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

This paper develops an adaptive elastic-net GMM estimator with many possibly invalid moment conditions. We allow for the number of structural parameters (p0) as well as the number of moment conditions increasing with the sample size (n). The new estimator conducts simultaneous model and moment selection. We estimate the structural parameters along with parameters associated with the invalid moments. The basic idea is to conduct the standard GMM combined with two penalty terms: the quadratic regularization and the adaptively weighted LASSO shrinkage. The new estimator uses information only from the valid moment conditions to estimate the structural parameters and 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 time and cross section dimensions are large. The new estimator is robust to possible serial correlations in the error terms of dynamic panel models.