At The Monkey Cage, Andrew Gelman takes issue with my post on union density and tax collections by state. I argued that states with higher percentages of workers covered by collective-bargaining contracts have higher tax collections as a percentage of personal income, and that the relationship is probably causal. Gelman argues that it is inappropriate to infer causation from a correlation among observational data. My UB colleague Phil Arena offers a qualified defense of my post.
I more or less agree with the points Phil makes, as well as Gelman’s main point. Yes, correlation does not automatically mean causation, and in my original post I moved very quickly between the two without acknowledging the difference – not the sort of thing I would do in a journal article. Nevertheless, the most natural interpretation of my results is indeed causal. It does not seem plausible that higher taxes cause higher union densities (I can think of no reason why this should be the case). On the other hand, it is quite plausible that higher union densities cause higher taxes: in my state the education unions have been lobbying heavily against spending cuts and a proposed property tax cap. What about endogeneity due to omitted variables? Well, the most plausible one would be ideology: liberal states have higher unionization rates and higher taxes. But I controlled for ideology, and indeed even “overfitted” taxation to ideology with a squared term.
Finally, the dynamic analysis showed a correlation between unionization rates in 2000 and change in tax burdens over the next eight years, although it was not quite statistically significant. But because it’s a short time period, we shouldn’t expect taxes to change all that much. Most of the dependent variable is going to be statistical noise. The effect found is also substantively impressive, even if not statistically significant, and as Ziliak and McCloskey remind us, that’s often what we really want to know.
So yes, Gelman is right that correlation doesn’t automatically imply causation, but I nevertheless contend that the most plausible interpretation of the relationship between union densities and tax levels in the states is that the former are affecting the latter.