Fixed effects in GMM estimation

[Daniel]

Dear all,

I am having trouble understanding what happens to fixed effects in GMM estimation. To be more precise, using two approaches:

i. equation in differences (IV in levels) - by definition eliminates fixed effects;
ii. equation in levels (IV in differences) - what then with FE? Do I need FE dummy? Is it removed by differencing in IV?

Than You for explanation!
D

[Daniel]

Oh, and one additional question (for now): if I deal with FE dummy in a regression, how should I properly test for endogeneity and further on if tests confirms it, what then?