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The generalized method of moments, commonly abbreviated as GMM, is a cornerstone econometric inferential technique developed by economist Lars Peter Hansen for which he was awarded Nobel Prize in 2013. It proceeds by extending the knowledge obtained from a substantive model that for some function $g(X,\theta)$ of the data $X$ and parameter vector $\theta_0$, one can establish a population relation $$E[ g(X,\theta_0)] = 0,$$ referred to as generalized moments (hence the name, the generalized method of moments); statisticians would call them estimating equations. Typical examples include the regression normal equations $E[ x'\varepsilon] = 0$, instrumental variable conditions $E[z'\varepsilon]=0$, and the likelihood score equations $E \frac{\partial l(x,\theta)}{\partial \theta}=0$. Then the sample analogue of the moment condition is formed as $$\frac1n \sum_{i=1}^n g(x_i,\theta)$$ in the i.i.d. case, and somewhat more complicated expressions for the dependent cases (time series, panel data, cluster samples). Minimizing a weighted sum of these conditions provides the parameter estimates $\theta$ and other inferential tools. The weights can be configured to pay a greater attention to satisfying conditions that are more interesting, informative, or better measured. GMM works with all of single- and multiple-equation cross-sectional, time-series, and panel data models. The theory of GMM also provides asymptotic standard errors and asymptotic tests.
Other uses of the GMM acronym in other areas of statistics include Gaussian mixture models and growth mixture models. Hence the use of the abbreviated tag gmm is discouraged, and method-specific unabbreviated tags should be used instead.