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

This paper develops the adaptive elastic net GMM estimator in large dimensional models with many possibly invalid moment conditions, where both the number of structural parameters and the number of moment conditions may increase with the sample size. The basic idea is to conduct the standard GMM estimation combined with two penalty terms: the quadratic regularization and the adaptively weighted lasso shrinkage. The new estimation procedure consistently selects both the nonzero structural parameters and the valid moment conditions. At the same time, it uses information only from the valid moment conditions to estimate the selected structural parameters and thus achieves the standard GMM efficiency bound as if we know the valid moment conditions ex ante. It is shown that the quadratic regularization is important to obtain the efficient estimator. We also study the tuning parameter choice, with which we show that selection consistency still holds without assuming Gaussianity. 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 terms. Keywords and phrases: Adaptive Elastic Net, GMM, many invalid moments, large dimensional models, efficiency bound, tuning parameter choice, dynamic panel.