This paper extends Andrews'[1993] median-unbiased estimation for autoregressive/unit root time series to panel data dynamic fixed effects models. It is shown that median-unbiased estimation applies straightforwardly to models that include linear time trends as well as to those including more general time specific effects. Using Monte Carlo simulations, median-unbiased LSDV estimators are computed and found to be robust to groupwise heteroskedastic and cross-sectionally correlated disturbances. The behavior of these estimators in the presence of exogenous regressors as well as AR parameter heterogeneity is also evaluated in this paper. As an application, these estimators are used to evaluate conditional convergence in the cases of 48 USA states, 13 OECD countries, and two wider samples from Summers and Heston's Penn World Tables, with 57 and 100 countries. It is found that median-unbiased estimates support conditional convergence only among USA states and OECD countries.