I was wondering if you wouldn’t mind writing a post on 3SLS. I recently sent in a research proposal and part of the feedback I got was that 3SLS was “outdated” and that I needed to find a natural experiment or a good instrument. What do we do when these things aren’t readily available?
Good question. Let me delay the answer a bit to talk about whether three-stage least squares (3SLS) is outdated.
First, a refresher on 3SLS (which I needed myself, as it has been at least 12 years since I haven’t thought about that estimator): 3SLS is 2SLS applied to a system of equations (e.g., a supply equation and a demand equation). Why would you want to apply 2SLS to a system of equations? Two reasons:
- Each equation in your system has one or more endogenous regressor on the right-hand side (RHS), and
- You want to take into account the fact that the error terms are correlated across the equations in the system.
In other words, in order to minimize bias (the 2SLS part) and maximize precision (the system part). Thus if you have endogeneity issues across a system of equations (e.g., an equation for quantity supplied, and an equation for quantity demanded, both with endogenous prices on the RHS), it might seem like a good idea to kill two birds with one stone by estimating both equations simultaneously by 3SLS. Continue reading