The generalized method of moments is a very general statistical method for obtaining estimates of parameters of statistical models. It is a generalization, developed by Lars Peter Hansen, of the method of moments. A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a best guess for an unknown (fixed or random) population parameter. ... Lars Peter Hansen was the inventor of GMM or the Generalized method of moments. ... In statistics, the method of moments is a method of estimation of population parameters such as mean, variance, median, etc. ...

The term GMM is very popular among econometricians but is hardly used at all outside of economics, where the slightly more general term estimating equations is preferred. The method is also closely related to the classical theory of minimum chi-square estimation. Econometrics literally means economic measurement. It is a combination of mathematical economics and statistics. ...

Description

The idea of the generalized method of moments is to use moment conditions that can be found from the problem with little effort. We assume that the data are a stochastic process In mathematical language, we start out with a (vector valued) function f that depends both on the parameter and a single observation and that has mean zero for the true value of the parameter, θ = θ₀, i.e.-1... In the mathematics of probability, a stochastic process is a random function. ... The factual accuracy of this article is disputed. ...

To turn this function into a parameter estimate, we minimize the associated chi-square statistic

where superscript T is used for transpose, and A is a positive definite matrix. A may be known a priori or estimated from the sample. In mathematics, and in particular linear algebra, the transpose of a matrix is another matrix, produced by turning rows into columns and vice versa. ... In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. ...

See also

• Instrumental variable, subclass of this method
• Method of moments

In statistics, an instrumental variable (IV, or instrument) can be used in regression analysis to produce a consistent estimator when the explanatory variables (covariates) are correlated with the error terms. ... In statistics, the method of moments is a method of estimation of population parameters such as mean, variance, median, etc. ...

Further reading

• Lars Peter Hansen (1982). "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica 50, 1029-1054.
• Kirby Faciane (2006). Statistics for Empirical and Quantitative Finance. H.C. Baird: Philadelphia. ISBN 0-9788208-9-4.
• Alastair R. Hall (2005). Generalized Method of Moments (Advanced Texts in Econometrics). Oxford University Press. ISBN 0-19-877520-2.