Are there economic studies surrounding the efficacy of gun control? In light of a recent mass shooting in Nova Scotia, the Prime Minister of Canada intends to ban a lot of firearms. I have seen both sides of this debate, notably whether or not gun control is an effective strategy to reducing violent crime. Gun control itself is a supply-reduction policy whereas loosening gun control coupled with more severe penalties for offenders who use guns is a demand-reduction policy. Both sides of this have valid arguments, though, which one is more effective? This is an economics policy question.

I have not seen very much attention given to this topic from economics. Is there a well defined economics literature surrounding gun control and its efficacy (does it work)? Maybe econometric studies examining gun control laws imposed in certain states as natural experiments? 

I am not simply asking "Does gun control work" as this would attract opinion-based answers. I am looking for studies that have examined the effects to better inform myself on the subject, on which I have not formed an opinion.
To answer the headline question directly: yes, there are. 

While economists are among the central participants, this is really an interdisciplinary policy-oriented question. The Science of Gun Policy is a fairly recent and comprehensive review of the research overall, published by the Rand Corporation. It's over 400 pages long and I haven't read it. But if you glance through it you will get a sense of the many complex angles that this question has been examined from. Relevant outcomes are not limited to violent crime per se.

Table 21.1 on pages 332-333 summarize the evidence for which policy measures may affect which outcomes, according to the current evidence. Regarding violent crime specifically, there is moderate evidence ("two or more studies—at least one of which was not compromised by serious methodological weaknesses... and contradictory evidence was not found in other studies with equivalent or stronger methods.") to show: 


waiting periods reduce total homicides
background checks by dealers reduce firearm homicides (evidence for private-seller background checks is less conclusive)
firearm prohibitions for individuals subject to restraining orders decrease intimate partner homicides.


I have not looked through the relevant studies for these particular findings to see which ones are specifically by economists, but in any event, these are probably the most conclusive findings you will find. Someone else might be able to give you a more in-depth look at the economics research per se.