I keep calling for more stringent gun laws in the U.S.; in fact, I would, if I were in charge, take the U.S. to the British system, in which private ownership of handguns is prohibited and rifles can be owned only for sports shooting or hunting—and under strict licensing. In contrast, many gun advocates say that the U.S. would become more dangerous should such legislation be enacted, and, regardless, the Second Amendment guarantees us private ownership of guns (the Supreme Court agrees; I don’t).
There is one “natural” experiment in banning guns: that in Australia, where, after mass shootings, stringent gun control was imposed in 1996. (Actually, the UK did another, but I know of no data like what I’ll show below.) And the data on homicides and suicides for periods of roughly two decades before and after the ban has just been analyzed and published in the Journal of the American Medical Association by Simon Chapman et al. (reference and free download below). The upshot is that there are some data suggesting that gun-related suicides and homicides decreased after the ban, but in some cases it didn’t reach statistical significance.
There are two problems here. First, firearm-related homicides and suicides were already decreasing before the gun ban, so the analysis had to determine whether the rate of decline of gun-related deaths increased after the gun ban, and that method involves estimating regression coefficients—an insensitive way to detect anything other than big changes in rate.
Second, there may have been other changes over time that decreased gun-related deaths after the ban, namely the wider use of cellphones, which allow one to report shootings faster, possibly saving more lives and thus reducing the homicide rates, as well as improvements in medical care, so a suicide or shooting is less likely to cause death. Since the data analyzed involve only deaths and not injuries, the authors can’t rule out these factors.
That said, the data show that the number of mass shootings (defined as shootings in which more then five people die) dropped to zero after the ban (19 years after the gun ban was enacted), while there were 13 such incidents in the 18 years before the gun ban was enacted. That itself is a significant difference if you use a simple two-sample chi-square test assuming equality of numbers, but that difference may reflect only the same trend of reduced homicides over time. However, the overall data show that in every case the rate of decline in gun-related deaths increased after the ban, and didn’t increase in any case, as the gun-lovers would have us believe. Moreover, in some cases the faster decline was statistically significant. The report then, is heartening but not decisive. It certainly gives us no cause to think that if a Western nation suddenly tightened its gun policies, gun-related deaths would rise.
First, the facts (all quotes from the paper):
In 1996, Australia’s state and federal governments introduced sweeping uniform gun laws that were progressively implemented in all 6 states and 2 territories between June 1996 and August 1998. The enactment of these laws followed a massacre on April 28, 1996, in which a man used 2 semiautomatic rifles to kill 35 people and wound 19 others. The new gun laws banned rapid-fire long guns (including those already in private ownership), explicitly to reduce their availability for mass shootings.
In addition, by January 1, 1997, all 8 governments commenced a mandatory buyback at market price of prohibited firearms. As of August 2001, 659 940 newly prohibited semiautomatic and pump-action rifles and shotguns had been purchased by the federal government from their civilian owners at market value, funded by a one-off levy on income tax, and destroyed. From October 1, 1997, large criminal penalties, including imprisonment and heavy fines, applied to possession of any prohibited weapon.
During a second firearm buyback in 2003, 68 727 handguns were collected and destroyed. Thousands of gun owners also voluntarily surrendered additional, nonprohibited firearms without compensation, and since 1996 thousands more privately owned firearms are known to have been surrendered, seized, and melted down.
The trends. The authors looked at overall suicide and homicide fatalities, and then separated them into those involving guns and those not involving guns. (They also gave separate and combined data for suicides and homicides.) I’ll show the trends only for the data separated by whether or not they involved firearms, leaving out the combined (firearm + nonfirearm) deaths:

You can see that both suicides and homicides involving firearms were already decreasing before the ban (vertical line), while suicides and homicides not involving firearms were either increasing or steady. In the latter case, though, both kinds of deaths decreased after the gun ban, suggesting that better medical care, increased cellphone use, or other factors were involved.
Here are the statistical analyses:

The column to look at is the P values in the RT column (ratio of trends happening before and after gun control; “RL” looks for a step change occurring in 1996). You can see that in every case (5 out of 5 non”total” cases involving separated firearm and nonfirearm deaths: rows 2-4 and 6-7 in Table 3), the death rates declined more steeply after than before gun laws. That alone is nearly statistically significant, but remember that two of these statistics are deaths not involving firearms. In one analysis of firearm deaths—suicide—the drop was significantly steeper after 1996, and for all homicides it was almost significant (p = 0.06). But the drops in non-firearm deaths also accelerated after 1996, which again may reflect other factors (including, in the case of suicide, better prevention techniques).
Largely because of the contribution from fewer suicides, the rate of decrease in total firearm deaths, involving both suicides and non-suicides, was larger after gun control than before. All of this shows that easy access to firearms, at least in Australia, seemed to promote more suicides than homicides.
What’s the lesson? As I said, it’s a bit problematic because of other factors, factors that could be reflected in a decrease in nonfirearm deaths as well. Nevertheless, there are no data here suggesting that firearm deaths will increase after guns are largely banned. In other words, these data show that such a ban is worth trying, as there appears to be no downside.
Ideally, we’d want more data from other countries, but we can’t get it from the one country everyone’s concerned about: the U.S. Until the Supreme Court interprets the Second Amendment correctly, and the legislature gets the moxie to buck the National Rifle Association and enact meaningful gun laws, we simply won’t know what will happen in the U.S. if we followed Australia’s lead. The data above, however, suggest that we should.
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Chapman, S., P. Alpers, and M. Jones. 2016. Association between gun law reforms and intentional firearm deaths in Australia, 1979-2013. J. Am. Medical Association. doi:10.1001/jama.2016.8752 Published online June 22, 2016.