Difference GMM or system GMM (Arellano-Bond)?

[Olaf Hotte]

If the endogenous variable is very persistent or almost follows a random walk, then the approach of Arellano-Bond's difference GMM is poorly suited. The lagged levels are only weakly correlated (= weak instruments) with the first differences of the variables. Then, often the system GMM estimator of Blundell and Bond (1998) is better suited. System GMM augments difference GMM by estimating simultaneously in differences and levels. However, an additional assumption that the differences used as instruments are uncorrelated with the error term is necessary.

How can I see, check, or test if my endogenous variable is persistent?

[Sebastian Kripfganz]

That's the tricky part. You need a consistent estimator of the autocorrelation parameter in the first place before you can judge the quality of the estimators. It's kind of a circular problem. Other estimators which are more robust to persistent dependent variables but do not require the additional Blundell-Bond assumption are the Ahn and Schmidt (1995) and Chudick and Pesaran (2022) GMM estimators with nonlinear moment conditions. You might want to try those with my xtdpdgmm command.