Estimating the Causal Effect of Gun Prevalence on Homicide Rates: A Local Average Treatment Effect Approach

This paper uses a "local average treatment effect" (LATE) framework in an attempt to disentangle the separate effects of criminal and noncriminal gun prevalence on violence rates. We first show that a number of previous studies have failed to properly address the problems of endogeneity, proxy validity, and heterogeneity in criminality. We demonstrate that the time series proxy problem is severe; previous panel data studies have used proxies that are essentially uncorrelated in time series with direct measures of gun relevance. We adopt instead a cross-section approach: we use US county-level data for 1990, and we proxy gun prevalence levels by the percent of suicides committed with guns, which recent research indicates is the best measure of gun levels for crosssectional research. We instrument gun levels with three plausibly exogenous instruments: subscriptions to outdoor sports magazines, voting preferences in the 1988 Presidential election, and numbers of military veterans. In our LATE framework, the estimated impact of gun prevalence is a weighted average of a possibly negative impact of noncriminal gun prevalence on homicide and a presumed positive impact of criminal gun prevalence. We find evidence of a significant negative impact, and interpret it as primarily "local to noncriminals", i.e., primarily determined by a negative deterrent effect of noncriminal gun prevalence. We also demonstrate that an ATE for gun prevalence that is positive, negative, or approximately zero are all entirely plausible and consistent with our estimates of a significant negative impact of noncriminal gun prevalence. The policy implications of our findings are perhaps best understood in the context of two hypothetical gun ban scenarios, the first more optimistic, the second more pessimistic and realistic. First, gun prohibition might reduce gun ownership equiproportionately among criminals and noncriminals, and the traditional ATE interpretation therefore applies. Our results above suggest that plausible estimates of the causal impact of an average reduction in gun prevalence include positive, nil, and negative effects on gun homicide rates, and hence no strong evidence in favor of or against such a measure. But it is highly unlikely that criminals would comply with gun prohibition to the same extent as noncriminals; indeed, it is virtually a tautology that criminals would violate a gun ban at a higher rate than noncriminals. Thus, under the more likely scenario that gun bans reduced gun levels more among noncriminals than criminals, the LATE interpretation of our results moves the range of possible impacts towards an increase in gun homicide rates because the decline in gun levels would primarily occur among those whose gun possession has predominantly negative effects on homicide.