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Firearms and Violence: A Critical Review
BOX 7-2 Monte Carlo Experiment
There is not enough information available from the published Monte Carlo design (Miller et al., 2002a, 2002b) to enable someone to replicate it. However, the committee did a Monte Carlo experiment that implied quite different results. The Monte Carlo simulates a study of the relation between the suicide rate and FS/S as a proxy for gun ownership. Let Z1, Z2, and Z3 denote unobserved independent standard normal variables, and let
FS = 10 + Z1;
NFS = 6 + Z2;
FS/S = FS/(FS + NFS);
POP = 50 + Z3; and
RATE = (FS +NFS)/POP,
where FS is the number of firearm suicides, NFS is the number of nonfirearm suicides, POP is the population size, and RATE is the total suicide rate for the population. With 1,000 replications, this design gave a mean value of FS/S in the neighborhood of 0.6 (similar to the fraction of suicides currently committed with a firearm in the United States). The correlation coefficient of FS/S and RATE was –0.29. The linear regression of RATE on FS/S gave a slope coefficient of –0.18 with a t-statistic of 9.6. So, according to this simulation, there is a negative association between the suicide rate and FS/S. In other words, if FS/S is a good proxy for ownership, gun owners are less likely than nonowners to commit suicide.
obvious why the simulation is at all relevant: the basic finding that proxies create biases is an analytical result that cannot be resolved by a simulation. It is very easy to create other plausible simulations that lead to substantial correlations between FS/S and suicide and, more importantly, substantial biases in the estimated relations of interest.
In Box 7-2, for example, we present the results of a simulation conducted by the committee. In this Monte Carlo simulation, we study the relation between the suicide rate and FS/S as a proxy for gun ownership, but we derive very different results than those reported by Miller et al. (2002a, 2002c). In particular, we find a negative association between the suicide rate and FS/S: in this simulation, if FS/S is a good proxy for ownership, gun owners are less likely than nonowners to commit suicide.
This exercise illustrates at least two things: (1) the design of the Monte Carlo simulation matters and (2) having suicide-related variables on both sides of the regression can produce perverse results. In the end, the biases created by proxy measures are application specific. Duggan (2003), for example, highlights the potential problems caused by using FS/S as an explanatory variable in a model whose dependent variable is also suicide-related. As demonstrated in the simulation above, unobserved factors associated with
