Cook and Ludwig (J Public Econ 90:379–391, 2006) use data on homicide rates and gun prevalence proxies from US counties over the period 1980–1999 and, in their panel data analysis, find a positive and statistically significant association between both variables. We reexamine their analysis and show that their findings are driven by spurious correlations arising from the use of a common denominator (ratio fallacy) to deflate both dependent and independent variables. When we attempt to replicate their results accounting for these issues, we no longer find any evidence that gun ownership is linked to homicides.
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Note, though, that Duggan (2001) and Lang (2013) estimate their models in first differences, which might mitigate the problems arising from the use of common denominators if the denominator was highly time persistent. Whether this is the case in their analyses would be an interesting venue for future research.
Sociodemographic controls for 1990 are taken directly from the Census Bureau’s 1990 census STF3A and not via the ICPSR study dataset 06054 as in C&L. Following C&L, we exclude the observation from Oklahoma County in 1995. A detailed list of variables and data sources is provided in “Appendix”.
Unfortunately, we could not use Cook and Ludwig’s original dataset and Stata codes. In our replication attempt, we modified our specification in several ways in order to achieve results matching those reported by C&L. For instance, we use population data from different sources for our analysis and apply different weights (e.g., average population, log population). However, our findings do not improve. It appears that there are some minor deviations between the descriptive statistics of the variables in our dataset and those reported by C&L. We believe that these differences are due to data revision.
Note that our sample contains two more observations than does C&L’s. Our findings remain robust when we include the years from 2000 to 2004 in our sample and when we employ a balanced panel dataset in which all counties with at least one missing observation are excluded.
Note the change in the sign of the population coefficient across Tables 2 and 3. In general, one might expect a positive association between population size and number of homicides. Moreover, given that our models include county-fixed effects and that the time period is relatively short, the population variable mainly captures differences in population density across counties. Hence, the negative sign of the estimate shown in Columns (2a) and (2b) appears to be counterintuitive. We believe, however, that the negative association is spurious and driven by the fact that population is also the denominator of the dependent variable in Eq. (1); that is, for a given number of homicides, an increase (decrease) in population size will lead to a decrease (increase) in the dependent variable. For that reason, we prefer the empirical specification of Eq. (2).
Results available on request.
With regard to the results for Eq. (1), the clustered standard error of the estimate for the gun prevalence proxy is 0.045 when control variables are omitted and 0.040 when employing the full set of controls (compared to 0.036 when computing Huber–White standard errors; see Table 1). Results available on request.
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Thanks to two anonymous reviewers, Michael Lechner (the editor), and participants of research seminars held in Göttingen and Marburg for their helpful comments on earlier versions of the paper. The usual disclaimer applies.
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Hayo, B., Neumeier, F. & Westphal, C. The social costs of gun ownership revisited. Empir Econ 56, 1–12 (2019). https://doi.org/10.1007/s00181-018-1496-6
- Gun ownership
- Social costs
- Ratio fallacy
- Spurious correlation
- Log ratio