The properties of L_p-GMM estimators

This paper considers generalized method of moment-type estimators for which a criterion function is minimized that is not the "standard" quadratic distance measure but instead is a general L_p distance measure. It is shown that the resulting estimators are root-n consistent but not in general asymptotically normally distributed, and we derive the limit distribution of these estimators. In addition, we prove that it is not possible to obtain estimators that are more efficient than the "usual" L₂-GMM estimators by considering L_p-GMM estimators. We also consider the issue of the choice of the weight matrix for L_p-GMM estimators.