Linear dynamic panel data methods are now convenient and practical tools available to the applied researcher. Despite wide usage, many of these methods present both theoretical and practical issues that have not been adequately resolved, especially for methods that have no software counterparts yet. In particular, we will study more intensively nonlinear moment conditions that have been proposed by Ahn and Schmidt (1995) but has been largely ignored by theorists and practitioners for a very long time. We show that estimators based on these nonlinear moment conditions are able to distinguish among not-so-persistent panel data, highly persistent panel data, and panel data with unit roots under certain model setups. It turns out that the widely available methods (in terms of existing software) either are unable to distinguish very well these three cases or are able to do so but under additional assumptions that are not plausible in empirical research. Nonlinear moment conditions will lead to the use of numerical algorithms which raise theoretical and practical issues for implementation. Instead of ignoring these issues, we show how to address them directly in order to make the estimators relevant to practitioners who need guidance for implementation.