This paper studies the averaging generalized method of moments (GMM) estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. It is an alternative to pre-test estimators that switch between the conservative and aggressive estimators based on model specification tests. This averaging estimator is robust in the sense that it uniformly dominates the conservative estimator by reducing the risk under any degree of misspecification, whereas the pre-test estimators reduce the risk in parts of the parameter space and increase it in other parts.

To establish uniform dominance of one estimator over another, we establish asymptotic theories on uniform approximations of the finite-sample risk differences between two estimators. These asymptotic results are developed along drifting sequences of data generating processes (DGPs) that model various degrees of local misspecification as well as global misspecification. Extending seminal results on the James-Stein estimator, the uniform dominance is established in non-Gaussian semiparametric nonlinear models. The proposed averaging estimator is applied to estimate the human capital production function in a life-cycle labor supply model.