Adaptive Elastic Net GMM Estimation with Many Invalid Moment Conditions: Simultaneous Model and Moment Selection

Abstract

Abstract This paper develops a new estimator. An adaptive elastic-net GMM estimator with possibly many invalid moment conditions is shown. We allow for the number of structural parameters (p_{0}) as well as the number of moment conditions increase with the sample size (n). We do simultaneous model and moment selection. We estimate the structural parameters along with parameters attached with invalid moments. The basic idea is to conduct the standard GMM with combining two penalty terms: the quadratic regularization and the adaptively weighted lasso shrinkage. Given many orthogonality restrictions, including the invalid ones, the new estimator uses information only from the valid moment conditions to achieve the semiparametric efficiency bound. The estimator is thus very useful in practice since it conducts the consistent moment selection and efficient estimation of the structural parameters simultaneously. We also establish the order of magnitude for the smallest local to zero coefficient to be selected as nonzero. We apply the new estimation procedure to dynamic panel data models, where both the time and cross section dimensions are large. The new estimator is robust to possible serial correlations in the regression error term.