Improved instrumental variables and generalized method of moments estimators

• Published in: Journal of econometrics Vol. 91; no. 1; pp. 145 - 169
• Main Authors: Qian, Hailong, Schmidt, Peter
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.1999; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Distribution theory; Economic models; Estimating techniques; Estimation; Exact sciences and technology; Generalized method of moments; GMM; Improved GMM estimators; Improved IV estimators; Linear models; Mathematics; Moment conditions; Monte Carlo simulation; Non-linear models; Nonparametric inference; Probability and statistics; Rational expectations; Regression analysis; Sciences and techniques of general use; Statistics; Studies; Improved GMM estimators; Moment conditions; C13; IV; GMM; Improved IV estimators; Error estimation; Correlation analysis; Non linear model; Moment method; Distribution function; Non parametric estimation; Statistical estimation; Probability distribution; Statistical forecasting
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/S0304-4076(98)00074-8

This paper considers GMM estimation with moment conditions of the usual type, plus extra moment conditions that do not depend on the parameters. The extra moment conditions improve efficiency if they are correlated with the original set of moment conditions. This is true in linear and nonlinear models, but in linear models we provide simple, explicit formulas for the improved estimators. Our results may be useful in rational expectations models, in which an equation's error is a forecast error and the extra moment conditions would be forecast errors in related variables.