Why should I use difference GMM instead of system GMM (Arellano-Bond)

[Olaf Hotte]

What are the reasons to use Arellano-Bond's difference GMM instead of system GMM? xtabond vs. xtabond2?

Reasons to apply a system GMM estimator:
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. In this case, the delayed levels are only weakly correlated with / weak instruments for 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

Reasons to apply a difference GMM estimator:
?

Now, I am looking for the reasons to apply a difference GMM instead of a system GMM. To me, the argumentation in literature sounds like system GMM is always superior compared to difference GMM because it exploits differences and levels simultaneously. Is there any case where a difference GMM should be preferred over a system GMM? And why?

[Sebastian Kripfganz]

System GMM requires the additional assumption that the differences used as instruments are uncorrelated with the error term (in particular with the unobserved unit-specific effects). A sufficient condition for this to hold would be joint mean stationarity of the dependent variable and the independent variables, which may not be easily justifiable in many applications.

An alternative would be the difference GMM estimator augmented by the Ahn-Schmidt nonlinear moment conditions. This estimator has better properties than the difference GMM estimator under high persistence but does not require the additional mean-stationarity assumption of the system GMM estimator.

More information:

• XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models
• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.