Suppose that A causes B and B causes A. We want to estimate the effect of A on B. Typically, we are told that we need an instrument for A to isolate these effects. The challenge of finding an instrument for A is often insurmountable. But the Erikson/Palfrey paper proposes that if certain restrictions are met, we can identify the effect of A on B by first finding an instrument for B, then identifying B's effect on A, and then using that to identify the effect of A on B. If it is possible to find an instrument for B, then we have solved our problem.
So this will be a running post. I haven't read the papers yet, but it would be good to know more about the restrictions of such an approach.
2 comments:
In the "chapter 9 and 10" approach, you don't say A causes B and B causes A. The thing that causes is an intervention, the thing that is caused is an outcome; they're not really parallel. We discuss in the book an example of policing and crime, I think. Can discuss more in class if you'd like.
Sure. The phrasing was just a shorthand way of describing this kind of two-way relationship.
For all others not aware yet, Andrew is referring to Chs 9 and 10 in Gelman/Hill. On Thursday 12/6 at 11am there will be a debate between Andrew and Piero on "Plausibly exogenous instrumental variables in comparative politics." Ch 9 and 10 from Gelman/Hill are required reading before the discussion.
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