Ben, you single-handedly helped me pass my econometrics MSc course. I watched all videos after being referred by Loise, and it made much more sense than the in-class lectures. You're the man!
Dear Professor, I am a student studying econometrics in South Korea. Specifically, I am interested in topics related to instrumental variables (IV). Your online lectures are wonderful sources for studying causal inference, and I truly appreciate them! I have a question about the exclusion restriction. In one of your slides, you mentioned that this assumption is untestable. I’ve come across many lecture materials stating the same. However, in Hansen’s econometrics textbook, I found an overidentification (Sargan-Hansen) test, which sets the null hypothesis as an exclusion restriction. I’m curious if it is possible to test the exclusion restriction using the overidentification test. I don’t quite understand the difference between the two tests. Thank you!
Hi! The J-Test (Sargan-Hansen) is not applicable in most applications because we only have one instrument for one endogenous regressor. In that case (which is called "just identified"), one cannot test whether the instrument is exogenous. All we can do is bring good arguments why this might be the case (and remember: you need to bring good arguments in favour of conditional independence AND the exclusion restriction). Tests for overidentifying restrictions like Sargan-Hansen can be used in overidentified models, i.e. in models where the number of IVs exceeds the number of endogenous regressors (as is the case in Hansen's GMM estimator). In that case, one needs one instrument that is definitely exogenous and then one can test whether the other m-1 instruments are exogenous as well. But that has very few applications in contemporary applied micro. I would not recommend using any test where the null hypothesis is that a regressor or instrument is exogenous (such as Hausmann or Sargan-Hansen). You should assume that the regressor of interest IS endogenous and then explain why in your empirical setting, under certain conditions, it can be considered exogenous. I hope this helps. Ben
@@ben_elsner Thank you for your kind reply! So, the bottom line is that the J-test assumes that one instrument MUST be exogenous, and it tests that other instruments are also exogenous as long as at least one instrument IS exogenous. Thank you! I understand!
@@philhwang151 yes exactly. You need one instrument that is valid beyond any doubt and then you can test the exogeneity of the remaining instruments. That is almost impossible in most settings (with the exception of some combined IVs like Shift-Share IVs).
Mr Elsner i have a question please; why the instrument does not have a direct causal effect on the outcome. In other words, what is the results of violation of this assumption (exclusion restriction assumption). Thank you in advance.
If the exclusion restriction is violated, the estimates are inconsistent because the instrument also affects the outcome through a channel other than the treatment. So you may get estimates that are systematically larger or smaller than the true effect. In what direction the bias (correct term: inconsistency) goes depends on the context. But the bias can be derived.
