GMM estimator can be constructed using the properties of the martingale-difference sequence . For a set of instruments zt known at period t − ∆(the authors suggest to use lagged right-hand side variables) the moment conditions are. Note that the set of instruments depends on the structural parameters of the model φ. Optimal GMM estimator φbGMM can then be constructed in a usual fashion either for exact- or over-identified case by minimizing HT (φ) in two steps in order to compute the optimal weight matrix W .