Judea Pearl sends along this article and writes:
This research note was triggered by a discussant on your blog, who called my attention to Wooldridge’s paper, in response to my provocative question: “Has anyone seen a proof that adjusting for intemediary would introduce bias?”
It led to some interesting observations which I am now glad to share with your bloggers.
As Pearl writes, it is standard advice to adjust for all pre-treatment variables in an experiment or observational study–and I think everyone would agree on the point–but exactly how to “adjust” is not always clear. For example, you wouldn’t want to just throw an instrumental variable as another regression predictor. And this then leads to tricky questions of what to do with variables that are sort-of instruments and sort-of covariates. I don’t really know what to do in such situations, and maybe Pearl and Woolridge are pointing toward a useful way forward.
I’m curious what Rosenbaum and Rubin (both of whom are cited in Pearl’s article) have to say about this paper. And, of course, WWJD.