important: (1) the l suicides or homici des; and (2) method effects of socio-economic or ot her policy changes on al 8

11 6 substitution. Unless it is possible to control for all conceivable time-varying shocks, it is not feasible to control for (1) and thus identify (2). tional variation in fire arms regulations. Since An alternative approach is to exploit sub-na this type have tended to use most countries regulate firearms at the national level, studies of has the advantage that crime statistics are more variation across jurisdictions within the US. This at sub-national restrictions can be circumvented by buyers who comparable, but the disadvantage th regulatory changes have been the introduction of are willing to travel interstate. The most studied sue laws, and restric tions on youth firearm laws allowing concealed carry permits, shall-is ownership. For example, Rosengart et al. tion of ‘shall-issue’ laws, (2007) found that the introduc implemented in 23 states over the 1980s and 1990s, led to an increase in the rate of firearm homicide of 1 per 100,000 individuals, after controlling for st ate-specific differences in death rates. There have also been studies of US firearm buybacks (Rosenfeld 1995; Callahan et al. 1994). These typically find the buybacks have little or no effect on death rates, but the programs evaluated are much more modest than the Australian NFA. Levitt (2004) includes changes in US gun cont rol laws over the 1990s as one of his six factors that do not explain declin es in crime over the same period. reasons why gun He notes three buybacks in particular would not be expected to be effective: (1) the guns surrendered are those least likely to be used in crimes because they are surrendered voluntarily; (2) replacement guns are easily obtained; and (3) the typical buyback is relativ ely small in scale. We describe the NFA in the next section, but to anticipate these arguments: we argue that none of thes e factors are relevant to the Australian buyback, since the NFA involved a large scale buyback of firearms, the buyback was compulsory in the sense that retaining possession of the firearms was illegal, and the guns could not be easily replaced with similar firearms. 6 the appendix to Neill and Leigh (2008). of this problem, see For a more technical discussion 9

12 3. Australian Firearms Regulation and Firearms Deaths 3.1 Trends in Australian suicides and homicides In the decade following the NFA, there has been a substantial drop in firearm deaths in Australia (Figures 1a and 1b). ed from 2.2 per 100,000 people in 1995 Firearm suicides have dropp to 0.8 per 100,000 in 2006. Firearm homicides ha ve dropped from 0.37 per 100,000 people in 1995 to 0.15 per 100,000 people in 2006. These are drops of 65 per cent and 59 per cent respectively, and among a population of 20 milli on individuals, represent a decline in the number of deaths by firearm suicide of about 300 and in the number of d eaths by firearm homicide of about 40 per year. At the same time, the non-firearm suicide rate has fallen by 27 per cen t, and the non-firearm 7 homicide rate by 59 per cent. It is also clear from Figure 1 that firearm d eaths have been falling on a consistent basis in 8 Firearm non-firearm deaths. recent decades, while a similar trend is not as clear in the case of deaths – both homicide and suicide – are current ly at exceptionally low levels by historical standards. The previous low in the rate of firearm suicide was in 1944, at 1.63 per 100,000. The vel since 1998. The fir firearm suicide rate has been below that le earm homicide rate is considerably more volatile, but for the years 2004 to 2007 has been recorded as at or below 0.15 per 9 100,000 on only one other occasion, in 1950. 100,000 people. It has dipped below 0.2 per 7 of death may be affected by changes to collection There are concerns that data on external causes methods in 2002 (AIHW 2009), leading in particular to a decline in deaths ca tegorised as self-harm (suicide) and an increase in deat hs that are identified as due to external causes of undetermined intent. 8 Note again that there may be some inconsistenc ies in the homicide (death by assault) statistics after 2002. The figures for 2004 and 2005 seem excepti onally low, and do not al ign with the justice statistics on homicides in those years. See Chapman et al. (2006). Recently released data from 2006 and 2007, however, do appear to be consis tent with the figures from 2004 and 2005. 9 Again, however, this may reflect an inconsistency in the data. 10

13 Non-firearm suicides, on the other hand, have remained relatively high compared to historical averages, desp ite declines in the earl y-2000s. The increase in non-firearm suicides from 1996 to 1998 is noteworthy, since some commentators (for instan ce, Baker and McPhedran, 2007) have pointed to this as possible evidence of substitution from guns to other methods of suicide following the gun buyback. Non-firearm homicide s have likewise remained relatively high compared to long-run historical averages, although they appear to have dropped sharply since 2004. 3.2 The National Firearms Agreement Following the April 1996 Port Arthur killings, the Australasian Police Ministers’ Council achieved agreement between fede ral and state governments to toughen and harmonize firearm laws across Australian states and territories. The key element of the Nati onal Firearms Agreement (NFA) was the ban of the sale, importation or posse ssion of particular type s of previously legal firearms – mostly automatic and semi-automatic long arms. A buyback scheme was implemented re of any newly illegal weapons. Reuter and to compensate owners for the compulsory forfeitu Mouzos (2003) state that the agreement “effectively introduced uniform licensing and regi stration of firearms in all eight states and territories of Australia, replacing a pa tchwork that included regimes of varying stringency. Moreover, certain classes of w eapons (self-loading ri fles, self-loading and pump-action shotguns) were prohibited, as was the importation of these weapons. To encourage compliance with the new prohibiti ons, the federal government financed a large-scale gun buyback program, conducted by the states. The buyback initially covered only newly prohibited weapons, prim arily long arms; later it was extended to include nonconventional weapons, such as submachine guns and heavy machine guns. 11

14 There was also an amnesty for handing in un licensed firearms during that same period, 10 but no payments were made for these weapons” (p. 129). rt committee, based on th e retail price of the Prices were centrally determined by an expe firearm, and did not vary across states. Altoge ther, almost 650,000 prohibited firearms were bought back during the initial amnesty. Substantial nu mbers of non-prohibited but unlicensed firearms 11 Although it is difficult to be certain, du e to the unreliability of survey data were also handed in. this most likely consti tuted a withdrawal of on gun ownership, Reuter and Mouzos (2003) state that of firearms from the community. around 20 per cent of the total stock firearms could have been quickly reversed in It is extremely unlikely that this withdrawal of rearms manufacturers, so that a ll firearms must be imported into Australia. There are no domestic fi Service show that in the three years prior to the country. Records from the Australian Customs 1996, Australian firearms imports averaged around 50,000 per year, of which about 25,000 were age imports fell to about 30,000 per year, of which 10,000 were rifles. After the buyback, aver rifles. Thus, if anything, there appears to ha ve been a slowdown in im ports after 1997. Although it appears that law enforcement the available data are incomplete, agencies were responsible for a es. For example, one source indica tes that more than one quarter large percentage of overall purchas e period 1999-2002 were by law enforcement. Even if we made the of all handguns purchases in th extreme assumption that all imported firearms were added to the civilian firearm stock and no firearms were ever destroyed, at current impor t levels of 30,000 per year it would take around 20 years for the civilian firearm stoc k to recover to pre-buyback levels . Publicly ava ilable data on 10 The distinguishing feature of self-loading and pump-action weapons is that they do not require the user to insert fresh ammuniti on after each pull of the trigger. 11 For NSW, Australia’s most populous state, Reuter and Mouzos (2003) were able to obtain data re handed in. In that state, 37,000 non-prohibited on the number of non-prohibited firearms that we firearms were handed in, for no compensation. That figure was 24 per cent of the 156,000 prohibited firearms handed in to NSW authorities. 12

15 imports by state suggests there may have been a slight negative relationship between subsequent – that is, states with a high buyback rate also imports of firearms per capita and the buyback rate This relationship is not , however, statistically saw somewhat lower growth in firearm imports. significant, and we do not have information that allo ws us to separate out civilian purchases from law enforcement and military purchas re that this reflects primarily civilian es, so we cannot be su purchases. Although the NFA buyback targeted firearms that were of the type that had been commonly used in crimes, an important feature of the buyback is that very few of th e firearms handed in to police were military-style automatic-fire weapons. For the state of Victoria (the only jurisdiction to provide a breakdown of the types of guns handed in), Reuter and Mouzos (2003) report that nearly half of the guns were .22 caliber rifles, and almost all the remainder were shotguns. Less than one in 1000 of the weapons handed back in Victoria was an automatic. Further, given the very strict Australian legislation restrict ing access to hand guns, there was limited opportunity to substitute other automatic or semi-automatic firearms. away from newly prohibited firearms towards National statistics on firearms deaths separate deaths caused by handguns from those caused 12 by long guns. This is useful because the NFA applied primarily to long guns. Prior to the 1997 law change, handguns accounted for 4 per cent of all firearm suicides and 8 per cent of all firearm the figures increased to 11 per homicides (Table 1). Afterwards, t respectively, cent and 21 per cen 13 largely because of a decline in d eaths attributable to long guns. Overall, 71 per cent of suicides were with identified long guns, and the same was true of 53 per cent of homicides. Of course, not 12 We were unable to obtain a brea kdown of firearms deaths by stat e by firearm type (which might otherwise have allowed us to estimate a triple-difference model). 13 Note that a tightening of handgun regulations wa s implemented in 2002. In general, this is thought to have been relatively ineffective compar ed with the 1997 NFA. However, the data do suggest that after the 2002 law change, handgun homicides and su icides dropped more than did using other firearms. homicides and suicides 13

