After the 2012 school shooting in Newtown, Conn., people across the country went out and bought guns.

A study published Thursday concludes that a subsequent increase in gun exposure led to more accidental firearm deaths than otherwise would have occurred in the months after the school shooting.

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David Studdert, a professor at Stanford University who studies trends in gun violence and who wasn’t involved in the new study.

“There’s clearly a strong relationship with firearm-related suicide,” he adds. “Some studies show a relationship with firearm-related homicide. But we need better evidence.”

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“It’s very challenging to estimate empirically,” says Studdert. “If we really wanted to understand the health effects of firearm ownership, we would randomize the ownership of weapons in different households and observe their effects over time. Of course, we can’t do that.”

He thinks the approach, using a surge in the supply of firearms to ask a question about accidental deaths, is a good one. But, he says, the study leaves larger questions unanswered.

“Accidental deaths are quite a small part of firearm mortality. Around 2 to 3 percent of all firearm related deaths are accidental deaths. The lion’s share are homicides and suicides,” Studdert points out. “The much bigger question is, ‘What effect does firearm exposure have on firearm-related suicide and homicide?’ The design of this study didn’t allow them to answer that.”