This paper proposes a new class of estimators for the autoregressive coefficient of a dynamic panel data model with random individual effects and nonstationary initial condition. The new estimators we introduce are weighted averages of the well-known first difference (FD) GMM/IV estimator and the pooled ordinary least squares (POLS) estimator. The proposed procedure seeks to exploit the differing strengths of the FD GMM/IV estimator relative to the pooled OLS estimator. In particular, the latter is inconsistent in the stationary case but is consistent and asymptotically normal with a faster rate of convergence than the former when the underlying panel autoregressive process has a unit root. By averaging the two estimators in an appropriate way, we are able to construct a class of estimators which are consistent and asymptotically standard normal, when suitably standardized, in both the stationary and the unit root case. The results of our simulation study also show that our proposed estimator has favorable finite sample properties when compared to a number of existing estimators.