8 Instrumental Variables (II)

In this lecture we focus on the logic of instrumental variables in the context of observational studies. We will also discuss a number of applied examples that use an IV strategy, paying attention to how they work, and how they can go wrong.

“We describe our lives, our big choices, in narratives that blend conviction and luck, articulate plan and stumbling, seizing opportunity and being in the wrong place at the wrong time. We may be less than candid with ourselves and others in these narratives, but few would deny a role to luck.”

The quote above, found in Paul Rosenbaum’s excellent “Observation and Experiment” book (p. 258), nicely illustrates how many IV designs come to be. While we may not believe that the treatment that we care about has been randomly assigned, we hope to find an instrument that means that some part of the variation in that treatment can be thought of as random. This week we cover a number of examples of both good and (often) bad candidates for plausible instrumental variables, many of which are featured in greater detail in this week’s reading list.

In addition, some of the more mechanical detail on two-stage least-squares estimation that we covered in the lecture can be found on pages 173-186 of MHE, and there is a nice discussion of the exclusion restriction (and the difficulty of testing that assumption empirically) on pages 301-303 of the Morgan and Winship textbook. Finally, if you are looking for a lighter read – and don’t mind spending some money on another causal inference book – you can have a look at the entire chapter on IV in the Rosenbaum book mentioned above. It is notable because it features a rare combination of clear explanation, detailed examples, and funny anecdotes. Not something you say every day about an econometrics book.

Finally, as a way to further nourish a healthy skepticism about instrumental variables in observational settings, you can find some good points in a recent paper from Lal et al (2024).

---