Dear Mr. Reynolds:
Given the attention that the exchange on Right-to-Carry Laws in the Stanford Law Review has received on InstaPundit, I would like to emphasize a few points that seem to have gotten lost in the public debate on this topic:
The piece that John Whitley and I prepared for the Stanford Law Review can be divided into two parts:
(a) a response to the analysis by Ayres and Donohue, using only their own published results (pp.1317-1335 and pp.1357-1364).
(b) an analysis of an extended data set with data from 1977 to 2000 (pp.1336-1357).
In their response to Whitley and my paper, Ayres and Donohue have pointed out that our extended data set contains errors. Correction of these errors leads to estimates that differ from those that we published in our paper in Tables 3 – 8. As far as I can tell, the public discussion of the three papers in the Stanford Law Review has focused exclusively on this fact, and has used it as a reason to dismiss our entire paper as irrelevant.
I suggest that those who participate in the debate consider the following two points:
errors in our data set do not affect our comments of Ayres and Donohue’s
analysis (pp.1317-1335 and pp.1357-1364), because these refer to Ayres and
Donohue’s own interpretation of their estimates. To mention only two of our various comments:
(i) Ayres and Donohue put much emphasis on the results of their “hybrid” model. We explain why we disagree with their interpretation of this model and therefore with their interpretations of their own estimation results (pp. 1326-1329, see especially our Figure 2).
(ii) We argue that it is incorrect to analyze count data with Ayres and Donohue's least-squares method, and that a count analysis with, for example, a Poisson model would be more appropriate (the first two paragraphs on p.1354).
fact that a least-squares analysis of count data is inappropriate is
well known by econometricians. In 2001, Nic Tideman and I published a
paper in the Journal of Law and Economics that specifically addresses this
problem in the context of the county-level crime data. That paper contains
a Monte Carlo analysis that shows the significant distortions that one gets
if one analyzes the crime data with least-squares methods.
Ayres and Donohue do not even acknowledge this problem that plagues all of their analyses. They also decided not to cite Nic Tideman’s and my paper in their footnote 3 (p.1197) among the papers that are supportive of the “More Guns Less Crime” thesis, even though our paper appeared in the same issue of the Journal of Law and Economics as several other papers that they cite. Any econometrician will agree that this ought to be one of the most relevant issues in the whole debate. However, the public debate (as well as Ayres and Donohue in their response to our paper) decided to completely ignore this issue.
In short, the fact that the extended dataset had errors does not provide card blanche to dismiss those comments that are not based on the extended data set. Even if one decides to completely ignore the results of the extended data set that we report on pp.1336-1357, it is still necessary to acknowledge (and address) our criticism of Ayres and Donohue’s own analysis. As far as I can tell, the public debate has not done this. Even Chris Mooney decided not to address our criticism in his MotherJones article.
(b) Our analysis of the extended data set included a technical method called “clustering by state.” If one analyzes the corrected 1977-2000 data set with this method, then some of the results become insignificantly different from zero. If one analyzes the corrected data set without this method, then the results remain statistically different from zero.
In their response to our paper, Ayres and Donohue have analyzed the extended data set using “clustering by state,” thereby replicating the analysis that we reported in our Table 3a. The public debate has used their results as an argument that the results that we published are flawed (although there has been no discussion of our results in the other tables), and that Ayres and Donohue have made a convincing case against “More Guns Less Crime.”
However, Ayres and Donohue (1) do not use “clustering by state” in any of their own analyses, and (2) do not even mention that they use “clustering by state” when they repeat our analysis with the corrected data set.
Ayres and Donohue (as well as everybody who agrees with their work) need to decide:
(i) either “clustering by state” is necessary, which means that Ayres and Donohue correctly use “clustering by state” when they repeat our analysis. In this case, all of Ayres and Donohue’s own estimates are wrong, because these estimates are obtained without “clustering by state.” This makes it impossible to claim that Ayres and Donohue have made a convincing case against “More Guns Less Crime.”
(ii) or “clustering by state” is not necessary. In this case, one cannot criticize Ayres and Donohue’s own estimates on the basis that they do not include clustering. But this implies that “clustering by state” is also inappropriate in our own analysis as well as in Ayres and Donohue’s repetition. If one omits “clustering by state,” then the results that one obtains with the corrected data set are very similar to the results that one obtains with the data set that we used. This makes it impossible to argue that Ayres and Donohue have shown that our results are incorrect.
You cannot have it both ways.
Assistant Professor of Economics
State University of New York at Binghamton