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Generalized method of moments
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<p>In <a href="/facts/Econometrics/7U52gzHt">econometrics</a> and <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the generalized method of moments (GMM) is a generic method for estimating <a href="/facts/Statistical_parameter/fkJju25M">parameters</a> in <a href="/facts/Statistical_model/jKkT5ftm">statistical models</a>. Usually it is applied in the context of <a href="/facts/Semiparametric_model/L5jTbkSc">semiparametric models</a>, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore <a href="/facts/Maximum_likelihood_estimation/0Yq2dpQD">maximum likelihood estimation</a> is not applicable. </p><p>The method requires that a certain number of <i>moment conditions</i> be specified for the model. These moment conditions are functions of the model parameters and the data, such that their <a href="/facts/Expected_value/1XV0JKL8">expectation</a> is zero at the parameters' true values. The GMM method then minimizes a certain <a href="/facts/Norm_(mathematics)/xIbR4uE1">norm</a> of the sample averages of the moment conditions, and can therefore be thought of as a <a href="/facts/Special_case/bKaJ85XJ">special case</a> of <a href="/facts/Minimum-distance_estimation/ASBy9yhj">minimum-distance estimation</a>. </p><p>The GMM <a href="/facts/Estimator/CbkjcKvN">estimators</a> are known to be <a href="/facts/Consistent_estimator/HAKDWYEM">consistent</a>, <a href="/facts/Asymptotic_distribution/dN7jVHqm">asymptotically normal</a>, and most <a href="/facts/Efficient_estimator/wTmgEqte">efficient</a> in the class of all estimators that do not use any extra information aside from that contained in the moment conditions. GMM were advocated by <a href="/facts/Lars_Peter_Hansen/hB3uSTLI">Lars Peter Hansen</a> in 1982 as a generalization of the <a href="/facts/Method_of_moments_(statistics)/Qfso3fMe">method of moments</a>, introduced by <a href="/facts/Karl_Pearson/fXB7GT5Q">Karl Pearson</a> in 1894. However, these estimators are mathematically equivalent to those based on "orthogonality conditions" (Sargan, 1958, 1959) or "unbiased estimating equations" (Huber, 1967; Wang et al., 1997). </p>