ŠT—v

This paper addresses the many instruments problem in dynamic panel data models where an unobservable heterogeneity may be large. We find that if we use the all instruments in levels, although the GMM estimator is robust to a large heterogeneity, the inference is inaccurate, and if we use minimum number of instruments in the sense that we use only one instrument for each period, the performance of GMM estimator is heavily affected by a large heterogeneity, that is, both the bias and the variance are proportional to the magnitude of a heterogeneity. To address this problem, we propose new form of instruments which are obtained from the transformation, called as the backward orthogonal deviation transformation. The asymptotic analysis shows that the GMM estimator with minimum number of new instruments has smaller asymptotic bias than the typical estimators, including the GMM estimator with all instruments in levels, LIML and within-groups estimator, whereas its asymptotic variance is equal to the lower bound. Thus both the asymptotic bias and variance of the proposed estimators become small. Simulation results show that our new GMM estimator outperforms the conventional GMM estimator with instruments in levels in term of the RMSE and the accuracy of the inference.