Given this evidence, Azrael et al. conclude that “FS/S is a superior proxy measure for cross-section analysis, easily computed from available data for state and large local jurisdictions and valid against survey based estimates” (p. 50). They also find, using similar methods, that FS/S is a useful proxy for measuring intertemporal variation in ownership. This finding appears to share some consensus. Many other researchers have also accepted FS/S as the best and in fact a nearly ideal proxy for studying the cross-sectional relationship between firearms and violence. One notable exception is Duggan (2003), who argues that the FS/S is a poor proxy for studying suicide, even in cross-sectional analyses.
After reviewing the existing evidence, the committee urges more caution in using FS/S as a proxy for gun ownership. As Duggan points out, the most obvious statistical problems concern the circularity of using FS/S as a proxy in a study of suicide, but the properties of FS/S in other kinds of studies (e.g., homicide) have also not yet been well described.
There are three basic problems with the existing analysis of proxies of firearms access. First, there is the problem of the accuracy of self-reported measures of firearm access, the standard against which the proxies are being compared. The effects of nonresponse and erroneous response in the surveys of firearms ownership, and random sampling errors more generally, have not been investigated. Certainly, response errors alone—as described both in Chapters 2 and 5—may result in biased estimates of the true prevalence of gun ownership. Moreover, if persons who are at risk for attempting suicide are less likely to participate in a household survey than other persons, then household surveys may not reflect the true relationship between gun ownership and method choice among persons who are actually at risk of attempting suicide. Existing research does not yet shed much light on these possible biases.
Second, there is the problem of aggregation bias in the correlation analysis. The primary reason for using a proxy is that more direct gun ownership data may not be available at the appropriate level of aggregation. But even if the proxy is highly correlated with observed ownership rates at one geographic level, it need not be correlated with gun ownership in smaller areas or in subgroups of the population. To explore this possibility, the committee reexamined the correlation between FS/S and gun ownership levels using the individual GSS survey responses aggregated to the 100 primary sampling units rather than the 9 census regions. In this case, we estimated the correlation between the percentage of suicides committed with a firearm and ownership levels to be 0.646 for firearms of any type and 0.639 for handguns, substantially less than the correlations reported by Azrael et al. (2004).
A similar problem is presented in Figure 7-1, which displays the relationship between FS/S and household gun ownership by age and gender.