Back to normal

 This is a return to my usual kind of subject, although I may give an update on my adventures with predatory publishing in a future post.  

A few weeks ago, Andrew Gelman posted about a paper by Julia Cagé, Anna Dagorret, Pauline Grosjean, and Saumitra Jha that was published in the American Economic Review last year.  The paper argued that the experience of fighting in the battle of Verdun under Marshal Pétain created a sense of attachment, so that when Pétain turned to the extreme right and later headed the Vichy France regime, the municipalities that had supplied his troops (people from the same place generally served in the same unit) produced more collaborators.  Some critics had raised objections involving data quality, especially the list of collaborators, but I'll leave that aside and take the data as it is.

Elite leadership is important and frequently overlooked as an influence on public opinion, the authors seemed to have put a lot of effort into compiling and checking the data, the general method of analysis was appropriate, and there were a variety of robustness checks, so I was inclined to accept their conclusions.  But there were a few things that I wondered about.  They had two analyses, one a least squares regression with the log of collaborators per capita as the dependent variable, and the other a Poisson regression with the number of collaborators as the dependent variable (and including the log of the population as an independent variable).  In the first, the estimate for service with Pétain was .067 with a standard error of .018; in the second, the estimate was .190 with a standard error of .109.  They treated the first one as primary and described the second as showing that their "results were robust to Poisson estimation," but they didn't seem all that robust to me.  The Poisson estimate was almost three times as big, but the standard error was six times as big, so the 95% confidence interval went from -.024 to .404, or about -2.5% to +50%.   Also, the Poisson distribution applies when you count the number of events across a large number of independent cases, each with a small probability of experiencing the event.  But people in a town generally know and influence other people in the town, so one collaborator may recruit other collaborators, so the counts are likely to be "overdispersed" relative to what the Poisson distribution allows.  In this situation, the negative binomial distribution is appropriate, so I wanted to try it--maybe it would produce results more like those of the least squares regression.  I downloaded the replication data and reproduced their results and then fit a negative binomial regression.  The estimates for service with Pétain:

LS        Poisson        Negbin
.067        .190            .089
(.015)       (.014)        (.053)

The negative binomial regression fit much better than the Poisson regression.  The estimate was similar to that from the least squares regression, but the standard error was much bigger, and the 95% confidence interval is -.015 to .203.  Also, I show the ordinary standard errors--the robust, clustered standard errors that Cagé et al. used would be larger.  So there is only weak evidence, at best, that service under Pétain increased the number of collaborators.* 

In my next post, I'll discuss the more general implications of this analysis.  

*The also had results suggesting that service with Pétain affected electoral support for extreme right parties in the 1930s, and the points I've raised here don't apply to that analysis.