Hansen Test

[Rania Shahine]

If I get p-values of the Hansen test for a set of System GMM regressions as follows; 0.0858, 0.0915, 0.0656. Is it safe to use the 0.05 significance level and conclude that I fail to reject the null hypothesis of the Hansen test and that my set of instruments are overidentified? I understand that exceeding the 0.1 significance level would be better, but what if I couldn't get these any higher? Would that be okay?
Thanks!

[Joro Kolev]

The null hypothesis in the Hansen test is that the over-identifying restrictions hold (i.e., that are valid), and not what you are saying.

These are very low p-values presenting strong evidence that either your over-identifying restrictions do not hold, or some other assumptions are violated.

Under the correct null hypothesis and the other assumptions needed to derive the distribution of the test statistic, the p-value is distributed as standard uniform.

The expectation of a standard uniform random variable is 1/2 and the standard deviation is sqrt(1/12) = .28867513

Therefore in this context I take it as bad news seeing p-values less than say 21%.

[Sebastian Kripfganz]

In this kind of models, not rejecting the null hypothesis when it is indeed false (type-II error), thus wrongly accepting a misspecified model, has potentially more severe consequences than rejecting the null hypothesis when it is actually true (type-I error). It is therefore advisable to choose a higher significance level than the usual 5%. Ideally, the p-value should even be considerably higher than 10%. Since you are using a system GMM estimator, you might want to relax some of your assumptions and initially look at a difference GMM estimator only.

You can find some rough guidance on model selection in my 2019 London Stata Conference presentation:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Rania Shahine]

Great, thank you so much Joro and Sebastian for your help!