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I don't know if linearmodels accept the new GMM models - I reproduced the following paper (correction for finite error identification, and iterative updated GMM models dealing with cluster with Over-identification J-test) on python, and got results consistent with the source code. I would love to have my code as part of linearmodels if possible.
INFERENCE FOR ITERATED GMM UNDER MISSPECIFICATION, BRUCE E. HANSEN, SEOJEONG LEE,Econometrica, Vol. 89, No. 3 (May, 2021), 1419–1447