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Appendix D Statistical Issues in the Evaluation of the Effects of Right-to-Carry Laws--Joel L. Horowitz
Appendix D Statistical Issues in the Evaluation of the Effects of Right-to-Carry Laws--Joel L. Horowitz
Pages 299-308
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From page 299... ...
The first relates to the difficulty of choosing the right explanatory variables for a model. The second relates to the difficulty of estimating the relation among crime rates, the explanatory variables, and the adoption of right-to-carry laws even if the correct explanatory variables are known.
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One possible solution to this problem consists of replacing the unobservable it by the difference between the crime rates after and before adoption of a right-to-carry law (in other words, carrying out a before-andafter study)
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laws are relatively Republican with large National Rifle Association memberships and low but rising rates of violent crime and property crime." Non-time-varying systematic differences among states are accounted for by the fixed effects, i , in Models 6.1 and 6.2 in Chapter 6. However, if there are time-varying factors that differ systematically among states with and without right-to-carry laws and that influence the laws' effects on crime, then the effects of enacting these laws in states that do not have them cannot be predicted from the experience of states that do have them, even if the other problems just described are not present.
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and Lott's response (Lott, 2000:213-215) .2 1This conclusion -- but with measures of health status in place of crime rates -- forms the justification for using randomized clinical trials to evaluate new drugs, medical devices, and medical procedures.
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estimated models in which future adoption of a right-to-carry law is used as an explanatory variable of crime levels prior to the law's adoption. He found a statistically significant relation between crime levels and future adoption of a right-to-carry law, even after controlling for what he calls "an array of explanatory variables." This result implies that there are systematic differences between adopting and nonadopting states that are not accounted for by the explanatory variables In other words, there are variables that affect crime rates but are not in the model, and it is possible that the omitted variables are the causes of any apparent effects of adoption of right-to-carry laws.4 3Bronars and Lott (1998)
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There is little prospect for achieving an empirically supportable agreement on the right set of variables. For this reason, in addition to the goodness-of-fit problems that are discussed next, it is unlikely that there can be an empirically based resolution of the question of whether Lott has reached the correct conclusions about the effects of right-to-carry laws on crime.5 ESTIMATING THE RELATION AMONG CRIME RATES, THE EXPLANATORY VARIABLES, AND ADOPTION OF RIGHT-TO-CARRY LAWS This section discusses the problem of estimating the average crime rate in counties that have the same values of a set of explanatory variables X and that have (or do not have)
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Nonparametric estimation is highly flexible and largely eliminates the possibility that the estimated model may not fit the data, but it has the serious drawback that the size of the data set needed to obtain estimates that are sufficiently precise to be useful increases very rapidly as the number of explanatory variables increases. This is called the curse of dimensionality.
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According to Model D.1, there is a statistically significant relation between the fraction of homeless and the indicator of rent control (p < 0.05) but not between homelessness and the vacancy rate (p > 0.10)
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Thus, the results of estimation in Model D.2 are consistent with the hypothesis that a low vacancy rate contributes to homelessness but rent control does not. In other words, Model D.1 and Model D.2 yield opposite conclusions about the effects of rent control and the vacancy rate on homelessness.
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1969 Tests for specification errors in classical linear least squares regression analysis. Journal of the Royal Statistical Society Series B 31(2)
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