Ivreg2 -Endogeneity and Hansen J statistics

[Shabeen Basha]

Hello all,

I'm currently working on a cross-section with iveg2 (gmm2s to address the heteroskedasticity in my data) . My baseline model passes the instrument validity and endogeneity tests. But when I go for channel testing with addition of other variables and interactions, sometimes I have a insignificant Hansen J statistic with insignificant Endogeneity test statistic and other times the opposite. As per my understanding, an insignificant Endogeneity test statistic would mean one of my instrument is exogenous but I'm confused how the joint test statistic (Hansen J) shows valid instruments.

Should I drop all the channels that have contradictory statistics or give preference to the validity of instruments over endogeneity test. Please note , I ran correlations before using the instruments, the instruments are not correlated with the dependent variable and are correlated with the endogenous variable . Also , the first stage R-squared is in the range of 16-21% depending on the set of instruments used . I also tried my model with only one instrument but ivreg2 does not have an option to check validity with one instrument. I have been looking for references that can guide me on this but a solution for this situation is not discussed other than looking for other set of instruments .

I would highly appreciate any support on this that will help me proceed with my analysis.

Thank you .

Regards,
Shabeen

[Sebastian Kripfganz]

The endogeneity test relies on the validity of the instruments. Thus, if the Hansen test rejects the null hypothesis that the overidentifying restrictions are valid, then the endogeneity test becomes essentially useless. Note that you can never test for the joint validity of all instruments, as the untestable assumption needs to be maintained that at least as many excluded instruments are valid as there are endogenous regressors. This also implies that testing the validity of a single instrument is not possible if that is the only instrument.

Raw correlations can be misleading. What matters is the partial correlation after accounting for the effect of the exogenous regressors. In that spirit, the first-stage partial R^2 should be more informative than the overall first-stage R^2. Even better, look at the weak identification / underidentification statistics.

[Shabeen Basha]

Thank you very much for the response Prof. Kripfganz . I now understand the Hansen and endogeneity tests better. I looked at the weak identification and under identification statistics, although it is significant, the Kleibergen-Paap rk Wald F statistic is inflated (over 1000). I tried the partialling out option and the endogenous variable is significant and has some explanatory power.

Should I be concerned with the very high under identification/ weak identification statistics. I control for industry effects (20 industries) and have one quadratic term in the baseline model. Other models include interaction with the endogenous variable with the following format of codes:

ivreg2 y x1 x2 c.x3##c.x3 (x4 c.x4#c.x2 = z1 z2 c.x2#c.z1 c.x2#c.z1) , gmm2s endog(x4) robust - for continuous moderators

ivreg2 y x1 c.x3##c.x3 (x4 c.x4#x2 = z1 z2 x2#c.z1 x2#c.z1), gmm2s endog(x4) robust - for dummy moderator variables

ivreg2 y x1 i.x2 c.x3##c.x3 (x4 c.x4#i.x2 = z1 z2 i.x2#c.z1 i.x2#c.z1),gmm2s endog(x4) robust - for other categorical moderator variables

Thank you once again for your kind support.

Best regards,
Shabeen

[Sebastian Kripfganz]

A large Kleibergen-Paap statistic is generally a good thing because you reject the null hypothesis of underidentification. In principle, if your instruments are highly correlated with your regressors, this could be reflected in the very large underidentification statistic. While you do not want the instruments to be weak, a too strong correlation could also be problematic. The more correlated/similar the instrument and the regressor are, the more difficult it becomes to justify that the instrument is exogenous while the regressor is endogenous.

I do not think I can say much about the interaction terms.

[Shabeen Basha]

Thank you Prof. Sebastian Kripfganz for your kind response.

Best regards,
Shabeen

[Dao DinhNguyen]

Dear Prof. Sebastian Kripfganz

Your comment "Thus, if the Hansen test rejects the null hypothesis that the overidentifying restrictions are valid, then the endogeneity test becomes essentially useless" is very useful for me. Thank you so much!
I really appreciate it if you could please recommend me a book or paper to discuss choosing which IV tests are suitable. Sometimes my work also shows that the Hansen test rejects the null hypothesis of overidentifying restriction, but I failed to reject the endogeneity test. I don't know how to explain it mathematically or theoretically.

Best wishes,
Dao Nguyen

[Muhammad Ejaz]

Hello everyone,
I am looking for a comprehensive course to learn GMM, 2SLS along with econometrics theories because I want to do panel data analysis that may involve endogenous variables. Can anyone suggest? plz