The presence of cross-sectionally correlated error terms invalidates much inferential theory of panel data models. Recently, work by Pesaran (2006) has suggested a method which makes use of cross-sectional averages to provide valid inference in the case of stationary panel regressions with a multifactor error structure. This paper extends this work and examines the important case where the unobservable common factors follow unit root processes. The extension to processes is remarkable on two counts. Firstly, it is of great interest to note that while intermediate results needed for deriving the asymptotic distribution of the panel estimators differ between the and cases, the final results are surprisingly similar. This is in direct contrast to the standard distributional results for processes that radically differ from those for processes. Secondly, it is worth noting the significant extra technical demands required to prove the new results. The theoretical findings are further supported for small samples via an extensive Monte Carlo study. In particular, the results of the Monte Carlo study suggest that the cross-sectional average based method is robust to a wide variety of data generation processes and has lower biases than the alternative estimation methods considered in the paper.