16 all of the long guns used in these homicides and suicides would have been subject to the buyback, among the type of firearm most affected by the but the fact that the drop in deaths was larger buyback provides suggestive evidence that the NFA played a role in the fall in firearm deaths. s remove mostly low risk guns (because only an individual The oft-heard claim that buyback who was not planning to use a fi rearm would hand it in) is typi cally based on US-style buybacks which are entirely voluntary. It is more an argu ment about the characteris tics of the owner than about the characteristics of the firearm. Such c oncerns have less force in the case of Australia’s program, which was accompanied by a ban, than in the US cases. In genera l, however, one might hypothesize effects in either directio n. For example, if firearms owners were more likely to hand in a firearm if they had a depressed teenager in the house, the guns handed back might reasonably be described as ‘high risk’. Conversely, if an ow ner’s probability of handing back a firearm is negatively correlated with his or her predispositi on towards violence, the guns handed back might reasonably be describe d as ‘low risk’. eted at firearms that police and the Because the Australian buyback was both targ government considered high risk, an d that had been relatively unre gulated previously, and because ban and other tightening of fir earm regulations, we do not think the buyback was accompanied by a it is reasonable to describe the program as ha ving removed primarily low risk weapons from the Australian community. This distinguishes it from programs in the US, where such a judgment appears more reasonable. We have focused here on the buyback elements of the NFA. However, there were other elements of the NFA that may have led to a strong er tightening of firearm ownership legislation and enforcement in some states than in othe rs. The most important of these were: ould be established (previously, only Victoria • that a national register of all firearms w required registration of long guns); 14

17 • valid reason for owning a firearm in order for that there would be a requirement to give a an individual to be licensed (personal s ecurity was specifically excluded as a valid reason); that a permit would be required to purchas e a firearm, with a required 28 day waiting • period; and 14 the introduction of storag e and safety standards. • To the extent, that states that had initially tes did so because of high firearm ownership ra weaker legislation surrounding, say, sale or licensing, the NFA may have had two effects: first, to reduce the number of firearms held per capita, and second to impose more stringent legislation. There is evidence that states with higher initial rates of gun ownership (i ncluding Tasmania and Queensland) had fewer legislative re strictions related to firearm owne rship than other states (Reuter and Mouzos 2003). It is important to keep this possibility in mind when interpreting the results in this paper. Insofar as a higher buyback rate is associated with greater stringency in the overall need to be interpreted as the effect of the regulatory and enforcement environment, our estimates entire NFA policy package. In summary, the NFA led to consistent le lian states, required gislation across Austra licensing of gun owners and regist ration of guns, and significantl y tightened rest rictions on the types of firearms that could be legally held. In focusing on long guns, the legislation covered the group of firearms that had been most commonly used in firearm suicides and homicides, and in particular outlawed firearms of the type that had been used in recent mass shootings in Australia. Internationally, the gun buyback associ ated with the Australian NFA was the largest of its kind in 14 A more complete description of the legal change s associated with the NF A is provided by several sources, including Reuter and Mouzos (2003). 15

18 recent decades, withdrawing one fifth of the st ock of firearms from the community and likely ds possessing a firearm. reducing the number of househol 4. Empirical Strategy and Results 4.1 Identification issues et al. While the time series evid ence suggests that the NFA reduced gun deaths (Chapman 2004), it suffers from the lack of a credible control group, or of a fully et al. 2006; Ozanne-Smith and homicide. An alternative to developing a full specified model of the determinants of suicide to use panel techniques, relying on variation in the intensity of the predictive model of death rates is law changes associated with the NFA at the sub-national level. Due to administrative limitations, the finest ge ographic level for which we are able to obtain 15 Australia has six states and two territories. Data on the buyback data is the state and territory. number of firearms bought back in each jurisd iction were provided to the federal Attorney- General’s department by each of these jurisdicti ons, and are tabulated in Reuter and Mouzos (2003). These data are set out in Table 2, which de mber of guns withdrawn monstrates that the nu per 100,000 state residents differed substantially acro ss Australian states and territories, ranging from a low of 1698 in the Australian Capita l Territory to a high of 7302 in Tasmania. In this paper, we ask whether firearm deaths dropped proportionately more in states where relatively more firearms were bought back. If the gun buyback itself was effective in reducing firearms-related deaths, then this re firearms were removed from would imply that states where mo the population should have seen a greater reduction in firearm d eath rates than the Australian 15 We inquired to see whether it was possible to obtain buyback statistics for smaller geographic statistics on the buyb units, but the Attorney -General’s Department (which collated ack) advises that such data do not exist in any systematic form. 16

19 average. Because we are comparing across states, we are able to account for time-specific shocks 16 impossible using a simple time series approach. affecting all of Australia, something that is This ‘differences-in-differences’ approach re lates changes in death rates to changes in buyback rates). It assumes that all Australian states’ gun ownership rates (caused by different gun ange in death rates if they had experienced the states and territories would have had the same ch same change in firearms ownership. If states w ith higher initial firearm ownership rates also had weaker firearm legislation or enforcement, and if the NFA led to a reduction in the relative weakness of the legislation and/or its enforcement, then any estimated effect cannot be interpreted purely as the impact of the buyback. Rather, it w e removal of firearms, ill be the result of both th and the tightening of firearms legislation and enforcement. A second assumption in using this identification strategy is that the buyback ra te in each 17 state was exogenous, in the se nse that it was not the result of pr e-existing trends at the state level. l or state-level trend We do, however, show that allowing for a nationa break beginning in 1988 – the time at which the decline in firearm homicide s and suicides appears to have begun – does not at to the extent that there is a e-existing trends affect our qualitative results, and th ny evidence that pr may bias our results, it would tend to bias our results towards the buyback having a larger impact on firearms deaths. that firearms are transported across state Implicitly, our strategy also ignores the possibility boundaries prior to being handed in. Given that the compensation regimes were similar across 16 This approach is similar to that taken by Ludw ig and Cook (2000), in evaluating the effects of the Brady Handgun Violence Prevention Act, which requi red all states to implement a system of background checks and waiting periods for the purchas e of handguns from licensed dealers. They ask whether death rates fell more in states that did not already meet the new federal requirements than in states that already had at least as stringent a system of checks in place, and find little evidence that death rates fell as a result of the Brady Act. 17 National-level time trends are controlled by year fi xed effects. We also include state-level linear check in all specifications. time trends as a robustness 17

20 nt that firearms were Australia, we believe this is unlikely. To the exte moved from one state to another, this will likely bias our estimates towards zero. For the purposes of our empirical strategy, what matters is that differences in buyback rates deaths. In particular, we are were not correlated with other fact ors that might have affected gun concerned about two potential conf ounders. First, if differences in re driven by buyback rates we pre-existing gun ownership rates, and if the relationship between gun ownership and gun deaths is urious correlation. However, al non-linear, this could lead to a sp though a non-linear relationship is theoretically plausible, we ha udies supporting such a theory. ve been unable to locate any st ssumption that the stat e-level gun buyback rate Second, our empirical strategy relies on the a is thus important to c onsider the various factors is exogenous with respect to firearms death rates. It that might explain why the buyback rate varied across states. By definition, the overall buyback rate is equal to the rate of ownership of the ne wly illegal firearms multiplied by the compliance rate. To the extent that differences are driven by initial differences in firearm ownership rates, the withdrawal of firearms can be c onsidered plausibly exogenous – dr l social norms, iven by the initia ws in each state. To test this, we estimated the relationship between industrial composition, and la nership rates in 1997 and the gun buyba ck rate. The first proxy is two proxies of state-level gun ow data on ownership rates of al l types of guns taken from th e 1989 and 1992 International Crime Victim Surveys (ICVS). Since the sa mple size at a state level is qui te small, we pool data from both waves. This is likely to be a good proxy for gun ownership when the buyback commenced, so long tially across states in the period 1989-97. The as gun ownership rates did not change differen second proxy, following Cook and Ludwig (2006), is th e percentage of suicid es in which a firearm 2 statistics, the correlations are was used. Results are shown in Ta ble 3. As can be seen from the R very high. Over 60 per cent of the state leve l variation can be accounted for by each proxy is significant at around the 1 per cent level. When both proxies individually, and the relationship 18

21 are included in the regression, the high degree of correlation between the 1989-1992 gun ownership arms leads to each indi rate and the percentage of suicides using fire vidual relationship being insignificant, but the combined effect of the two is statistically significant at the 5 per cent level. ntial proportion of the va These results strongly suggest that a very substa riation in the gun buyback rate was simply due to differen ces in prior gun ownership rates. Differences in compliance rates are nonetheless likely to play some role. Combining data from several sources, Reuter a nd Mouzos (2003) estimat e that compliance was about 50 per cent in Queensland and New South Wales, 70 (the only state that previously required per cent in Victoria firearms to be registered) and 90 per cent in Tasmania. Due to the paucity of data on firearm ownership rates prior to 1997, howev er, these estimates are imprecise. Differences in compliance rates would not be a concern if they were driven by factors unrelated to changes in death rates, or if they were driven by factors that are controlled in our regression. For instance, farmers were more likely to be granted a license for a firearm than urban residents, so that the less urban states would Since we include both stat e fixed effects and the be expected to have had lower buyback rates. percentage of the populati any such correlatio n will not bias on in urban areas as controls, however, estimates of the effect of the buyback rate on death rates. However, if the compliance rate was in part determined by factors that may also have driv en differences in death rates across states, this could bias our estimates. d back varied according to the impact of the It is also possible that the number of guns hande Port Arthur massacre on each state. The most dire ct way in which states were affected by the massacre was if a significant number of their reside nts were killed. If a large number of state residents were victims of the massacre, this mi ght have led the state’s media to devote more coverage to the massacre, and slanted public deba te in the state in favor of the buyback. To the extent that states with more victims had higher rates of compliance with the buyback, this can be 19

