Intuition for tight bounds under noncompliance
From Erich Battistin, University College, London:
I'm a Ph.D. student in statistics at the Dept. of Economics of UCL, London; in the last few months I went through your papers (and your book) about causality – in particular, I paid more attention to your result on the improvement of Manski's bounds on treatment effects when we have imperfect compliance. This result is certainly powerful but – leaving out technicalities – I don't really understand which information your approach exploits that the one by Manski does not. What is the intuition behind? I didn't find this point explained in any paper I read (but obviously to deal with an 'econometric-based' audience as the one here at UCL you need to make this point clear).
We used the same information as that used by Manski, but we managed to derive the tight bounds. As I state in my book (page 269) Manski's bounds happen to be tight under certain conditions, e.g., no contrarians. This means that one can get narrower bounds ONLY when there are contrarians in the population, as in the examples discussed in reference (Pearl 1995b). It is shown there how data representing the presence of contrarians can provide enough information to make the bounds collapse even to a point. This reference (R-203-AIM) also gives intuitive explanation of how this can happen.
Best wishes,
========Judea Pearl
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