Asymptotic probability concentrations and finite sample properties of modified LIML estimators for equations with more than two endogenous variables

This paper investigates the distributional properties of a class of modified limited information maximum-likelihood (LIML) estimators. It is shown that the asymptotic distributions of these estimators are more concentrated than those of the modified LIML estimators suggested by Fuller. Additionally, the results of an extensive Monte Carlo investigation of the finite sample properties of the proposed estimators show that when the equation of interest has more than two endogenous variables, the LIML estimator is often highly inefficient so that substantial gains in precision are realized by using the modified estimators in place of the LIML estimator.