When we estimate system equations by instrumental variables, we need to use GMM under the case of over identification (the rank of IV is larger than the rank of endogenous variables).

Suppose the previous equation is Y=XB+u, where X is endogenous, and Z is IV, then we have GMM estimator:

B^hat=(X'ZWZ'X)^(-1)(X'ZWZ'Y), W is the weight.

Following Econometric Analysis of Cross Section and Panel Data by Wooldridge, we need to first assume W1=(Z'Z)^(-1), and get residual u^hat. Then let W2=(Z'u)^(-1), and use W2 to obtain optimal GMM estimator.

However, the expression is similar to 3SLS estimator (three stage least equare estimator). So may I ask what are the differences between those two estimators? Thank you very much.