One thing I often see authors doing in some of the papers I get to handle as an editor or comment on as a reviewer is using a Durbin-Wu-Hausman test–for the sake of brevity, I will just say “Hausman test” throughout this post–to test for exogeneity. The idea for this post came from my reading of Jeff Woolridge’s article on the control function approach (more on that approach in a moment, and yes, the same Wooldridge who wrote what is perhaps the best microeconometrics text on the market) in the latest issue of JHR.
Typically, this is done in an effort to argue that some variable of interest is not really endogenous to the outcome of interest, and it proceeds as follows (note that I am describing a situation where researchers have to rely on observational data):