Two-stage Huber estimation

In this paper we propose a new robust estimator in the context of two-stage estimation methods directed towards the correction of endogeneity problems in linear models. Our estimator is a combination of Huber estimators for each of the two stages, with scale corrections implemented using preliminary median absolute deviation estimators. In this way we obtain a two-stage estimation procedure that is an interesting compromise between concerns of simplicity of calculation, robustness and efficiency. This method compares well with other possible estimators such as two-stage least-squares (2SLS) and two-stage least-absolute-deviations (2SLAD), asymptotically and in finite samples. It is notably interesting to deal with contamination affecting more heavily the distribution tails than a few outliers and not losing as much efficiency as other popular estimators in that case, e.g. under normality. An additional originality resides in the fact that we deal with random regressors and asymmetric errors, which is not often the case in the literature on robust estimators.