A Note on Instrumental Variables and Maximum Likelihood Estimation Procedures

This paper presents two alternative formulations of the instrumental variables (IV) procedure. One of the formulations, termed the "completed model", serves to show, in a general way, that the IV estimator of a vector of regression parameter is asymptotically as efficient as the maximum likelihood estimator, under the hypothesis of normality. The expressions for the information matrix and its inverse are obtained. The calculation of this inverse requires some new results of matrix algebra that are demonstrated in an appendix.