Statistics and the Death Penalty 

 A few days ago, the AP moved a story reporting on academic studies of the deterrent effect of the death penalty on potential murderers.  Many media outlets picked up the story under headlines such as " Studies say death penalty deters crime ", " Death penalty works: studies ", and my favorite, " Do more executions mean fewer murders? "  Presumably the answer to the last question is yes, at least in the limit; if the state were to execute everyone (except the executioner, of course), clearly there would be fewer murderers.   

 I was surprised when I read the article on Monday morning,  since my sense of the state of play in this area is that it is probably impossible to tell one way or the other.  Those are the findings of a recent study by  Donohue and Wolfers , which finds most existing studies to be flawed and, more importantly, points out a variety of reasons why estimating the correct deterrent effect is difficult in principle.  Here is some of what  Andrew Gelman  had to say about their study last year: 

 My first comment is that death-penalty deterrence is a difficult topic to study. The treatment is observational, the data and the effect itself are aggregate, and changes in death-penalty policies are associated with other policy changes.... Much of the discussion of the deterrence studies reminds me of a little-known statistical principle, which is that statisticians (or, more generally, data analysts) look best when they are studying large, clear effects. This is a messy problem, and nobody is going to come out of it looking so great.

 My second comment is that a quick analysis of the data, at least since 1960, will find that homicide rates went up when the death penalty went away, and then homicide rates declined when the death penalty was re-instituted (see Figure 1 of the Donohue and Wolfers paper), and similar patterns have happened within states. So it's not a surprise that regression analyses have found a deterrent effect. But, as noted, the difficulties arise because of the observational nature of the treatment, and the fact that other policies are changed along with the death penalty. There are also various technical issues that arise, which Donohue and Wolfers discussed.  

 Given the tone of the article (and certainly the headlines), you would have thought that the Donohue and Wolfers paper had been overlooked by the reporter, but no: he cites it in the article, and he interviewed Justin Wolfers!  He seems to have missed the point, however; the issue is not that some studies say that "there is a deterrent effect" and some say "we're just not sure yet".  The problem is that we aren't sure, and we probably never will be unless someone gets to randomly assign death penalty policy to states or countries.  This raises a problem that we often face in social science: there are questions that are interesting, and there are questions that we can answer, and the intersection of those two categories is probably a lot smaller than any of us would like.  This doesn't seem to be a realization that has crept into the media as of yet, so it is no surprise that studies that purport to give answers to interesting questions will get more coverage than those pointing out why those answers probably don't mean very much.