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| Generalized Method of Moments | |
|---|---|
| Name | Generalized Method of Moments |
| Inventor | Lars Peter Hansen |
| Introduced | 1982 |
| Field | Econometrics |
| Notable users | Lars Peter Hansen, James Heckman, Robert Engle, Clive Granger |
Generalized Method of Moments The Generalized Method of Moments is an econometric estimation technique introduced by Lars Peter Hansen in 1982 that generalizes moment-based estimation to overidentified systems and complex models. It provides a unifying framework for estimators used across empirical work by connecting moment conditions derived from economic models to consistent parameter estimates, and it has influenced practice in central banks such as the Federal Reserve System and institutions like the World Bank and the International Monetary Fund.
GMM emerged in the context of work by Arthur Cecil Pigou-era moment ideas and the modern synthesis involving scholars such as Trygve Haavelmo, Christopher Sims, and Clive Granger. Hansen formalized how to exploit population moment restrictions implied by models considered by John Maynard Keynes-era macroeconomists and finance theorists like Eugene F. Fama and Kenneth J. Arrow. The method has been adopted by researchers at Harvard University, Massachusetts Institute of Technology, University of Chicago, and policy analysts at the European Central Bank and Bank for International Settlements.
GMM is built on moment conditions E[m(X_t, θ)] = 0 derived from structural or reduced-form relations proposed by scholars such as Milton Friedman, Paul Samuelson, and Robert Solow. Theoretical foundations connect to identification concepts developed by Herman Wold and hypothesis testing traditions from Neyman–Pearson lemma-related work and applications by Ronald A. Fisher. Identification criteria relate to rank conditions similar to those invoked in instrumental variables work used by Angus Deaton and James Heckman.
Estimation proceeds by selecting sample analogs of population moments and minimizing a quadratic form using a weighting matrix inspired by results from Andrey Kolmogorov-style asymptotics and variance estimation approaches of Jerzy Neyman and Egon Pearson. The standard two-step procedure references large-sample covariance estimators developed in the literature by Robert Engle and Clive Granger, and optimization routines often employ algorithms popularized in computational work at Bell Labs and by researchers at Stanford University.
Under regularity conditions akin to those in the work of Thomas S. Ferguson and classical asymptotic theory of Andrey Markov, GMM estimators are consistent and asymptotically normal, with asymptotic variance achieving a lower bound when the optimal weighting matrix is used, paralleling efficiency results proven by Lars Peter Hansen and contemporaries such as Peter C. B. Phillips. Hypothesis testing for overidentifying restrictions uses a J-test connected to chi-squared distributions featured in the work of Jerzy Neyman and Eg? N. Pearson traditions.
Practical implementation leverages numerical optimization libraries and software environments developed at institutions like Microsoft Research, IBM Research, Bell Labs, and universities including Columbia University and University of California, Berkeley. Common software packages at Stanford University and Massachusetts Institute of Technology incorporate GMM routines; practitioners at Goldman Sachs, J.P. Morgan Chase, and central banks apply these in empirical finance and macroeconomic forecasting. Computational concerns include choosing instruments suggested by research from James Heckman and handling serial correlation using approaches related to Robert Engle's work on autoregressive conditional heteroskedasticity models.
GMM has been applied in empirical studies by researchers at Princeton University and Yale University on consumption and asset pricing inspired by John L. Campbell and N. Gregory Mankiw, in labor economics following frameworks by James Heckman and Gary Becker, and in macroeconomics in DSGE model estimation by scholars affiliated with New York University and London School of Economics. Finance applications include testing the Capital Asset Pricing Model as in work by Eugene F. Fama and Kenneth R. French, and term structure estimation in central bank studies at the Federal Reserve Bank of New York.
Extensions and related methods include the continuously-updated GMM influenced by contributions from Quang H. Vuong, Limited Information Maximum Likelihood connected to work by Clive Granger and Olav Bjerkholt, Generalized Empirical Likelihood linked to researchers at University College London, and efficient GMM variations developed in literature involving James Stock and Mark Watson. Connections exist to methods such as Maximum Likelihood Estimation applied in studies by Ronald A. Fisher and Bayesian approaches used by scholars at University of Oxford.