Instrumental variable estimation of the simple errors-in-variables model

Alternative instrumental variable estimators for the slope in the simple errors-in-variables model are discussed. The maximum likelihood estimator is derived for the model in which the error covariance is known to be zero and for the model in which the error covariance is unknown. Modified maximum likelihood estimators and randomly weighted average estimators similar to those studied by Huntsberger are discussed. The limiting distributions of the estimators are presented and the estimators are compared in a Monte Carlo study.