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The executive summary doesn't make sense:

"Two common proxies for gun availability are used, the percentage of suicides with a firearm, and the"Cook index," the average of the percentage of suicides with a firearm and the percentage of homicides with a firearm."

"In simple regressions (no control variables) across 26 high-income nations, there is a strong and statistically significant association between gun availability and homicide rates."

So, if I'm reading this correctly, gun availability is calculated by percentage of deaths by firearm, and using that info they determine that gun availability leads to a higher homicide rate? Also no control variables? Why?

Using such source numbers, it's a foregone conclusion. If you use percentage of firearm deaths as a proxy for gun ownership, you will by definition have a strong correlation between gun ownership and deaths.

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