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Firearms and Violence: A Critical Review
TABLE 7-2 Correlation Coefficient Between a Proxy and Gun Ownership Rates
N = 9 regions
N = 21 states
N = 48 states
Guns & Ammo
NOTE: GSS = Generalized Social Survey; BRFSS = Behavioral Risk Factor Surveillance Survey; HICRC = Harvard Injury Control Research Center.
SOURCE: Azrael et al. (2004: Table 3). Used with kind permission of Springer Science and Business Media.
As a result of these limitations, many ecological studies evaluating the relationship between firearms and suicide (and homicide) rely on proxies of ownership, rather than direct measures. Proxies have included the fraction of homicides committed with a firearm (FH/H), the fraction of suicides committed with a firearm (FS/S), subscription rates to Guns & Ammo (G&A), and other similar measures.3
The primary advantage of these proxies, as opposed to survey information, is that they can be readily computed at state, county, and other finer geographic levels. The disadvantage is that the proxy is not the variable of interest; ownership is. Thus, except in very particular circumstances, proxy measures result in biased estimates of the relationships of interest.
Several studies have explicitly evaluated different proxy measures of ownership. These assessments generally involve computing a correlation coefficient between the proxy and self-reported ownership measures from the GSS or other surveys.4 Azrael et al. (2004), for example, systematically assess a number of commonly used proxies. Their basic results using the GSS and other ownership surveys are displayed in Table 7-2. The fraction of suicides committed with a firearm has the highest correlation among all of the measures considered, ranging from 0.81 in the state level data to 0.93 when using ownership data from the nine census regions. The fraction of homicides committed with a firearm has the lowest correlations, and G&A subscription rates lie between the two.
See Azrael et al. (2001) for a summary of the different proxy measures used in the literature.
These correlations are computed using both geographic and time-series variation in the ownership and proxy measures. Duggan (2003), in addition to comparing the G&A proxy to the GSS data, also uses other indicators that are thought to be highly correlated with ownership, such as the location of gun shows and community characteristics thought to be associated with ownership.