xtdpdgmm interpretation of overidentification test

[Tom Ford]

Hello I am running a two step GMM model using the xtdpdgmm command.

To examine the validity of my model I am using `estat overid` but I am a bit confise. I get two results one suggesting that my model passes the overidentification test, the other suggesting that I do not.

. estat overid

Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid

2-step moment functions, 2-step weighting matrix chi2(49) = 45.5558
Prob > chi2 = 0.6136

2-step moment functions, 3-step weighting matrix chi2(49) = 80.6907
Prob > chi2 = 0.0029

What is the difference between these two tests? and which one should I trust?

Sebastian Kripfganz

thanks a lot in advance for your help

Best

[Sebastian Kripfganz]

The two tests are asymptotically equivalent. The first is the one that is usually reported in published research articles. The second re-estimates the weighting matrix one more time based on the two-step estimation residuals. Any substantial difference between these tests would indicate a potential problem with the estimation of the weighting matrix, which in turn would cast doubt on the estimation results. The simplest explanation would be that there are still too many instruments.

[Tom Ford]

Thank you, this is really helpful!