[Sara Zakaryan]

Thanks a lot Carlo,

I will do more research, and read carefully, I should find something I guess. This is a standard growth model and it cant be no one mentioned about instrumental variables in that case.
Thanks a lot for support.

Sara

[Carlo Lazzaro]

Sara:
I do sponsor your wise approach.

[Sebastian Kripfganz]

It is unfortunately indeed the case that in many published articles the authors merely mention that they used the "system GMM estimator" or something alike without explicitly stating the instruments, the weighting matrix etc. Without this information, it is impossible to replicate their studies and even hardly possible to judge whether their estimation method is reasonable.

A justification for exogeneity or endogeneity of the variables should primarily come from economic theory. Subsequently you can use tests such as the Hansen test to support your choice.

[Eric de Souza]

Have a look at:
GMM Estimation of Empirical Growth Models
https://econpapers.repec.org/paper/nufeconwp/0121.htm