Improved instrumental variables and generalized method of moments estimators

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.