Instrumental variable regression_ Exclusion test

[Fimi Karimi]

Hi everyone,

I need to use instrumental variable regression in my project to address an endogeneity problem. I have conducted the under-identification test and weak instrument test (using the Kleibergen-Paap rk LM statistic and the Cragg-Donald Wald statistic) and results were satisfying. I read that the test for the exclusion of variables is the Hansen J-test, but when I run it, I get "exactly identified" because I have only one instrument. My model includes one endogenous variable and one instrument.

Could you please let me know if there is another way to test this? I found literature that this instrument affect my endogenous variable and in first stage regression they are correlated.

[Andrew Musau]

Statistical tests used to assess the validity of over-identifying restrictions, cannot be applied when there are no extra instruments. You can only establish relevance of the instrument by showing that it is strongly correlated with the endogenous variable it is intended to replace. This is tested empirically using the first-stage regression, where the endogenous variable is regressed on the instrument. When it comes to exogeneity of the instrument (instrument is uncorrelated with the error term in the structural equation), you must rely on economic theory, prior research, or institutional knowledge to argue that the instrument satisfies this condition.

[Tomas Reissling]

HI Andrew: I peformed these tests but a journal reviewer asked that I also perform balance and placebo tests. I am using xtivreg. I am completely unfamiliar with approach and am finding limited information on it for IV regressions. Can you advise?

[Andrew Musau]

Placebo tests can only provide indirect evidence of validity. Failure to reject the null hypothesis (that the instrument has no effect on the placebo outcome) does not guarantee that the instrument is valid. There are many resources that discuss these if you search. See, e.g., https://chabefer.github.io/STCI/Placebo.html.

[Tomas Reissling]

Andrew, thank you for taking the time to answer my question and for sharing this resource, esp. on a Sunday.

May I take up a little bit more of your time regarding implementation for an IV regression?

Do I simply identify a pre-treatment variable and regress the instrument(s) on it. And, if the instrument(s) are not statistically related to the pre-treatment variable, this is indirect evidence that the instrument(s) is valid?

[Andrew Musau]

Exactly. If your study, e.g., examines the effect of education on wages using distance to college as an instrument, you might use political preferences or unrelated health outcomes as placebo outcomes to test whether distance to college influences them.

regress y_placebo distance_to_college

Following the placebo regression, look at the coefficient on the instrument (distance to college). If distance to college significantly predicts y_placebo, this raises concerns about instrument validity.

[Fimi Karimi]

#2: Andrew, thank you so much for your helpful explanations and comments.

[Tomas Reissling]

Yes, thank you very much, Andrew!