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This paper studies how identification is affected in GMM estimation as the number of moment conditions increases. We develop a general asymptotic theory extending the set up of Chao and Swanson and Antoine and Renault to the case where moment conditions have heterogeneous identification strengths and the number of them may diverge to infinity with the sample size. We also allow the models to be locally misspecified and examine how the asymptotic theory is affected by the degree ofdoi:10.6084/m9.figshare.12845117.v1 fatcat:gxnozxlkxndcjmgqgr76vals6a