22 regarded as a valid source of variation (in the sens e that it would only affect firearms deaths through so the case that a higher number of victims had a its effect on the buyback). However, if it is al direct effect on the propensity of residents in that st ate to use a firearm for homicide or suicide, this it might affect firearms deaths directly). From the perspective would not be a valid variation (since of our empirical strategy, we woul d be concerned if exposure to the Port Arthur massacre affected social norms about gun use in a state, but not if it affected a stat e’s gun buyback rate. The data do indeed show that states with gr eater exposure to the Port Arthur massacre had higher buyback rates (Table 2). We observe a co rrelation between the numbe r of massacre victims and the number of guns handed back per 100,000 reside nts of 0.5. However, this relationship is not robust to also including the gun ow nership rate in the regression. Wh en we regress the buyback rate on both the previous gun ownership rate and the numb er of massacre victims, the former is positive and statistically significant, while the latter becomes insignificant, though the coefficient remains positive. As we have noted, this would be a valid s ource of variation, but it appears that relatively little of the cross-state variation in buyback rates was actually driven by st ates’ ‘exposure’ to the Port Arthur massacre. We have been unable to find a ppropriate attitudinal data that would allow us to test the social norms about gun use. However, two things impact of the Port Arthur massacre on a state’s can be noted about this. First, to the extent that the Port Arthur massacre affected social norms about gun use in a state, we believ e that it is more li kely to have affected gun homicides than gun suicides (since the event itself was a mass homici de). And second, such an impact would likely have ‘faded out’ within a few y ears after the massacre. In our em pirical results, we test this by separately looking at the effects of the buyback on firearm deaths in the short-run and medium-run. Another possibility is that some people kept their firearms in order to defend themselves ndividuals were able to correctly predict trends in against the threat of violence in the future. If i 20

23 future crime rates (including homicide), this c ould lead to a negative correlation between the are of the population) in crime rates. To number of guns handed back (as a sh and the future change address this, we use the same information that such a 'rational home defender' would have had - 18 namely the past trend in crime rates. If this defensive gun-us e hypothesis is valid, we would expect to see our results disappear when we control for state-specific time trends. Finally, it is possible that buyback rates varied across stat es due to differences in enforcement of the new legislation across states. Fo r instance, the state police forces may have been more active in encouraging firearm owners to hand in their newly illegal weapons in some states than in others. However, it seems improbable that this type of variati on would be related to expectations of future changes in death rates. Indeed, to the exte nt that any relationship existed, state authorities who anticipated a rise in gun deaths would probabl y have enforced the legislation more strictly. This would bias the results toward s finding that a higher buyback rate led to higher death rates. 4.2 Main Results ber of guns (per 100,000 We begin by plotting the change in the num people) against the change in homicide and the change in suicide, in each case comparing the period 1990-95 with the period 1998-2003. Note that this comparison drops 1996 (the year in which the Port Arthur massacre took place), as well as 1997 (the year during which the buyback occurred). It also omits the most recent years in which fi rearm death rates have been very low. Figure 2 shows graphically the results from this exercise . For both gun homicide and gun suic ide, we observe a negative relationship between the death rate and the buyback rate. A similar relationship is not visible in the case of non-firearm deaths. 18 The assumption that the general public forecasts future crime rates by using past trends seems reasonable to us, though we know of no empirical evid ence on this point. In the US context, Levitt through linear projection. ict future crime rates (2004) shows that even experts appear to pred 21

24 More formally, these results can be shown in the stripped-down regression model: D ∆ = α + β ∆ (1) + ε G s s s where s indexes states, ∆ D is the change in the gun death rate, ∆ G is the change in the gun ownership rate and is an IID error term. Econometrically, this differenced specification is similar ε 19 to a model with state and year fixed effects. The results are shown in Table 4. The effect of the buyback on firearm suicides is clear. Withdrawing 3,500 guns per 100,000 individuals (approxim ately the rate of withdrawal due to the NFA) is estimated to reduce the firearm suicid es by 1.9 per 100,000. This represents a 74 per cent decline from the 1990-95 average of 2.55, or 376 fewe r deaths per year given Australia’s population t confidence interval on the fire of around 20 million. The 95 per cen arm suicide rate ranges from -0.8 deaths per 100,000 (a 33 per cent fall compar ed with the 1990-95 averag e death rate) to -2.9 larger than the average firear deaths per 100,000, a figure that is m suicide rate during 1990-95. The point estimate on firearm homicides is negative a nd large relative to the actual rate of firearm homicides – implying a decrease in firearm homicides of 36 per cent. The results on firearm homicide and suicide highlight a difficulty with th is estimation method. The variability in the data means that the confidence intervals built around estim ates based on the level of the death rate often 20 extend so far that they could not exclude a drop in death rates greater than the initial death rate. We deal with this concern later in th e paper by using a Tobit model (Section 4.1.4). The point estimates for non-fi are smaller in magnitude rearm suicides and homicides relative to their associated death rates, and have larger standard errors. They are also smaller 19 This model is one of the two recommended by Bertrand, Duflo and Mullainathan (2004) to deal with serial correlation in a differe nces-in-differences model. The other key method they suggest is to use a full panel model, but to cluster the standa rd errors at the jurisdictional level to allow for unspecified forms of serial correlation, which we estimate as equation (2). 20 nd 6 degrees of freedom. s only 8 observations a This is not surprising given that the model ha 22

25 relative to the pre-existing death rates. Because there are so ma ny more non-firearm suicides (and homicides) than firearm deaths, we cannot reject the possibility that there was 100 per cent method substitution – i.e. that any reductio n in firearm deaths was accompanied by an increase in deaths by other methods. This is unfortunate t is the inevitable result of the from a statistical perspective, bu fortunate fact that Australia already had relatively few firearm deaths relative to non-firearm deaths. 1.2 – suggests that the time path of non-firearms However our panel specification – in Section 4. per cent method subs titution occurred. deaths makes it improbable that 100 While the differenced specification is one approach for dealing with differences-in- differences models with serial co rrelation, it does have some importa nt disadvantages. In particular, it does not provide a natural way for dealing with th e possibility that pre-existing trends in firearm deaths were correlated with gun buyback rates. Nor does it allow us to examine the dynamics of the process, or to introduce other socio-economic variable s that vary at the state-year level. For these reasons we also consider the model in a levels sp ecification – that is, we use a dataset containing annual data on death rates from each state from 1968 to 2006, so that the total number of observations is now 8 stat es/territories by 39 years = 312. In this case, the policy change variable (guns bought back) takes a zero value for all y ears prior to 1996, and for 1997 and later takes a constant value for each state equal to the buyback rate for that state. This variable can be considered in the same light as a typical pol icy change variable in a differences-in-differences study except that the state-level variation comes not from differences in the timing of the po licy change, but rather from differences in its magnitude. Although our main specification includes 1996 and 1997, we show below that most results are robust to droppi ng the victims of the Port Arthur massacre and/or 1997 firearms deaths. The regression here, then, is: (2) + μ τ + Y = α + β ∆ G σ post97 + S D s st t s t st 23

26 where ∆ G is a full per 100,000 population in the state, S is the number of guns bought back post97 s t s is a full set of year fixed effects, and μ is an IID error term. We include set of state fixed effects, Y t a vector of socio-economic vari ables in some specifications, in cluding the unemployment rate, the urban area, the proportion aged 20-24, and the share percentage of the population that is living in an 21 hough not the unemployment rate) is reliably Unfortunately, much of this data (alt aged over 65. available only for Census years – we use a simple linear interpolation to estimate data between years where necessary. All standard errors are clus tered at the state level. Note that there are andard errors in a model with only 8 clusters. Bertrand, Duflo disadvantages to using clustered st power of such tests to correctly reject the null and Mullainathan (2004) note in particular the weak when there is in fact a true effect. In the pres ence of substantial serial correlation and few clusters, it is also likely that actual rejection rates will rema in higher than the asymptotic level of the test. (In simulations with Current Popul ation Survey data, Bertrand, Dufl o and Mullainathan look at how r cent level. With 50 states, they observe a 6 per often a clustered model rejects the null at the 5 pe observe an 8 per cent rejection rate.) cent rejection rate, and with 10 states, they Table 5 shows the results of these regressions. For each of the six key outcome variables, porate state and year fixed effects. The second four regressions are shown. All regressions incor d adds in the socio-econo mic variables, and the column adds state-specific time trends, the thir fourth includes both of these. The results are fairly consistent across these specifications, and in line with the results in Table 4. Intr oducing the socio-economic variab les has little effect on the 21 We also examined models including controls fo r the prisoners and police per capita in any given state/year. There is an extensiv e literature regarding concerns on inference in reduced form models that include these types of variab les, due to likely endogeneity (e.g. Levitt 2004). We also included controls for the number of men aged 15-19 and 20-24. Including these controls did not change our main estimates, but did reduce the number of st ate-year combinations we could include in our regressions, due to missing observati ons in some cases. Including in formation on the percentage of had little effect on our main the population that is indigenous also estimates, but reliable data was only available after 1991 (see Appendix Table 1). 24

