The Vox piece you quote references this study:
Which is a multivariate analysis that controlled for these factors:
Analyses controlled for state-level rates of aggravated assault, robbery, unemployment, urbanization, per capita alcohol consumption, and a resource deprivation index (a construct that includes median family income, the percentage of families living beneath the poverty line, the Gini index of family income inequality, the percentage of the population that is black and the percentage of families headed by a single female parent). Multivariate analyses found that states with higher rates of household firearm ownership had significantly higher homicide victimization rates of men, women and children.
…but it’s behind a paywall.
My article linked above also referenced another multivariate analysis which controlled for similar factors:
…but it’s public, so we can also look at their results, which are probably similar. These were their factors:
We controlled for the following factors, which have been identified in previous literature (29,32,34–37,41–45,54,56,57) as being related to homicide rates: proportion of young adults (aged 15–29 years), proportion of young males (aged 15–29 years), proportion of Blacks, proportion of Hispanics, level of urbanization, educational attainment, poverty status, unemployment, median household income, income inequality (the Gini ratio), per capita alcohol consumption, nonhomicide violent crime rate (aggravated assault, robbery, and forcible rape), nonviolent (property) crime rate (burglary, larceny–theft, and motor vehicle theft), hate crime rate, prevalence of hunting licenses, and divorce rate. To account for regional differences, we controlled for US Census region. In addition, to capture unspecified factors that may be associated with firearm homicide rates, we controlled for the annual, age-adjusted rate of nonfirearm homicides in each state. We also controlled for state-specific incarceration rates and suicide rates. The definitions and sources of these data are provided in Table 1.
These were their results:
So you can see plainly that other factors dominate the firearm homicide rate, most especially Gini coefficient and black population ratio. The first line of their study is very instructive, though, because it gives us an estimated “rate of homicide reduction due to gun reduction,” if we presume that the correlations are causal, and we further presume that a gun reduction method would take the guns out of the hands of current or future murderers, instead of grandmas who want to sell the guns back on a buyback for some spending cash, or people who want to sell their guns back to buy a bigger gun.
So those two presumptions are bad, but let’s presume them anyway, and do the math.
When you do the math, even with those bad presumptions, you find that you’ll have to buy 61 million dollars worth of guns to save a single life from a gun homicide. The reason why, quite simply, is that we already have so many guns.
For reference, you’d spend the same as the entire municipal budget for the City of Atlanta to save ten lives. And Atlanta has about 80 homicides per year.
So that doesn’t work. Homicide reduction via reduction in gun proliferation is impossible here. So if we want to reduce homicides, we must do so through other means.
I have some ideas, here: