The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems

Abstract

This paper examines the discussion in the econometric literature of the conditioins which instruments should satisfy in order to be used in the single equation Iiistrumental Variable (IV) estimation of structural parameters in a simultaneouIs equation system. The Two Stage Least Squares (TSLS) estimator can be interpreted as an IV estimator. It is consistent and, under normality assumptions for disturbances, asymptotically efficient. A new IV estimator is proposed which is also consistent and asymptotically efficient but whose instruments satisfy a stronger condition than the TSLS instruments. The finite sample bias of the new IV estimator is examined and found to be non-zero but a condition is presented for its bias to be smaller than that of TSLS.