This note derives the correct limit distributions of the Anderson Hsiao (1981) levels and diﬀerences instrumental variable estimators, provides comparisons showing that the levels IV estimator has uniformly smaller variance asymptotically as the cross section ( n ) and time series ( T ) sample sizes tend to inﬁnity, and compares these results with those of the ﬁrst diﬀerence least squares (FDLS) estimator.
Phillips, Peter C.B. and Han, Chirok, "True Limit Distributions of the Anderson-Hsiao IV Estimators in Panel Autoregression" (2014). Cowles Foundation Discussion Papers. 2377.