Here is a decent, comprehensive look:
http://www.cjcj.org/uploads/cjcj/documents/jpj_firearm_ownership.pdf
Here is an interesting excerpt in the meat of the paper:
“At the regional level, the researchers found that, regardless of the proxy, there was a significant and positive association between firearm prevalence and unintentional firearm deaths and suicides. Miller, Azrael, and Hemenway (2002, pg. 271) pointed out that children living in high firearm prevalent states were “16 times more likely to die from unintentional firearm injury, 7 times more likely to die from firearm suicide, 3 times more likely to die from firearm homicide, and overall, twice as likely to die from suicide and homicide” than children living in states with low firearm prevalence.
Siegel, Ross, and King III (2013) examined firearm prevalence and firearm homicides from 1981 to 2010. The authors collected information for the fifty states from 1981 to 2010 and used suicide by firearm as a proxy for firearm prevalence. Using a negative binomial regression model the researchers found that firearm prevalence was a significant predictor of firearm homicide. In fact, Siegel, Ross, and King III (2013) stated that a one standard deviation increase in firearm prevalence was associated with a 12.9% increase in the homicide rate.
Branas et al. (2009) explored whether having a firearm would reduce the risk of harm from an attack. They compared a sample of individuals in Philadelphia from 2003 – 2006 who were victims of assault, including those who had a firearm and those who did not have a firearm. Branas et al. (2009) matched the subjects on a number of factors, such as age. They found that victims who were in possession of a gun were 4.46 times more likely to be shot in an assault and 4.23 times more likely to be fatally shot in an assault. Further, in assaults where the victim had a chance to resist, individuals in possession of a firearm were 5.45 times more likely to be shot. Branas et al. (2009) stated that firearm possession may falsely empower individuals to think they can handle dangerous situations and that individuals who are in possession of a firearm may be more likely to enter a dangerous situation and be in harm’s way because of their overconfidence.
Other scholars have examined firearm prevalence and crime using a cross-national research design. Using the International Crime Survey, Killias (1993) found wide variation in firearm ownership. For instance, only 2% of households in the Netherlands owned a gun, while 48% of homes in the United States reported owning a gun. Killias (1993) was also interested in whether a lack of availability of firearms would lead individuals to compensate by using other means to commit suicide and homicide. He found that firearm prevalence was positively correlated with national homicide and suicide rates and positively correlated with homicide and suicides committed by a firearm. Killias (1993) demonstrated that there is no weapon substitution effect for countries with low firearm prevalence rates.
Individuals did not find other means to commit homicide and suicide when a firearm was not present.
Examining 26 high-income countries, Hemenway and Miller (2000) used the Cook’s Index and suicides by firearm as proxies for firearm prevalence. They found that, regardless of the proxy utilized, there was a significant and positive correlation between homicide rates and firearm prevalence. Killias, van Kesteren, and Rindlisbacher (2001) examined firearm prevalence and suicide and homicide. Using data from the International Crime Victimization Surveys for 1989, 1992, and 1996 for 21 countries, the researchers found that firearm prevalence increased rates of suicide by firearm, homicide by firearm for female victims, and firearm assault.”