Hi, I am trying to estimate a model that contains 30 countries N-30 and T=20.
my research question is to see if immigration affects GDP per capita. theoretically the model suffers from reverse causality, so estimating it with fixed effects with get biased results. to deal with the endogeneity I wasn to use system GMM. before i proceed i did a unit root test and all the variables are stationary at first difference. if i create time dummies for each year, then after estimating the model using GMM , the number of instruments are larger than the group. even if i use the collapse option. my questions are:

1- are the variables being stationary at first difference enough to use them in GMM method?
2- is creating year dummies essential or can I proceed without year dummies?(because then my number of instruments are lower than the grouo)
please help me with this! I really appreciate it.

regards