27 magnitude of the coefficients for firearm suicide or homicide, and typically they are not either the regressions. This may reflect the fact that individually or jointly statistically significant in ed with our reliance on interpolations, making demographics change quite slowly over time, combin it difficult to separate them out from the Australia -wide year fixed effects. We would not want to conclude from this that socio-economic factors do not affect homicide or suicide rates, since our of the effects of these factor s in either the state or year empirical strategy likely soaks up much fixed effects. The estimates show very consistently a marked relative decline in firearm suicides in states with higher buyback rates af ter 1997. The point estimates are sli ghtly smaller than those in Table 4, and suggest that a buyback of 3500 guns per 100,000 individuals (the size of the 1997 buyback) in one state would reduce firearm suicide rates by between 1.1 and 2.0 deaths per 100,000 relative to a state with no reduction in firearms; that is betw een 45 per cent and 78 per cent compared with the average firearm suicide rate in 1990-1995 of 2.5 5 per 100,000. The 95 per cent confidence interval in all specifications suggests a minimum decline in firearm suicides of 18 per cent compared with the average firearm suicide rate in 1990-1995. The estimates on firearm homicides are less c onsistent, likely because of the greater volatility in firearm homicides. Most of the point estimates suggest that a buyback of 3500 guns per 100,000 individuals would reduce d eath rates to below zero, beginning from a baseline equal to the average firearm homici This is in part due to the inclusion of de rate between 1990 and 1995. the deaths from the Port Arthur in cident in 1996 in the model. We show in Section 4.1.3 that if we introduce a dummy variable equal to 1 in Tasmania in 1996 and zero elsewh ere that the estimated coefficients fall to more closely resemble the result in Table 4. Once again, the estimates show no evidence that higher buyback rates were associated with any statistically significant difference in non-firearm homicide or suicide rates. Point estimates on 25

28 non-firearm suicide rates are larger than those in Table 4, largely due to the inclusion of years after 2003 in the analysis (see Section 4.1.2). 4.1 Robustness checks 4.1.1 Controlling for state-specific trends in death rates nds appears to increase the magnitude of the The introduction of state-specific time tre 22 estimated effects of the gun buyback on firearm death rates. This suggests that guns were actually returned at a lower rate in states where firearm d eaths had been falling more rapidly. We check this arm buyback rate and trends in death rates prior result by estimating the correlation between the fire icide rates had been increasing faster in states to 1997 (Table 6). The results show that firearm su ior to 1995, but that th e buyback rate had no effect on the growth with high firearm buyback rates pr is is not consistent with the notion that different compliance rates rates of other types of deaths. Th were the result of either a self-defense motivation or a desire to retain firearms in order to carry out If anything, more guns were handed back in already established suicide plans. states where firearm suicides and homicides had been falling at a slower rate. Table 7 shows the effect of including a state- specific linear year trend and allowing for a break in that trend in 1988, around the time when fir earm suicide and homicide rates appear to have begun to decline nationwide. Consis tent with the evidence in Table 6, this does li ttle to change the qualitative results. Indeed, if anything, the relationship between th e buyback rate and firearm death rates becomes stronger, particular cides. Similar results obtain if ly in the case of firearm homi instead of allowing for a break in trend in 1988, the model is estimated on data from 1988 onwards (see Appendix Table 3). These results are not sens itive to moving the year in which the trend break is estimated to occur forward or backward by severa l years. The results reported here are clearly, 22 r a linear trend, but models All results here allow fo with quadratic trends yield similar results (see Appendix Table 2). 26

29 then, not an artifact of the decline in deaths evident in the national level data beginning in the late 1980s. e impact of the policy change 4.1.2 Allowing for dynamics in th While it has become common to include state-specific time trends to account for the possibility of either serial co policy quasi-experiment studies, rrelation or policy endogeneity in Wolfers (2006) argues that this may lead to biased estimates of the policy ch ange in the event that there are important dynamics in the influence of a policy on outcomes. In this case, we might expect that the effects of the differences in gun buyback rates across states might fade out over time as cross-state movements or subsequent firearm purchases mitigated the initial effects of the buyback. In that case, the estimates in Table 5 would underestimate the short-run impact of the buyback on cross-state differences in death rates, and overstate the long-run impact. Table 8 shows that this does not appear to be the case. Here, the gun buyback variable has b een interacted with a dummy variable for each of three post-pol icy change year groupings (1997-1999, 2000-2002 and 2003-2006). In neither the case of firearm homicides nor firearm suicides is it possible to reject that equal across the three time periods. the effect of the firearm buyback is There do appear to be some interesting dynamics in the case of non-firearm suicides, however. The results sugge buybacks initially expe rienced a slight st that states with larger firearm relative decline in non-firearm suicides, but then saw a large increase in non-firearm suicides in 2002-2006. Note that the bump-up in non-firearm suicid es seen in the time series data (Figure 1a) in the 1996-1998 period is not easily attributable to her factors associated method substitution or ot with firearm withdrawals or other ch anges in firearm legislation that varied at the state level, since in that case we would expect to see states that had larger falls in firearm suicide also experience increases in non-firearm suicide. There is no empiri cal support for that in the data. The very late increase in non-firearm suicides in states with higher buyback rates is somewhat of a mystery. The 27

30 magnitude of the later increase is two to five times the magnitude of the relative reduction in firearm suicides in the same period. Taken at f ace value as an indicator of method substitution, it tituting to other methods six years after the gun would suggest that individuals only began subs buyback, and that the rate of subst It seems unlikely that this itution was greater than 100 per cent. is consistent with any reasonable model of method s ubstitution. It is possibl e that this reflects a change in the collection of suicide data post 2002 – that possi bility is explored in Section 4.1.5. 4.1.3 Examining sensitivity to the Port Arthur incident hs from Tasmania’s Port Arthur massacre Two other important checks are excluding the deat from the analysis, and consider ing the possibility th at the buyback had no effects on death rates until 1998. We do the first simply by including a dummy variable for Tasmania in 1996, and the second by dropping the year 1997 from the analysis. The results are shown in Table 9. As expected, including a dummy variable for Port Arthur only affects the magnitude of the estimates of firearm homicides. The point estimate falls by ju st under 40 per cent in the model with no state- specific time trends, but by considerably more in th e model including those tr ends. It appears that may particularly influence estimates of policy models incorporating state-specific time trends effects if either the initial or the final observations are unusually high or low. The inclusion of the standard errors of the estimate d effect of the buyback on firearm Port Arthur dummy increases the homicides enough that the estimated effect is now not statistically significantly different from zero, consistent with the ‘stripped down’ model. The point estimate on firearm homicides in the model with no trends remains large relative to actual de ath rates, however – it suggests that the buyback of 3500 guns per 100,000 individuals would lead to a decline in firear m homicide death rates of 0.22 per 100,000, or about 50 per cent of the 1990-95 aver age firearm homicide death rate. Excluding 1997 from the analysis has no importan t effect on the results. This is consiste nt with the finding that there are few dynamics in the effects of the buyback on death rates – firearm death rates appear 28

31 to have fallen to a permanently lower level in relative terms around 1997 in states which had a relatively high buyback rate. 4.1.4 Ensuring that estimated deat h rates post 1997 remain above zero The use of the simple levels specification has some drawbacks – in actuality death rates are the levels specificati on allows for a non-zero pr bounded at zero, and the use of obability to attach to negative death rates. That said, the only o ccasions on which there are negative in-sample predictions of death rates from th ese models are in several states ’ firearm homicide rates in the years 2004 and 2005, which have already been noted to have abnormally low firearm homicide (and 23 overall homicide) rates. Nonetheless, it is desirable to estimate a model that did not allow this at all. Use of the log specificati on is not possible here because of the large number of observations where zero homicide deaths are re corded (both firearm a nd non-firearm). An alternative is to use the Tobit model, which allows for the fact th at firearms deaths have a lower bound at zero. 24 The results indicate that the point estimates Estimates are shown for the homicides in Table 10. are robust to accounting for censoring at zero. 4.1.5 Allowing for possible endogeneity of buyback rates Above, we discuss a number of potential ways in which the number of guns bought back in 25 While we regard each a state might be endogenous with respect to the future firearms death rate. nonetheless to see whether our re instrumenting of these as unlikely, it is useful sults are robust to e possibility that the gun buyback rate may itself have varied the state buyback rate. Allowing th 23 This is largely due to the use of year fixed effects in the mode ls; because of these year fixed effects, it is not possible to ma ke out-of-sample predictions of death rates for Australia overall. 24 in every state that cens oring is not a problem. There is typically a sufficient number of suicides As a result, Tobit estimates of the effect of the gun buyback on suicides are, like those for homicides, very similar to OLS estimates. 25 These include the possibility th at a state’s residents are able to forecast non-linear trends in firearms death rates, and these forecasts affected their propensity to hand back their firearms under the NFA; or that the buyback rate in a state was affected by its exposure to the Port Arthur massacre, and the exposure also had a direct impact on subsequent firearms death rates. 29

