Robust inference with GMM estimators

The local robustness properties of generalized method of moments (GMM) esti mators and of a broad class of GMM based tests are investigated in a unifie d framework. GMM statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the und erlying model is bounded. Since in many applications this function is unbou nded, it is useful to have procedures that modify the starting orthogonalit y conditions in order to obtain a robust version of a GMM estimator or test , We show how this can be obtained when a reference model for the data dist ribution can be assumed, We develop a flexible algorithm for constructing a robust GMM (RGMM) estimator leading to stable GMM test statistics. The amo unt of robustness can be controlled by an appropriate tuning constant. We r elate by an explicit formula the choice of this constant to the maximal adm issible bias on the level or land) the power of a GMM test and the amount o f contamination that one can reasonably assume given some information on th e data. Finally, we illustrate the RGMM methodology with some simulations o f an application to RGMM testing for conditional heteroscedasticity in a si mple linear autoregressive model. In this example we find a significant ins tability of the size and the power of a classical GMM testing procedure und er a non-normal conditional error distribution. On the other side, the RGMM testing procedures can control the size and the power of the test under no n-standard conditions while maintaining a satisfactory power under an appro ximatively normal conditional error distribution. (C) 2001 Elsevier Science S.A. All rights reserved. MSC: C12; C13; C14.