Further Results on the Weak Instruments Problem of the System GMM Estimator in Dynamic Panel Data Models

Abstract

In this paper, we investigate the weak instruments problem of the generalized method of moments (GMM) estimator for dynamic panel data models. Bun and Windmeijer (2010) demonstrate that the system GMM estimator combining models in first differences and levels suffers from the weak instruments problem when the variance ratio of the individual fixed effects to the errors is large, mainly because of the model in levels. In this paper, we alternatively consider first-difference and level models transformed by using the forward GLS transformation and demonstrate that this transformation yields a higher concentration parameter compared with the original models. This finding indicates that the proposed transformation yields stronger instruments despite the same first-differenced variables being used as instruments. The Monte Carlo simulation results show that the system GMM estimator for the transformed model, called the forward system GMM estimator, performs better than the conventional system GMM estimator for the first-difference and level models and that the performance of the new system GMM estimator is reasonable even when the variance ratio is large.