Judea Pearl points me to this discussion with Kosuke Imai at a conference on causal mediation. I continue to think that the most useful way to think about mediation is in terms of a joint or multivariate outcome, and I continue to think that if we want to understand mediation, we need to think about potential interventions or “instruments” in different places in a system. I think this is consistent with Pearl’s view although in different language. Recently I was talking with some colleagues about estimating effects of the city’s recent Vision Zero plan on reducing traffic deaths, and some of this thinking came up, that it makes sense to think about effects on crashes, injuries, serious injuries, and deaths. I also agree with Pearl (I think) that it’s generally important to have a substantive model of the process being studied. When I was a statistics student I was somehow given the impression that causal inference could, and even should, be done from a sort of black-box perspective. You have the treatment assignment, the outcomes, and you estimate the causal effect. But more and more it seems that this approach doesn’t work so well, that it really helps to understand at some level the causal mechanism.
Another way of putting it is that most effects are not large: they can’t be, there’s just not room in the world for zillions of large and consistent effects, it just wouldn’t be mathematically possible. So prior information is necessarily relevant in the design of a study. And, correspondingly, prior information will be useful, even crucial, in the analysis.
How does this relate to Pearl’s framework of causal inference? I’m not exactly sure, but I think when he’s using these graphs and estimating whether certain pathways are large and others are zero, that corresponds to a model of the world in which there are some outstanding large effects, and such a model can be appropriate in certain problem-situations where the user has prior knowledge, or is willing to make the prior assumption, that this is the case.
Anyway, perhaps the discussion of Imai and Pearl on these topics will interest you. Pearl writes, “Overall, the panel was illuminating, primarily due to the active participation of curious students. It gave me good reasons to believe that Political Science is destined to become a bastion of modern causal analysis.” That sounds good to me! My colleagues and I have been thinking about causal inference in political science for a long time, as in this 1990 paper. Political scientists didn’t talk much about causal inference at that time. Then a bunch of years later, political scientists started following economists in the over-use, or perhaps I should say, over-interpretation, of various trendy methods such as instrumental variables and regression discontinuity analysis. Don’t get me wrong—IV and RD are great, indeed Jennifer and I discuss both of them in our book—but there got to be a point where researchers would let the instrument or the discontinuity drive their work, rather than stepping back and thinking about their larger research aims. (We discuss one such example here.) A more encouraging trend in political science, with the work of Gerber and Green and others, is a seriousness about causal reasoning. One advantage of tying causal inference to field experiments, beyond all issues of identification, is that these experiments are expensive, which typically means that the people who conduct such an experiment have a sense that it might really work. Skin in the game. Prior information. Now I’m hoping that the field of political science is moving to a new maturity in thinking about causal inference, recognizing that we have various useful tools of design and analyses but not being blinded by them. I don’t agree with everything that Judea Pearl has written about causal inference, but one place I do agree with him is that causal reasoning is fundamental, and causal inference is too important to be restricted to clean settings with instruments, or discontinuities, or randomization. We need to go out and collect data and model the world.