In econometrics, generalized method of moments (GMM) is a generic method for estimating parameters in statistical models. Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the distribution function of the data may not be known, and therefore the maximum likelihood estimation is not applicable.
The method requires that a certain number of moment conditions were specified for the model. These moment conditions are functions of the model parameters and the data, such that their expectation is zero at the true values of the parameters. The GMM method then minimizes a certain norm of the sample averages of the moment conditions.
The GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that don’t use any extra information aside from that contained in the moment conditions.
GMM was developed by Lars Peter Hansen in 1982 as a generalization of the method of moments.
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