Dynamic panel GMM estimators with improved finite sample properties using parametric restrictions for dimension reduction

For the GMM estimation of the dynamic panel data model, we propose reducing finite sample bias by imposing parametric restrictions on the expected first derivative matrix and the covariance matrix of the sample moment functions. We find that the small-sample bias of the usual GMM can be considerably reduced especially for models with many overidentifying moment conditions. The resulting estimator is consistent under regularity irrespective of the correctness of the extra restrictions and is first-order efficient if they are indeed correct. Simulations demonstrate that the proposed estimator shows considerable bias reduction in comparison to the conventional GMM estimators. Our method is applied to a dynamic cigarette consumption model.