Adaptive GMM Shrinkage Estimation with Consistent Moment Selection

Abstract

This paper proposes a GMM shrinkage method to efficiently estimate the unknown parameters identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties, i.e. it consistently selects the correct moment conditions in the second set and at the same time, its estimator achieves the semi-parametric efficiency bound implied by all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify the structural parameters. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981) and Altonji (1986). Our empirical findings support the validity of the IVs used in both papers and confirm that wage is an endogenous variable in the labor supply equation.