32 with expectations of future changes in the state- level violent crime rate, we estimate instrumental eed an appropriate instrument – a ffects the buyback variable models. To do this, we n variable that a firearms death rates after 1997 rate but is not correlated with except through its impact on the buyback rate. We use cross-state differences in fi rearms ownership in the pre-buyback period as an instrument for the change in firearms ownershi p that occurred as a result of the buyback. This approach is akin to the use of existing immigrant stocks as an instrument for new immigrant inflows (see, eg. Okkerse 2008). In such specifications, res earchers exploit the fact that new immigrants tend to settle in places with large existing migrant stocks. This provides a means of identifying the exogenous ‘supply-push’ effect of immigration on native wages. Sim ilarly, we use the fact that some states have larger number s of firearms in the pre-buyback period as a means of identifying differences in buyback rates after the NFA came into effect. We use our two proxies of gun ownership rates prior to 1997 as instruments. The percentage of all suicides that use firearms is not , however, a valid instrument for models of suicide error term in the base regression – a positive shock rates, since it will clearly be correlated with the to firearm suicides will clearly increase the propor tion of suicides committed with a firearm. For e estimated rate of gun ownership prior to 1996, firearm suicides, our instrument set is therefore th estimated from the 1989 and 1992 ICVS surveys. For firearm homicides, we add the percentage of suicides that were completed us ing a firearm over the period 1 994-1996 (using a thre e-year average helps to reduce measurement error). The F-statis tics on the first-stage regr ession range between 8 and 14, suggesting that our instruments have good predictive power. The resu lts in Table 11 show that IV estimates of the effect of differences in the gun buyback rate on suicides are statistically indistinguishable from OLS estimates, and in part icular, the IV estimates do not move in a positive direction relative to the OLS estimates. The IV results, then, provide further evidence that the 30

33 findings of a statistically signifi cant negative effect of the NFA on firearm homicides and suicides gative bias due to endogene ity of the buyback rate. in the OLS estimates is not the result of a ne 4.1.5 Testing for inconsistencies in data collec tion for external causes of death post-2002 As noted by the Australian Institute of Hea lth and Welfare (AIHW, 2009), there are some concerns that a change in the Australian Bureau of Statistics’ method of collection of data on external causes of death after 2002 might have led to systemic underestimates of suicide deaths in particular. If this underestimation were consiste nt throughout Australia, then underestimates would not affect our results, since we include a full set of year fixed effects. However, if there were differences in under-reporting rate s by state, and these happened to be correlated w ith the firearm buyback rate, our estimates might be biased. There is evidence that there were differences under- reporting by state. Interestingl y, however, the AIHW report shows that Tasmania and the Northern Territory, which had the highest buyback rates, had almost no under-reporting, as did the Australian Capital Territory which had the lo west buyback rate (see Table 7.5). This would certainly not give e results in this pape r would be biased downw ards. Further, there much reason, then, to think that th appears to be little reason to think there is much mis-reporting in the data on firearm deaths. The AIHW report records very few cases in their audit of the data where firear m deaths were mis-coded. Unlike other studies, our results are relatively insensitive to the particular time period chosen, and the results in Table 5, which show th e dynamic effects of the NF A, show that the key estimates of reductions in firearm homicides and suic of the years after 2002. ides are not an artifact Indeed, if anything, the only result s that do appear to be affect ed by the post-2002 years are those on non-firearm suicides, which show a larger increase in non-firearm suicide rates in states that had higher buyback rates. As discussed earlier, this is the most important reason for the overall positive point estimates of the effect of the NFA on non-firearm suicide rates. If this is a result of the anything stronger. en our results are if change in data collection practices in 2002, th 31

34 Nonetheless, concerns about the effect of these data problems on our results may remain. Unfortunately, there is no plan es for death rates be tween 2002 and 2006, so to revise ABS estimat data in the future. We can, however, examine we cannot expect significant improvements in this icides to other external causes of death – in whether there is any evidence that a recoding of su particular accidental deaths or d eaths of undetermined intent – could have affected our results. We do this by simply running the same set of regressi ons for cases of accidental death and deaths of undetermined intent that we ran for homicides and that the NFA appears to suicides. If we find have led to an increase in either of these categorie s of death, we would be c oncerned that our results of a relatively large fall in firearm homicide and suicides in states with higher buyback rates represents a recategorisati on of deaths, rather than a decrease in actual deaths. In the case of firearm deaths, the small numbers of accidental deat hs and deaths of undetermined intent mean that we are forced to group these together. They can be separated in the case of non-firearm deaths, however. The estimates using equation (1) show a very small negative and st atistically insignificant (p-value 0.344) effect of the buyback rate on deaths due to firearm accidents and deaths of undetermined intent. There is no reason to think, then, that the estimates on firearm homicides and suicides in particular are a result of mis-classifi cation of deaths. The results are the same for non- firearm deaths in those two categories, for all acci dents, all deaths of unde termined intent, and for 26 deaths due to ill-defined causes (p -values 0.306, 0.247, 0.922 and 0.594 respectively). 5. Discussion and Conclusions In most developed countries there are consider able restrictions on the availability of firearms, including outright bans on some types of firearms, licensing requirements which often require individuals to show a need for a firearm, and requirements for the registration of firearms. 26 See Appendix Table 4 32

35 Evaluating the effectiveness of th ese regulations is extremely diffi cult. Australia’s NFA provides a effects of a large-scale buyback of firearms on homicide and unique opportunity to examine the suicide. With just under a decade of post-NFA deaths data now available, key studies based on time series data have agreed that there has been a signi ficant fall in the number of firearm suicides in Australia since 1997. Firearm homicides too appear to have declined s ubstantially, though with a smaller number of deaths per year, it is more difficu lt to be sure that this change was caused by the NFA. At a minimum, there is some time series evidence against the notion that stricter gun laws have led to increases in total homicides. The results in this paper – us ing a different and more reliable source of identification – support the general findings of thos e time series studies. We show th at the largest fa lls in firearm deaths occurred in states where more firearms were bought back. Compared to time series studies, this approach has some key benefits . First, it allows us to control for national level trends in death rates through the use of na through state-specific time and at the state level tional-level fixed effects, lling for such trends, th ere was a statistically trends – the results show that even after contro earm deaths in states with higher firearm buyback rates. Second, we are significant decline in fir able to examine in more depth the time pattern of any response of deaths to the NFA – the results show that firearm deaths in states with highe r buyback rates fell relative to those with lower buyback rates, and that this relative reduction in the firear m death rate was maintained subsequently. Finally, we use an instrumental variables strategy to allo w for possible endogeneity in the gun buyback rate, and find that this makes no substantive difference to the results. That the that the relationship results in the baseline regressi on are robust to all thre e approaches suggests between buyback rates and death rates is likely causal. 33

36 The estimated change in both firearm homicides and suicides is very large relative to their intervals on the estimated respons e of non-firearm homicides and earlier averages, but confidence suicides are large enough that it is not possibl e to rule out method substitution of a sufficient magnitude to offset the changes in firearm deaths. This is largely due to the fact that there are so many more non-firearm suicides (a nd non-firearms homicides) than firearm deaths. However, two findings mitigate against the notion of substantia l method substitution. First, non-firearm suicides and homicides fell substantially on aggregate in Aust ralia in the period 1997-2006. Secondly, the estimated time pattern of the response of non-firearm icular) is not what we deaths (suicides in part would expect to see in the case of method substitution. It is also inconsistent with suggestions, based on time series analysis, that the uptick in non-firearm suicides in the period 1997-2000 could have been a consequence of the buyback. Our resu lts show, by contrast, that that jump occurred primarily in the states where the fewest guns were handed in, and wher e the gun buyback would have been expected to have the least effect. For a firearm withdrawal equi valent to Australia’s buyback, using quite conservative point estimates, our estimates suggest th at over 200 firearm deaths per year – mostly suicides – would be lia’s. The leading estimat e of the value of a averted in a population roughly the size of Austra 27 If we assume that there was no statistical life in Australia (Abelson 2003) is A$2.5 million. offsetting increase in non-fire arm deaths, the economic valu e of the gun buyback was A$500 million per year, or more than A$800,000 per firear m bought back. This estimate is very sensitive 27 Valuing homicide and suicide deaths at A$2.5 million may be an underestimate if the typical victim is aged less than 40 years of age (the benc hmark age in Abelson’s estimates), or if society’s willingness to pay to avert a death is higher in the case of violent deaths. On the other hand, for cases of rational suicide, one might argue that a lower value should be placed on suicid e deaths than hould be considered very rough indicators of the on other deaths. Regardless, the figures here s overall benefits of the NFA. 34

37 to the assumptions, however, and in particul ar the assumption of no method substitution. The s of more stringent firearms legislation. calculation also fails to account for any cost There is a question as to whether it is reasona ble to suggest that a withdrawal of about 20 per cent of the stock of firearms could have pl about 74 per cent in the ausibly led to drops of firearm suicide rate, and perhaps 35 to 50 per cent in firearm homicide rates. It should be noted that the standard errors on these estimates are fairly larg e, so that estimates of the declines in firearm homicide rates are usually not statistically signifi cantly distinguishable from no effect. In the case of firearm suicides, however, the estimated 95 per cent confidence intervals show that a buyback of 3500 guns per 100,000 people would have reduced fi rearm suicides by a minimum percentage decline of 8 per cent. As we have noted above, the av ailable data do not allow us to be sure as to whether the firearms withdrawn were relatively ‘high risk’ or ‘low risk’ firearms (i.e. whether they were more or less likely to have es than firearms that were not been used in homicides or suicid withdrawn through the NFA). This is partly because firearms deaths data are not well disaggregated by the type of firearm, but also because whether or not a firearm is ‘high risk’ also depends on unobservable characteristics about its owner and other probable users. A possible interpretation of the magnitude of ou r results is that the guns handed back were not low risk firearms. The buyback focused mostly on automatic and semi-automatic long guns. In Australia, unlike some other countries, long guns have been the most common type of firearm used in both firearm homicides and firearm suicides , likely because handguns were already quite restricted well before the NFA. There is no da ta available on how import ant semi-automatic guns were in firearm deaths compared with other gu ns, however. While semi-automatic or automatic e of homicides, it is not clear that this would guns would be potentially more dangerous in the cas also apply to suicides. 35

