robust estimation, trimming The generalized method of moments (GMM; Hansen, 1982) is an important econometric tool for estimation and inference in models based on moment conditions. Minimizing a squared norm of moment conditions, which are typically unbounded, GMM can be very sensitive to data contamination or heterogeneity not presumed by a model. To address the lack of robustness of the standard GMM, various GMM-type methods robust to small deviations from the assumed model were developed, either for specific models such as instrumental variable regression or fully general. These methods are typically based on M-estimation or M-moments (e.g., Krisnakumar and Ronchetti, 1997; Ronchetti and Trojani, 2001) or on median or quantile conditions (e.g., Honore and Hu, 2004; Chernozhukov and Hansen, 2008), and consequently, they are only locally robust (e.g., see Ronchetti and Trojani, 2001). Even though the M-estimators can be made more robust by means of one-step estimation as in Wagenvoort and Waldman (2002), for instance, such a procedure nevertheless requires an initial highly robust estimator, which is not available for general GMM estimation so far
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