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GMM was developed by Lars Peter Hansen in 1982 as a generalization of the method of moments, (norm of m, denoted as
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Before we can make a statement about the asymptotic distribution of the GMM estimator, we need to define two auxiliary matrices: So far we have said nothing about the choice of matrix W, except that it must be positive semi-definite.
In fact any such matrix will produce a consistent and asymptotically normal GMM estimator, the only difference will be in the asymptotic variance of that estimator.