* Corresponding author. E-mail: schmidtp@pilot.msu.edu Journal of Econometrics 91 (1999) 145 — 169 Improved instrumental variables and generalized method of moments estimators Hailong Qian, Peter Schmidt*  Econometrics Group, School of Economics and Finance, Victoria University of Wellington, P.O. BOX 600, Wellington, New Zealand  Department of Economics, Michigan State University, East Lansing, MI 48824, USA Abstract 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.  1999 Elsevier Science S.A. All rights reserved. JEL classification: C13 Keywords: IV; Improved IV estimators; GMM; Improved GMM estimators; Moment conditions 1. Introduction Suppose that we have a set of moment conditions E[  (y*  ,   )]"0 which identify the unknown parameter   , so that the generalized method of moments (GMM) estimation of   is feasible. However, suppose that we also have available a set of additional moment conditions E[  (y*  )]"0, where   is observable because it depends only on the observed data y*  . Then the question 0304-4076/99/$ - see front matter  1999 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 - 4 0 7 6 ( 9 8 ) 0 0 0 7 4 - 8