A call for a truce in the DGU war.

AuthorSmith, Tom W.
PositionDefensive gun use

For almost a decade scholars have been debating about how

many defensive gun uses (DGUs) occur annually. Gary Kleck and

colleagues,(1) citing a series of polls culminating in the 1993 Kleck-Gertz

survey, argue that at least 2.55 million people use a firearm for

protection against criminals each year. Hemenway and others,(2) relying on

the National Crime Victimization Surveys (NCVSs), contend that only

about 55,000 to 80,000 victims use guns against offenders in a given

year. The estimates are wide apart and their academic champions

staunchly defend their respective figures as correct and accurate,

while dismissing the opposing figures as invalid and implausible.

Neither side seems to be willing to give ground or see their

opponents' point of view. This is unfortunate since there is good reason to

believe that both sides are off-the-mark. Below the main shortcomings

of the two approaches and some of the keys issues of contention are


First, it appears that the estimates of the NCVSs are too low.

There are two chief reasons for this. First, only DGUs that are

reported as part of a victim's response to a specified crime are

potentially covered. While most major felonies are covered by the NCVSs, a

number of crimes such as trespassing, vandalism, and malicious

mischief are not. DGUs in response to these and other events beyond the

scope of the NCVSs are missed.

Second, the NCVSs do not directly inquire about DGUs. After a

covered crime has been reported, the victim is asked if he or she "did

or tried to do [anything] about the incident while it was going on.

Indirect questions that rely on a respondent volunteering a specific

element as part of a broad and unfocused inquiry uniformly lead to

undercounts of the particular of interest.(3)

However, some other proposed reasons for under-reporting on

the NCVSs are questionable. The claim that DGUs are

under-reported because the NCVSs suffer from "the taint of being conducted

by, and on behalf of employees of the federal government"(4) and that

respondents see themselves in effect as "speaking to a law

enforcement arm of the federal government"(5) is improbable. The survey

literature does not indicate that Bureau of the Census surveys are held

in special suspicion.(6) If anything, it indicates that cooperation is

greater than usual in part because of the high quality of Census

interviewers and because most people accord the Bureau of the Census

more legitimacy than given to other surveys.(7)

Second, the estimates of the Kleck-Gertz study and other

cross-sectional surveys using a direct question are too high. First, unlike the

panel NCVs which uses bounded recall to minimize telescoping (i.e.,

the misreporting of past events as having occurred within a more

recent specified time period), nothing in these surveys mitigates against

such over-reporting. Kleck and Gertz (K-G) are correct to note that

forgetting would tend to off-set errors from telescoping,(8) but these

two cognitive errors are rarely balanced. While no definitive study of

the relative telescoping versus forgetting rate for DGUs exists, given a

one-year reference period and the saliency of DGUs, it is likely that

telescoping is greater than forgetting.(9)

Second, there is a significant amount of sampling error around

the direct DGU estimates. While K-G are correct that, broadly

speaking, all of the direct estimates are compatible with one another (i.e.,

probably mostly within the confidence intervals),(10) this is in part

because the sampling variation is often rather large. To say that the

high-end K-G estimate is not statistically implausible, given results

from other similar surveys, is not to say that it is correct. What is

needed is a meta-analysis that takes comparable estimates from similar

surveys and produces the best overall estimate. Since the K-G estimate

is near the high end of the range of estimates based on national

samples covering specific reference periods, this means that the best

estimate is lower. Giving equal weight to all estimates,(11) the composite

annual estimate based on one-year recall would be 1.81-2.01 million,

the annual estimate based on five-year recall period would be about

1.34-1.38, using the K-G multiple occurrence adjustment, and around

0.9-1.0 without that revision (Table 1).(12)


Number of Adults with DGUs per annum


Based on One Based on Five Study Variant Year Recall Year Recall K-G 1993(13) A 2.55 1.88 K-G 1993 B 2.16 1.68 K-G (Hart, 1981)(14) 1.80 K-G (Mauser, 1990) 1.49 K-G (Tarrance, 1994) 0.76 NSPOF(15) 1 1.46 0.65 NSPOF(16) 2 1.46 0.97

Third, as Hemenway (H) points out, the K-G estimate is likely to

suffer from false positives,(17) although the situation is not nearly as

clear as H asserts. As K-G note in their response to H's critique, the

basic medical misreport model assumes that the errors are random.(18)

As such, the rarer the event the greater the over-reports because there

are many more true negatives that can be "accidently" misclassified as

false positives than there are true positives that could by chance be

misreported as false negatives. In medicine, this problem is addressed

by a definitive and independent follow-up test to confirm or refute the

more error-prone, screening test. K-G in effect argue that they apply

such a test, by asking up to nineteen follow-up questions to verify that

the reported positive is a true rather than a false positive.(19) To their

credit, they use these follow-ups to eliminate both probable and some

possible false positives.

But there are two serious limitations to this procedure. First, the


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