Improving the Efficiency of GMM Estimators for Dynamic Panel Models

In dynamic panel models, the generalized method of moments (GMM) has been used in many applications since it gives efficient estimators. This efficiency is affected by the choice of the initial weighted matrix. It is common practice to use the inverse of the moment matrix of the instruments as an initial weighted matrix. However, an initial optimal weighted matrix is not known, especially in the system GMM estimation procedure. Therefore, we present the optimal weighted matrix for level GMM estimator, and suboptimal weighted matrices for system GMM estimator, and use these matrices to increase the efficiency of GMM estimator. By using the Kantorovich inequality (KI), we find that the potential efficiency gain becomes large when the variance of individual effects increases compared with the variance of the errors.