On Certain Small Sample Properties of k-Class Estimators

Abstract

variables (assumed to be identical in repeated samples and not to contain lagged values of endogenous variables), u is a vector of jointly normally distributed error terms with mean zero and covariance matrix A, y is a vector of endogenous variables, and B (nonsingular) and F are matrices of coefficients. It has been shown recently [5] that the fullinformation maximum likelihood method of estimating the coefficients of structural equations is a generalization of the least squares principle. These estimates are consistent and efficient. Nevertheless, the properties of other types of estimator continue to be of interest because of the computational difficulty of obtaining full-information estimates [4], [6]. Noteworthy among alternative methods are limited-information maximum likelihood, indirect least squares, two-stage least squares, direct least squares (the last two being special cases of the general k-class of estimators) and several others.' With the exception of direct least squares these methods also possess the property of consistency although they yield biased estimates in finite samples. Relatively little is known about the finite sample distributions of the various estimators. The exact finite sample distributions of limitedinformation maximum likelihood estimates and two-stage least squares estimates have been derived by Basmann in certain special cases [2],