The study acknowledges this downward trend, and shows that the trend accelerated after the ban. They are quite clear that this is not enough to conclude the ban

The study acknowledges this downward trend, and shows that the trend accelerated after the ban. They are quite clear that this is not enough to conclude the ban worked as intended, but it is plausible. Quoting from the discussion section (http://jama.jamanetwork.com/article.aspx?articleid=2530362#Discussion http://jama.jamanetwork.com/article.aspx?articleid=2530362#D...): This study has several issues related to terminology and limitations that should be considered in the interpretation of these findings. ... Second, the observational nature of the data in this article precludes assigning causality between enactment of the 1996 gun laws along with the buyback program and subsequent elimination of mass shootings and reduction in rates of total firearm-related deaths and gun-related suicide. Even though the rates of firearm-related homicides and suicides were declining before gun law reforms, banning rapid-fire weapons, and removal of a substantial number of firearms, it is plausible that reducing the availability of weapons may have been related to the acceleration in the rates of declines for these deaths after gun reform.