This paper evaluates the first-differenced maximum likelihood (FDML) and the continuously updating system generalized method of moments (CU-GMM) estimators of dynamic panel models when the data is close to non-stationary. This case is far from trivial, as a high degree of persistence is the norm rather than the exception in economic panels, particularly in financial management. While the CU-GMM is shown to have lower bias and higher power, it suffers from severe size distortions, which are exacerbated when the data approaches non-stationarity.