Thursday, November 29, 2007

Instrumental Variables in Reverse

Here's a proposition about using instrumental variables for causal effects that Kelly makes based on 1998 and 2000 papers by Robert Erikson and Thomas Palfrey on campaign spending and electoral success (find the papers in Google Scholar here):

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:

Andrew Gelman said...

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.

Cyrus said...

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.