This is a follow-up to my earlier post on techniques for observational studies. Sarah Hamersma, University of Florida Assistant Professor of Economics, has written a very nice set of lecture notes introducing instrumental variables. Anyone who understands ordinary least squares regression ought to be able to follow it. If you read it, be sure to stick with it all the way through until the “Pitfalls” section at the end. The points made there are crucial.
One thing not quite right is that Hamersma writes that there is no way to test for bad instruments, by which she means ones that fail to be exogenous (uncorrelated with u in her equation (3)). That’s not universally true. One can perform a test of “overidentifying restrictions” in cases for which there is more than one instrument. This test is described in Steve’s paper, though it can be found elsewhere.