This short note derives the probability limits of several estimators for panel AR(1) models under misspecification using sequential asymptotics. The results show that GMM estimators based on the forward orthogonal deviation transformation converge to the first-order autocorrelation coefficient.

We consider the estimation of autocovariances using panel data with incidental trends under double asymptotics. The conventional autocovariance estimator suffers from a bias whose value is approximated by twice the long-run variance. We propose a bias-corrected estimator.