38 Perhaps a more likely explanation of the strengt h of the relationship found is that the NFA led states with relatively weak legislation or enforcement relating to sale, ownership and storage of firearms to strengthen their regi mes relative to states with initially stronger standards. There is evidence that states with relatively high fire arm ownership and therefore high gun buyback rates also had relatively weak regulation prior to 1996. Then, our estimates need to be interpreted as reflecting a combination of both the removal of firearms and the rela tive strengthening of legislation and enforcement. We might expect to see smaller effects in the case of a buyback that was not accompanied by stricter firearm legislation. Several factors are important in assessing the ex tent to which the results from the Australian buyback can be extrapolated to other countries. Au stralian borders are more easily controlled than in countries that have land borders . In addition, Australia’s governme nt in general, and its policing and customs services in particul ar, are highly organized and effective. The NFA also had an extremely high degree of political support, and was quite competently executed. And the buyback was accompanied by a uniform national system for licensing and registration of firearms. These factors should be borne in mind in considering the extent to which the results from the Australian other countries. NFA might generalize to 36

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42 Figure 1 Firearm related deaths, and non-firearm related deaths, Australia a. Suicides (self-harm) Non-firearm suicides Firearm suicides per 100,000 per 100,000 14 4 Firearm suicide (RHS) 3.5 12 3 10 2.5 8 2 Non-firearm 6 1.5 suicide (LHS) 4 1 2 0.5 0 0 2004 2006 1976 1974 1978 1980 1982 1984 1986 1970 1968 1988 1990 1992 1994 1996 1972 2000 2002 1998 b. Homicides (assault) Non-firearm Firearm homicides homicides per per 100,000 0.9 2 1.8 0.8 1.6 Non-firearm 0.7 homicide (LHS) 1.4 0.6 1.2 0.5 1 0.4 0.8 0.3 0.6 0.2 0.4 Firearm homicide 0.1 0.2 (RHS) 0 0 2002 2004 2006 1998 1996 1994 1992 1990 1988 2000 1984 1982 1980 1978 1976 1974 1972 1970 1968 1986 Source: Australian Bureau of Statistics, Cause of Death coll ection (data available on request). Data is deaths by self- harm and death by assault. 40

43 Figure 2 Change in firearm suicides and homicides relative to guns a. Firearm suicides 0 AC T WA NSW Vi c -1 SA -2 Qld NT 1990-95 vs 1998-2003 -3 Tas Cha nge in fi rearm sui cides per 100,000 -4 20 00 4000 60 00 8000 Guns bought back per 100,000 (Mouzos) Firearm homicides b. SA 0 ACT Vic NSW Tas WA Qld -.5 1990-95 vs 1998-2003 -1 Change in firearm ho micides per 100,000 NT 8000 2000 4000 6000 Guns b ought back per 100 ,000 (M ouzos) 41

44 c. Non-firearm suicides NT 10 8 6 4 1990-95 vs 1998-2003 Qld 2 SA WA Tas Change in non-firearm suicides p er 100,000 ACT NSW Vic 0 2000 4000 6000 8000 Guns b ought back per 100 ,000 (M ouzos) d. Non-firearm homicides 1 ACT Tas 0 SA Vic Qld NSW WA -1 -2 1990-95 vs 1998-2003 -3 Change in non-firearm homicid es per 100,000 NT 2000 4000 6000 8000 Guns b ought back per 100 ,000 (M ouzos) of Death collection (data available on request). Source: Australian Bureau of Statistics, Cause 42

45 Table 1. Number and type of firearm used for homicides and suicides Suicide Homicide Rifle/ Rifle/ Other/ Other/ shotgun unspec Handgun unspec Handgun shotgun 1990-95 (A) 118 Number of deaths 675 34 242 180 1891 Rate per 1 million 1.1 17.9 6.4 0.3 2.3 1.7 % of deaths 4.4% 70.5% 25.1% 7.5% 53.1% 39.5% 1998-2003 (B) Number of deaths 998 242 64 112 131 153 1.3 8.6 2.1 0.6 1.0 1.1 Rate per 1 million % of deaths 11.0% 71.6% 17.4% 20.8% 36.5% 42.7% Change in deaths (B-A) Change in # of deaths 35 -893 -433 30 -130 -49 -67.3% -33.7% % change in death rate 18.1% -51.9% 71.5% -57.8% Death collection (data available on request). Source: Australian Bureau of Statistics, Cause of Table 2. Guns collected by state Total guns Guns collected per Gun ownership Victims in Port collected rate (SE) Arthur massacre 100,000 residents 5,246 Australian Capital Territory - 0 1698 New South Wales 2482 0.134 (0.009) 155,774 6 9,474 5069 0.176 (0.067) Northern Territory 0 Queensland 130,893 3856 0.213 (0.016) 0 South Australia 4375 0.208 (0.022) 64,811 2 Tasmania 7302 0.435 (0.050) 34,584 12 207,409 4512 0.154 (0.011) Victoria 12 Western Australia 51,499 2869 0.209 (0.022) 1 659,690 3563 0.174 (0.006) 33 Total Notes: Resident calculation is based on 1997 population. Gun ownership rate is the share of households with a firearm, and is estimated from the 1989 and 1992 International Crime Victim Surveys. These surveys did not contain a separate designation for residents of the ACT, though Harding (1981) estimated that in the 1975-77, the gun ownership rate in the ACT was similar to the rate in NSW. Port Arthur mass acre victim breakdown by state of residence excludes two victims from Malaysia. 43

46 Table 3. Relationship between the gun buyba ck rate and proxies of firearm ownership 123 15241 7147 Gun ownership (1989-92) t-statistic (0.94) (3.51) 0.012 0.391 p-value 15092 24480 % of suicides that are firearm t-statistic (1.27) (3.82) 0.009 0.261 p-value Joint significance F7.58 0.031 p-value 2 R 0.6759 0.8073 0.7082 ntheses. All regressions have 8 observations. Note: p-values are in italics, t-statistics in pare We assume that the gun ownership rate in the ACT is the same as in NSW. 44

47 Table 4. Estimates of the effect of th e gun buyback: ‘stripped down’ method Guns coefficients represent the impact of buying back 1000 firearms Non-firearm Firearm suicide suicide ll suicides A Guns bought back 0.497 -0.041 -0.537*** (0.66) t-statistic (4.46) (0.06) -value p 0.004 0.956 0.532 2 R 0.7685 0.0683 0.0006 2.55 12.7 10.2 1990-1995 average death rate -1.9 Implied change in death rate 1.7 -0.1 Implied % change in death rate -74% 17% -1% -2.9 -4.7 Lower limit of 95% CI for death rate -6.2 Upper limit of 95% CI for death rate -0.8 8.2 5.9 Implied change in number of deaths (at 2005 population) -376 348 -28 Lower limit of 95% CI for number of deaths -582 -935 -1230 1173 1631 Upper limit of 95% CI for number of deaths -170 Firearm Non-firearm A ll homicide homicide homicides -0.044 -0.115 -0.160 Guns bought back (0.54) (0.45) (0.47) t-statistic -value 0.60 8 0.671 0.654 p 2 R 0.0464 0.0322 0.0358 0.43 1.47 1.91 1990-1995 average death rate Implied change in death rate -0.40 -0.41 -0.16 Implied % change in death rate -36% -27% -22% Lower limit of 95% CI for death rate -0.9 -2.6 -3.5 Upper limit of 95% CI for death rate 0.5 1.8 2.3 Implied change in number of deaths (at 2005 population) -31 -81 -82 -691 -172 -522 Lower limit of 95% CI for number of deaths Upper limit of 95% CI for number of deaths 468 361 110 Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. Robust t- statistics in parentheses. Sample is one differenced observation per state for a total of 8 observations. * significant at 10 per cent; ** significant at 5 per cent; *** significant at 1 per cent level. 45

48 y y y y 275 0.569 6.365 (1.49) (0.89) (0.49) (0.99) (1.60) (4.10) (0.05) (1.14) (0.88) (2.88) -0.212 -3.286 -9.122 -0.892 -0.383 16.034 0.6331 0.8919 -0.264** 0.166*** y y y 275 9.535 0.655 0.266 (0.33) (1.91) (0.67) (1.16) (1.71) (1.47) (2.06) (1.51) (0.67) (1.15) -3.264 -4.745 -4.972 -7.042 -0.266 5.851* 0.4908 0.8423 -2.518* y y y Total 312 (0.07) (1.11) -0.301 -0.041 0.5896 0.8649 y y , except for those using socio- 312 0.833 0.469 (0.76) (0.74) -0.250 nt; *** significant at 1 per cent level. 0.4032 y y y y 275 0.84 2.102 2.268 0.737 0.112 (0.35) (0.48) (1.30) (2.10) (1.11) (1.35) (0.91) (3.18) (0.81) (0.92) -3.757 -3.117 -0.402 -0.079 16.988 y y y 275 0.447 6.353 6.777 0.691 (1.71) (0.68) (0.89) (1.73) (0.57) (1.75) (0.71) (1.45) (2.08) (0.15) -1.813 -8.113 -2.068 1.844** -3.142 12.689* -0.129 0.5645 0.8102 -1.841* te measured in deaths per million) y y y 312 0.528 Non-firearm (0.97) (0.39) -0.101 0.6915 0.8415 y y 312 0.796 (1.20) (0.54) -0.150 0.4968 0.8159 y y y y 275 (3.20) (1.90) (1.72) (0.19) (1.93) (1.75) (1.08) (1.04) (3.01) (0.19) -6.32* -2.479 -0.169 -1.533 -0.954 -0.678 -0.489 -5.36** 0.7934 0.4973 -0.184* -0.494** y y y 275 0.18 2.758 0.207 3.141 (6.83) (2.49) (2.06) (1.37) (0.74) (1.51) (1.26) (1.56) (2.17) -0.502 -1.196 -0.677 0.7749 0.4287 -2.932* -3.900* -0.138** bought back on death rates (death ra y y y Firearm 312 (6.39) (4.13) 0.7476 0.4382 -0.200*** -0.569*** -0.424*** y y 312 0.731 (5.17) (1.57) -0.100 0.4028 -0.327*** 2 2 % of pop >65yo R % of pop 20-24 yo Unemployment rate Guns bought back % of pop urban % of pop 20-24 yo % of pop >65yo R % of pop urban Guns bought back Unemployment rate Suicide State Fixed Effects Socio-economic controls State-specific Time Trends Year Fixed Effects Number of obs Homicide Guns coefficients represent the impact of buying back 1000 firearms Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. Observations: 312 Table 5. Estimated effects of firearms economic controls which have 275. Robust t-statistics in parentheses. * significant at 10 per cent; ** significant at 5 per ce

