Generalized Method of Moments Estimation
Later version available View entry history
Abstract
Generalized method of moments estimates econometric models without requiring a full statistical specification. One starts with a set of moment restrictions that depend on data and an unknown parameter vector to be estimated. When there are more moment restrictions than underlying parameters, there is family of such estimators. The tractable form of the large sample properties of this family facilitates efficient estimation and statistical testing. This article motivates the method, presents some of the underlying statistical properties and discusses implementation.
Keywords
Calibration Central limit theorems Gauss–Markov theorem Generalized method of moments Identification Instrumental variables Lagrange multipliers Law of large numbers Likelihood Martingales Maximum likelihood Rational expectations models Sequential estimation Statistical inference Stochastic discount factor models Wald testJEL Classifications
C10Notes
Acknowledgments
I greatly appreciate comments from Lionel Melin, Monika Piazzesi, Grace Tsiang and Francisco Vazquez-Grande. This material is based upon work supported by the National Science Foundation under Award Number SES0519372.
Bibliography
- Amemiya, T. 1974. The nonlinear two-stage least-squares estimator. Journal of Econometrics 2: 105–110.CrossRefGoogle Scholar
- Arellano, M. 2003. Panel data econometrics. New York: Oxford University Press.CrossRefGoogle Scholar
- Bontemps, C., and N. Meddahi. 2005. Testing normality: A GMM approach. Journal of Econometrics 124: 149–186.CrossRefGoogle Scholar
- Carrasco, M., and J.P. Florens. 2000. Generalization of GMM to a continuum of moment conditions. Econometric Theory 20: 797–834.CrossRefGoogle Scholar
- Chamberlain, G. 1986. Asymptotic efficiency in estimation with conditional moment restrictions. Journal of Econometrics 34: 305–334.CrossRefGoogle Scholar
- Chernozhukov, V., and H. Hong. 2003. An MCMC approach to classical estimation. Journal of Econometrics 115: 293–346.CrossRefGoogle Scholar
- Christiano, L.J., and M. Eichenbaum. 1992. Current real business cycle theories and aggregate labor market fluctuations. American Economic Review 82: 430–450.Google Scholar
- Cochrane, J. 2001. Asset pricing. Princeton: Princeton University Press.Google Scholar
- Cumby, R.E., J. Huizinga, and M. Obstfeld. 1983. Two-step two-stage least squares estimation in models with rational expectations. Journal of Econometrics 21: 333–335.CrossRefGoogle Scholar
- Eichenbaum, M.S., L.P. Hansen, and K.J. Singleton. 1988. A time series analysis of representation agent models of consumption and leisure choice under uncertainty. Quarterly Journal of Economics 103: 51–78.CrossRefGoogle Scholar
- Ghysels, E., and A. Hall. 2002. Editors’ Introduction to JBES twentieth anniversary issue on generalized method of moments estimation. Journal of Business and Economic Statistics 20: 441.CrossRefGoogle Scholar
- Gordin, M.I. 1969. The central limit theorem for stationary processes. Soviet Mathematics Doklady 10: 1174–1176.Google Scholar
- Hall, A.R. 2005. Generalized method of moments. New York: Oxford University Press.Google Scholar
- Hall, P., and C.C. Heyde. 1980. Martingale limit theory and its application. Boston: Academic Press.Google Scholar
- Hansen, L.P. 1982. Large sample properties of generalized method of moments estimators. Econometrica 50: 1029–1054.CrossRefGoogle Scholar
- Hansen, L.P. 1985. A method for calculating bound on asymptotic covariance matrices of generalized method of moments estimators. Journal of Econometrics 30: 203–238.CrossRefGoogle Scholar
- Hansen, L.P. 1993. Semiparametric efficiency bounds for linear time-series models. In Models, methods and applications of econometrics: Essays in Honor of A.R. Bergstrom, ed. P.C.B. Phillips. Cambridge: Blackwell.Google Scholar
- Hansen, L.P. 2001. Method of moments. In International encyclopedia of the social and behavior sciences. New York: Elsevier.Google Scholar
- Hansen, L.P., J. Heaton, and E. Luttmer. 1995. Econometric evaluation of asset pricing models. Review of Financial Studies 8: 237–274.CrossRefGoogle Scholar
- Hansen, L.P., and J.J. Heckman. 1996. The empirical foundations of calibration. Journal of Economic Perspectives 10(1): 87–104.CrossRefGoogle Scholar
- Hansen, L.P., and R. Jagannathan. 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52: 557–590.CrossRefGoogle Scholar
- Hansen, L.P., and K.J. Singleton. 1982. Generalized instrumental variables of nonlinear rational expectations models. Econometrica 50: 1269–1286.CrossRefGoogle Scholar
- Hansen, L.P., and K.J. Singleton. 1996. Efficient estimation of linear asset pricing models with moving average errors. Journal of Business and Economic Statistics 14: 53–68.Google Scholar
- Hansen, L.P., J.C. Heaton, J. Lee, and N. Roussanov. 2007. Intertemporal substitution and risk aversion. In Handbook of econometrics, ed. J. Heckman and E. Leamer, Vol. 6A. Amsterdam: North-Holland.Google Scholar
- Hayashi, F., and C. Sims. 1983. Nearly efficient estimation of time-series models with predetermined, but not exogenous, instruments. Econometrica 51: 783–798.CrossRefGoogle Scholar
- Heckman, J.J. 1976. The common structure of statistical methods of truncation, sample selection, and limited dependent variables and a simple estimator of such models. Annals of Economic and Social Measurement 5: 475–492.Google Scholar
- Kleibergen, F. 2005. Testing parameters in GMM without assuming that they are identified. Econometrica 73: 1103–1123.CrossRefGoogle Scholar
- Newey, W. 1993. Efficient estimation of models with conditional moment restrictions. In Handbook of statistics, ed. G.S. Maddala, C.R. Rao, and H.D. Vinod, Vol. 11. Amsterdam: North-Holland.Google Scholar
- Newey, W., and D. McFadden. 1994. Large sample estimation and hypothesis testing. In Handbook of econometrics, ed. R. Engle and D. McFadden, Vol. 4. Amsterdam: North-Holland.Google Scholar
- Newey, W.K., and K.D. West. 1987a. Hypothesis testing with efficient method of moments estimation. International Economic Review 28: 777–787.CrossRefGoogle Scholar
- Newey, W.K., and K.D. West. 1987b. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708.CrossRefGoogle Scholar
- Ogaki, M. 1993. Generalized method of moments: Econometric applications. In Handbook of statistics, ed. G.S. Maddala, C.R. Rao, and H.D. Vinod, Vol. 11. Amsterdam: North-Holland.Google Scholar
- Pagan, A.R. 1984. Econometric issues in the analysis of models with generated regressors. International Economic Review 25: 221–247.CrossRefGoogle Scholar
- Sargan, J.D. 1958. The estimation of economic relationships using instrumental variables. Econometrica 26: 393–415.CrossRefGoogle Scholar
- Sargan, J.D. 1959. The estimation of relationships with autocorrelated residuals by the use of instrumental variables. Journal of the Royal Statistical Society: Series B 21: 91–105.Google Scholar
- Singleton, K.J. 2006. Empirical dynamic asset pricing: Model specification and econometric assessment. Princeton: Princeton University Press.Google Scholar
- Stock, J.H., and J.H. Wright. 2000. GMM with weak identification. Econometrica 68: 1055–1096.CrossRefGoogle Scholar
- West, K.D. 2001. On optimal instrumental variables estimation of stationary time series models. International Economic Review 42: 1043–1050.CrossRefGoogle Scholar