You can use GMM estimation when using Panel VARs. Check  Abrigo and Love (2015):

http://paneldataconference2015.ceu.hu/Program/Michael-Abrigo.pdf

Thanks Hector

GMM is a kind of Instrumental variable approach (IV).Since it uses a richer set of instruments, it is generally considered to be a more efficient estimator.Some cases where we find GMM useful are the following :- 

1)When you include lagged dependent variable as one of the independent variables in a model. But, be careful about not associating GMM with such cases only. For eg., dynamic panel models(such models where you include lagged dependent variable as one of the regressors ) cannot be estimated by simple OLS, as it give biased estimators.There,GMM is useful.

2) Whenever you face the issue of endogeneity (i.e. endogenous regressors), again, you cannot employ OLS, you should use either IV or GMM.

3)Also, in cases where external instruments are not easily available(as it is in most of the cases),we prefer to use GMM. 

Thanks

Thanks Rashmi

 The problem arises when there are no more than four consecutive years of data. In this case would GMM be recommended?

Here is a link to some lecture notes in downloadable pdf format available online that provides a good first introduction to the topic of GMM...

http://www.otaru-uc.ac.jp/~qliu/panel.pdf

Thanks Muhammad

You can use GMM when you want to have the lagged dependent variable as your independent variable or when the dependent variable has high persistence or long memory. If that is the case then, fixed and random effects estimate would be inconsistent. Better to use 3 step GMM estimation procedure. As for cross section, there is not just one GMM for panel data. You can actually interpret the RE and the FE as GMM. Furthermore there are, for instance, the Difference and System GMM which take into account other specificities of the data. So you would probably need to know, what properties your data has in order to identify the appropriate method. Otherwise you can maybe specify your question for a more detailed answer.your major concern is that the estimated model is dynamic, so standard panel data estimators, such as fixed effects and random effects  are biased. Standard approach to addressing this problem is to apply an instrumental variable estimator, such as that proposed by Arellano and Bond (1991) or Arellano and Bover (1995) - these estimators are asymptotically consistent, but their properties are unsatisfactory in the case of short samples as yours. In such a case it is possible to correct the bias of the standard estimators without affecting their efficiency e.g. by corrected least square dummy variable estimator proposed by Bun and Kiviet (2002) and modified for the analysis of the unbalanced panels by Bruno (2005). This estimator is available for STATA as user written procedure “xtlsdvc”.s I understand your major concern is that the estimated model is dynamic, so standard panel data estimators, such as fixed effects and random effects  are biased. Standard approach to addressing this problem is to apply an instrumental variable estimator, such as that proposed by Arellano and Bond (1991) or Arellano and Bover (1995) - these estimators are asymptotically consistent, but their properties are unsatisfactory in the case of short samples as yours. In such a case it is possible to correct the bias of the standard estimators without affecting their efficiency e.g. by corrected least square dummy variable estimator proposed by Bun and Kiviet (2002) and modified for the analysis of the unbalanced panels by Bruno (2005). This estimator is available for STATA as user written procedure “xtlsdvc”.

https://www.researchgate.net/post/What_is_GMM_estimation_in_Panel_Data_Analysis

Thanks a lot Prem for your very insightful answer.

thanks for invitation....i don't have a domain knowledge, but keenly tracking the answers from other experts...

https://www.econstor.eu/bitstream/10419/90860/1/wp9904.pdf

Panel data analysis and Generalized Method of Moments (GMM) are both statistical techniques used for modeling data with observations collected on multiple individuals or entities over time. GMM is a method for estimating parameters in econometric models, including panel data models, by exploiting moment conditions. In panel data analysis, GMM can be used to estimate parameters in models that account for individual-specific effects, time-specific effects, or both, making it a powerful tool for addressing issues like endogeneity, heterogeneity, and unobserved factors in panel data settings.