Thought I just submitted a comment, but it looks like it didn’t go through. Apologies if this is posted twice.
I was a bit confused by both this blog post and the Aronow and Samii paper. I haven’t read the Aronow and Samii paper, but it seems like they are just reiterating the often forgotten point that linear regression doesn’t consistently estimate average treatment effects in some situations where people think it does (namely, when there are heterogeneous treatment effects). This is a good point, but one that seems irrelevant to the debate over whether there is any potential advantage of quasi-experimental techniques in terms of increased external validity since matching and other similar methods don’t suffer this same disadvantage.
I, and probably many other readers of this blog, have long assumed that even though there is a potential theoretical advantage of quasi-experimental techniques in terms of increased external validity this doesn’t matter in practice due to the bias of quasi-experimental methods. This paper (which I also have read) calls this assumption into question: http://www.cgdev.org/publication/context-matters-size-why-external-validity-claims-and-development-practice-dont-mix
I would be very interested in hearing your thoughts on this.