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Several estimators have been suggested for estimating the model parameters.A standard estimation procedure is to first-difference the model, so as to eliminate the unobserved heterogeneity, and then base GMM estimation on the moment conditions implied where endogenous differences of the variables are instrumented by their lagged levels.It can be shown that taking will result in the most efficient estimator in the class of all asymptotically normal estimators. Consistency is a statistical property of an estimator stating that, having a sufficient number of observations, the estimator will converge in probability to the true value of parameter: The second condition here (so-called Global identification condition) is often particularly hard to verify.There exist simpler necessary but not sufficient conditions, which may be used to detect non-identification problem: Asymptotic normality is a useful property, as it allows us to construct confidence bands for the estimator, and conduct different tests.In this case the formula for the asymptotic distribution of the GMM estimator simplifies to The proof that such a choice of weighting matrix is indeed optimal is often adopted with slight modifications when establishing efficiency of other estimators.As a rule of thumb, a weighting matrix is optimal whenever it makes the “sandwich formula” for variance collapse into a simpler expression.The GMM method then minimizes a certain norm of the sample averages of the moment conditions.

The GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that do not use any extra information aside from that contained in the moment conditions.

This is the well known Arellano-Bond estimator, or first-difference (DIF) GMM estimator (see Arellano and Bond ).

The DIF GMM estimator was found to be inefficient since it does not make use of all available moment conditions (see Ahn and Schmidt ); it also has very poor finite sample properties in dynamic panel data models with highly persistent series and large variations in the fixed effects relative to the idiosyncratic errors (see Blundell and Bond ) since the instruments in those cases become less informative.

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As a result, the SYS GMM estimator has been widely used for estimation of production functions, demand for addictive goods, empirical growth models, etc.