A dynamic panel data model is considered that contains possibly stochastic individual components and a common fractional stochastic time trend. We propose four different ways of coping with the individual effects so as to estimate the fractional parameter. Like models with autoregressive dynamics, ours nests a unit root, but unlike the nonstandard asymptotics in the autoregressive case, estimates of the fractional parameter can be asymptotically normal. Establishing this property is made difficult due to bias caused by the individual effects, or by the consequences of eliminating them, and requires the number of time series observations T to increase, while the cross-sectional size, N; can either remain fi…xed or increase with T: The biases in the central limit theorem are asymptotically negligible only under stringent conditions on the growth of N relative to T; but these can be relaxed by bias correction. For three of the estimates the biases depend only on the fractional parameter. In hypothesis testing, bias correction of the estimates is readily carried out. We evaluate the biases numerically for a range of T and parameter values, develop and justify feasible bias-corrected estimates, and briefly discuss implied but less effective corrections. A Monte Carlo study of …finite-sample performance is included.