Hansen Test and Sargan Test

[zaineb belkhiria]

Hello everyone.
I hope you could assist me.
I am using the two-step GMM model. Below the estimation table, Stata shows me the Sargan test and the Hansen test. I didn't understand exactly the difference between these two tests.
What is their H0 and their alternative hypotheses H1 ?
How can I validate my model using these two tests?
Thank you for your time and assistance.

[Sebastian Kripfganz]

The null hypothesis is that all overidentifying restrictions are valid; the alternative hypothesis is that at least one of them is invalid. Not rejecting the null hypothesis - while desirable - is providing only limited information. It does not imply that your model is correctly specified, which still relies on untestable assumptions. A rejection of the null hypothesis - clearly undesirable - could indicate that there is some model misspecification, although it might not be specific about the nature of the misspecification. The Sargan test (for one-step GMM) makes stronger assumptions about the model's error term than the Hansen test. With two-step GMM, only the Hansen test is relevant.

More on this topic:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.
• Kiviet, J. F., and S. Kripfganz (2021). Instrument approval by the Sargan test and its consequences for coefficient estimation. Economics Letters 205, 109935.

[zaineb belkhiria]

Thank you so much for the response.
If I understand the hansen test correctly, the H0 indicates that the instruments are valid. right ?

[Sebastian Kripfganz]

Not precisely. Suppose you have K regressors and L>K instruments. You can think about the Hansen test as checking whether L-K instruments - the overidentifying restrictions - are valid, assuming that there are already K valid instruments. You can never test the joint validity of all instruments. Moreover, unless you have a very strong prior about which K instruments are valid by assumption, a rejection of the test would not even tell you which L-K instruments are invalid. In that regard, the test can never give you a definite answer but only an indication if there could be some concerns.

[zaineb belkhiria]

Thank you very much.