49 y y in (3.10) (0.87) y 0.146 -0.421 (1.36) (0.32) y Total (1.07) (0.08) , except for those using socio- nt; ** significant at 5 per cent; *** 0.235 -0.050 (1.05) (0.46) -0.295 -0.298 -0.276 -0.228** 0.5588 0.6029 0.5697 0.6404 0.8607 0.8658 0.8652 0.8967 nt; *** significant at 1 per cent level. y y (1.17) 0.8865 -0.0059 0.073 (0.37) (0.21) Homicide y ate-specific trends, with a break in trend 0.586 (0.52) (1.39) (1.41) 0.4878 0.0203 y Suicide Non-firearm 0.519 (0.39) (0.92) yyyy yyyy yyyy yyyy (0.84) 0.8515 -0.0039 0.683 (0.45) (1.33) -0.128 -0.101 -0.099 -0.027 0.6673 0.7025 0.6616 0.7419 0.8343 0.8422 0.8243 0.8575 homicide 47 Non-firearm y y (2.78) (2.71) (0.17) 0.7962 0.5119 0.0019 0.6167 -0.494** -0.201** suicide y Non-firearm (6.03) (6.58) 0.4982 0.7872 ack rate and prior trends in death rates ht back on death rates – allowing for st (1.14) 0.5227 -0.0019 y Firearm Firearm homicide (6.08) (3.99) 0.7513 0.4611 yyyy yyyy (2.68) 0.6759 0.0184** suicide Firearm (4.17) 0.4565 0.7433 (10.89) -0.448*** -0.570*** -0.440*** -0.168*** -0.197*** -0.177*** t-statistic Guns bought back Guns bought back 2 2 2 Guns bought back * year R Suicide R State Fixed Effects State-specific Time Trends State-level socioeconomic controls Homicide Year Fixed Effects R Table 6. Estimated correlation between buyb significant at 1 per cent level. Note: Gun buyback rate is measured as guns per thousand people. Robust t-statistics in parentheses. * significant at 10 per ce Table 7. Estimated effects of firearms boug Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. Observations: 312 1988 economic controls which have 275. Robust t-statistics in parentheses. * significant at 10 per cent; ** significant at 5 per ce Guns coefficients represent the impact of buying back 1000 firearms

50 y y 0.279 (0.80) (1.50) (0.76) (1.88) -0.304 -0.124 -0.346 (-2.42) (-0.46) 0.8926 0.6472 -0.715** -0.306** y -1.16 (0.93) (0.93) (2.15) (0.83) (0.25) -0.158 -0.119 -0.344 -0.325 -0.342 0.895* 0.5145 0.8431 y Total 0.66 (2.02) (0.98) (1.36) (0.93) (0.98) (0.04) -0.034 -0.368 -0.354 -0.526 0.8653 0.6077 -0.174* yyyy yyyy 4, except for those using socio- 1.1 0.329 (0.88) (0.76) (1.81) (0.39) (0.68) (0.40) -0.332 -0.121 -0.288 -0.208 0.8334 0.4262 nt; *** significant at 1 per cent level. y y 0.38 0.201 0.075 (0.66) (0.58) (3.03) (1.01) (0.44) -0.185 -0.093 -0.263 0.7545 0.8466 0.858** y 0.583 0.030 (0.74) (0.31) (0.64) (3.17) (0.07) (0.98) -0.173 -0.233 -0.027 0.8114 0.5917 1.369** y Non-firearm 0.547 0.047 (0.37) (0.75) (0.53) (2.76) (0.07) (0.72) -0.123 -0.207 -0.034 0.7148 0.8422 1.327** yyyy yyyy 48 0.658 0.075 (0.53) (0.06) (0.61) (2.22) (0.13) (0.77) -0.183 -0.256 -0.003 1.464* 0.5221 0.8166 y y (1.96) (2.74) (2.74) (3.87) (3.23) (2.86) -0.162 0.7941 0.4979 -0.213* -0.505** -0.452** -0.199** -0.579*** back on death rates – incorporating dynamics y (2.56) (2.02) (2.39) (5.54) (5.62) (5.42) 0.7753 0.4291 -0.148* -0.152** -0.111** -0.473*** -0.424*** -0.369*** y Firearm (4.78) (3.25) (2.97) (9.81) (5.03) (5.54) 0.7486 0.4392 -0.221** -0.161** -0.667*** -0.231*** -0.580*** -0.493*** yyyy yyyy (1.35) (1.31) (2.42) (6.58) (3.32) (5.57) -0.118 -0.105 0.7312 0.4031 -0.076** -0.360** -0.329*** -0.282*** 2 2 R 2002-2005 2000-2002 1997-1999 R 2002-2005 2000-2002 1997-1999 Guns bought back interacted by years: Guns bought back interacted by years: Homicide State Fixed Effects Socio-economic controls State-specific Time Trends Year Fixed Effects Suicide Guns coefficients represent the impact of buying back 1000 firearms Table 8. Estimated effects of firearms bought Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. Observations: 30 economic controls which have 275. Robust t-statistics in parentheses. * significant at 10 per cent; ** significant at 5 per ce

51 include state and year fixed 0.546 0.707 0.528 (0.46) (0.40) (0.97) (1.31) (0.97) (0.39) -0.110 -0.097 -0.101 Incl. state- specific trend 49 Non-firearm 0.799 0.796 0.930 (0.54) (1.40) (1.20) (1.20) (0.54) -0.150 -0.150 -0.150 (-0.62) No trend (0.20) (7.82) (6.39) (4.13) (4.31) -0.018 (-5.22) -0.650*** -0.569*** -0.200*** -0.594*** -0.210*** Incl. state- specific trend Firearm (5.61) (1.51) (4.63) (5.17) (1.57) -0.062 -0.100 -0.104 (-0.81) -0.327*** -0.338*** -0.337*** No trend Port Arthur dummy Basic Basic Drop 1997 Drop 1997 Port Arthur dummy Homicide Suicide Table 9. Robustness to Port Arthur and dropping 1997 Guns coefficients represent the impact of buying back 1000 firearms * significant at 10 per cent; ** significant at 5 per cent; *** significant at 1 per cent level. effects, but not socio-economic controls. Each cell is a separate regression. Robust t-statistics in parentheses. Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. All specifications

52 include state and year fixed 0.087 0.049 (1.98) (1.72) 0.8431 0.8330 -0.212* -0.250** between Tobit and OLS estimates. * 0.208 0.207 (1.26) (1.26) -0.150 -0.150 0.8159 0.8159 Non-firearm Total 0.141 0.056 (1.92) (1.48) -0.062 0.6197 0.4028 -0.100* OLS estimates (no clustering) Firearm des: Tobit vs OLS 50 6 4 0.051 0.027 (2.23) (1.96) 0.1843 0.1782 -0.263* -0.224* 7 8 ntheses are not clustered at the state level, for comparability 0.085 (1.73) (1.74) 0.0083 0.1730 0.1730 -0.195* -0.195* Tobit estimates Non-firearm Total gun buyback on homici 46 46 0.131 0.314 (1.01) (1.51) -0.090 -0.048 0.1378 0.0815 Firearm 2 Guns bought back (t-statistic) Pseudo-R2 Pseudo-R Number censored: Number censored: p-value (t-statistic) Guns bought back p-value No Port Arthur Dummy Port Arthur Dummy Guns coefficients represent the impact of buying back 1000 firearms effects, but not socio-economic controls. t-statistics in pare Table 10. Estimates of the effect of the Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. All specifications significant at 10 per cent; ** significant at 5 per cent; *** significant at 1 per cent level.

