  This paper establishes the almost sure convergence and asymptotic normality
of levels and differenced quasi maximum-likelihood (QML) estimators of dynamic
panel data models. The QML estimators are robust with respect to initial
conditions, conditional and time-series heteroskedasticity, and
misspecification of the log-likelihood. The paper also provides an ECME
algorithm for calculating levels QML estimates. Finally, it uses Monte Carlo
experiments to compare the finite sample performance of levels and differenced
QML estimators, the differenced GMM estimator, and the system GMM estimator. In
these experiments the QML estimators usually have smaller --- typically
substantially smaller --- bias and root mean squared errors than the panel data
GMM estimators.
