This chapter reviews developments to improve on the poor performance of the
standard GMM estimator for highly autoregressive panel series. It consider
s the use of the 'system ' GMM estimator that relies on relatively mild res
trictions on the initial condition process. This system GMM estimator encom
passes the GMM estimator based on the non-linear moment conditions availabl
e in the dynamic error components model and has substantial asymptotic effi
ciency gains. Simulations, that include weakly exogenous covariates, find l
arge finite sample biases and very low precision for the standard first dif
ferenced estimator Tile use of the system GMM estimator not only greatly im
proves the precision but also greatly reduces the finite sample bins. An ap
plication to panel production function data for the U.S. is provided and co
nfirms these theoretical and experimental findings.