Maximum likelihood vs generalized method of moments From the answer to the above question, we can draw a conclusion that GMM and ML can get the same parameters' estimators when the model is exactly identified and the weight matrix in GMM is an identity one. In this case, the estimators' variance from the two methods will not same. So the significance test based on GMM's variance estimator will be more reliable, especially when the regularity conditions for a model's error items are not met. Is it right?