53 (0.44) (1.82) (0.24) (1.07) -0.693 -0.086 -0.213 -0.797 0.8437 0.5802 Trend Total (0.61) (0.40) (0.23) (0.99) -0.617 -0.293 -0.081 -0.157 0.3825 0.8428 No trend 0.006 (0.47) (0.01) (0.22) (0.95) -0.540 -0.171 -0.061 0.6850 0.8415 Trend m, using data from 1994 to 1996. the stripped down version of the include state and year fixed estimated rate of firearm ownership Non-firearm 0.171 (0.57) (0.40) (0.24) (0.94) -0.628 -0.217 -0.067 0.8157 0.4751 ant at 10 per cent; ** significant at 5 per No trend Including Port Arthur Dummy (0.34) (7.14) (0.27) (1.23) -0.153 -0.042 -0.024 0.6429 0.7437 -0.803*** Trend Firearm 0.011 (5.49) (0.20) (0.19) -0.077 -0.015 0.6195 0.7344 -0.327*** ows the first stage regressions in No trend 0.312 (1.05) (0.76) (1.77) (1.10) (1.03) -0.652 -0.411 -0.611 0.8647 0.5805 Trend 51 Total 0.255 (0.73) (0.37) (0.74) (0.98) -0.139 -0.337 -0.608 0.8327 0.3822 No trend me as that in NSW.) Table 3 sh tics in parentheses, clustered at the state level. * signific 0.024 0.078 (0.46) (0.07) (0.30) (0.92) -0.156 -0.504 0.6854 0.8415 Trend s of the effect of the gun buyback Non-firearm 0.172 0.117 (0.58) (0.41) (0.42) (0.94) -0.216 -0.624 Basic models 0.8157 0.4752 No trend (3.49) (7.48) (1.13) (1.19) -0.106 -0.055 0.4371 0.7469 -0.675*** -0.255*** Trend Firearm 0.015 (1.96) (5.20) (0.34) (0.24) -0.122 -0.022 0.4024 0.7309 -0.312*** No trend t-statistic Difference t-statistic Difference 2 2 Gunsbought t-statistic R Hausman test Hausman test R Gunsbought t-statistic Homicide (Instruments = gun ownership and % of suicides that are firearm) Suicide (Instrument = estimated gun ownership, 1989 and 1992) cent; *** significant at 1 per cent level. model. Results are similar for the panel model. Robust t-statis (We assume that the firearm ownership rate in the ACT is the sa effects, but not socio-economic controls. The panel to the right includes the Port Arthur dummy. Instruments used are (a) the from the 1989 and 1992 ICVS surveys (figures provided in Table 2); and (b) the percentage of suicides undertaken with a firear Guns coefficients represent the impact of buying back 1000 firearms Table 11. Instrumental variable estimate Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. All specifications

54 y y y y 128 0.070 (0.55) (0.51) -0.234 0.6431 0.8718 * y y y 128 0.141 0.574 (0.32) (0.35) -0.040 0.8625 y y y y 237 per cent; *** significant 0.269 (0.03) (0.50) -0.006 0.6155 0.8211 * y y y that the sample is restricted to r comparison with specifications include state and year fixed 237 Non-firearm 0.527 (1.41) (0.59) -0.113 0.5858 0.8143 y y y y ** significant at 5 275 .576 0 (1.51) (0.28) -0.048 0.5818 0.8198 y y y 275 .5645 .8102 0.691 (1.71) (0.68) -0.129 0 0 ) y y y y 128 0.343 (9.00 (2.15) 0.8317 -0.180* * y y y 128 (3.33) .186** 0.8244 0.3427 (14.25) 52 -0.394*** -0.341*** y y y y 237 (4.65) (3.34) 0.7884 0.4276 * y y y rate is measured as guns per thousand people. All specifications Firearm 237 (6.72) (2.67) 0.7844 0.4402 y y y y 275 (7.02) (2.75) 0.7758 0.4361 y y y 275 (6.83) (2.49) 0.7749 0.4287 uding additional control variables -0.138** -0.118** -0.141** -0.201** -0 -0.424*** -0.409*** -0.462*** -0.520*** Guns bought back Guns bought back Include % indigenous Include Prisoners & Police Include % male 15-24 Homicide Suicide Year Fixed Effects Number of observations State Fixed Effects State-level controls effects and basic socio-economic controls. Results from Table 5 shown for comparison (first columns). Columns with * indicate Appendix Tables Note: Death rates are deaths per million people. Gun buyback Appendix Table 1. Effects of incl states and years for which we have information on prison population and police, and percentage of the population indigenous, fo that include those variables. Robust t-statistics in parentheses, clustered at the state level. * significant at 10 per cent; at 1 per cent level.

55 y y (2.90) (0.89) 0.265** - y (2.88) (0.88) 0.264** - y Total (1.12) (0.08) include state and year fixed tics in parentheses, clustered at the yyyy yyyy yyyy (1.11) (0.07) -0.041 -0.047 -0.383 -0.387 -0.301 -0.302 0.8649 0.8652 0.8919 0.8919 0.5896 0.5904 0.6331 0.6334 y y 0.107 (0.48) (0.33) y 0.112 (0.48) (0.35) y Non-firearm 0.523 (0.39) (0.96) yyyy yyyy yyyy 0.528 53 (0.39) (0.97) -0.101 -0.101 -0.079 -0.079 0.8415 0.8417 0.8456 0.8456 0.6915 0.6924 0.7370 0.7373 y y (1.89) (3.18) -0.185 0.4973 0.7934 rate is measured as guns per thousand people. All specifications y (1.90) (3.20) 0.4973 0.7934 y Firearm (4.13) (6.34) 0.4385 0.7476 y y y y y y y y y y y y (4.13) (6.39) 0.4382 0.7476 allowing for quadratic trends -0.200*** -0.201*** -0.184* -0.569*** -0.570*** -0.494** -0.494** s Guns bought back Guns bought back State Fixed Effects State-specific Time Trend Year Fixed Effects Suicide Homicide State-level socioeconomic controls Quadratic State-specific Time Trend effects and basic socio-economic controls. Results from Table 5 including linear trends shown for comparison. Robust t-statis state level. * significant at 10 per cent; ** significant at 5 per cent; *** significant at 1 per cent level. Note: Death rates are deaths per million people. Gun buyback Appendix Table 2. Effects of

56 y y (2.47) (3.10) (1.80) (0.87) y 0.146 -0.421 (1.15) (1.36) (0.15) (0.32) y Total 0.669 0.5554 0.7055 (3.03) (1.07) (1.17) (0.08) yyyy yyyy 0.235 -0.741 -0.056 -0.923 0.235 -0.050 (0.92) (1.05) (0.42) (0.46) -0.249 -0.678** -0.140 -0.603** -0.295 -0.298 -0.276 -0.228** 0.4953 0.8088 0.8536 0.8386 0.8619 0.8607 0.8658 0.8652 0.8967 0.5588 0.6029 0.5697 0.6404 include state and year fixed comparison. Robust t-statistics in y y r cent level. 0.073 (0.57) (0.37) (1.55) (0.21) y 0.413 -0.819 0.001 -0.220 0.586 (0.01) (0.52) (1.19) (1.39) y Non-firearm 0.673 0.5105 0.7127 0.519 (0.79) (0.39) (0.90) (0.92) yyyy yyyy 0.690 -0.617 0.683 (0.35) (0.45) (1.27) (1.33) -0.083 -0.279 -0.128 -0.101 -0.099 -0.027 0.7911 0.8111 0.8054 0.8176 0.8343 0.8422 0.8243 0.8575 0.4317 0.6673 0.7025 0.6616 0.7419 y y 54 (1.63) (2.78) (2.28) (2.71) -0.382 0.4519 0.5119 0.8595 0.7962 -0.105* -0.201** -0.494** y (2.48) (6.03) (7.07) (6.58) 0.3993 0.4982 0.8195 0.7872 -0.141** rate is measured as guns per thousand people. All specifications y Firearm (1.76) (6.08) (3.99) (2.04) -0.400 0.4378 0.4611 0.8539 0.7513 -0.123* -0.469*** y y y y y y y y (3.35) (4.17) (9.84) 0.3344 0.4565 0.8135 0.7433 (10.89) -0.166** -0.168*** -0.197*** -0.177*** -0.455*** -0.448*** -0.570*** -0.440*** ning time period to 1988 and after Guns bought back Guns bought back Guns bought back Guns bought back R2 1988 and on R2 1979 and on, trend break in 1988 R2 1979 and on, trend break in 1988 1988 and on R2 State-specific Time Trends Year Fixed Effects State-level socioeconomic controls State Fixed Effects Homicide Suicide parentheses, clustered at the state level. * significant at 10 per cent; ** significant at 5 per cent; *** significant at 1 pe effects and basic socio-economic controls. Results from Table 7 including a break in state-specific trends in 1988, shown for Appendix Table 3. Effects of shorte Note: Death rates are deaths per million people. Gun buyback

57 0.344 0.922 0.247 0.594 0.281 0.306 p-value (1.03) (0.56) (0.10) (1.28) (1.19) (1.12) on used is equation 1. * likely categories in which a 0.009 -0.035 -0.419 -0.116 -0.569 -1.129 hs of undetermined intent refer to the Coefficient t-statistic (2009) as the most 34)+(Y22-Y34)) identified in AIHW 55 W75-W84; W00-W19; W65-W74; X40-X49 (V01-X59)+(Y10-Y34)-((W32-W R99 Y10-Y19; Y20; Y21; Y30; Y31 (W32-W34)+(Y22-Y34) (V01-X59)+(Y10-Y34) ICD 10 codes or coded as a death of undetermined intent. intent threats to breathing, drowning and falling, ning time period to 1988 and after Suicide-like non-firearm undetermined intent* Total accident + undetermined intent Non-firearm accident + undetermined Firearm accident + undetermined intent Suicide-like non-firearm accident* Ill-defined causes Accidents and undetermined intent suicide could be mis-coded as an accidental death, Note: Death rates are deaths per million people. Gun buyback rate is measured as guns per thousand people. Regression equati Appendix Table 4. Effects of shorte significant at 10 per cent; ** significant at 5 per cent; *** significant at 1 per cent level. Suicide-like accidents and deat ICD-10 categories associated with poisoning,

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