Jan Kmenta

Small Sample Properties of Alternative Estimators of Seemingly Unrelated Regressions

Abstract A Monte Carlo experiment is carried out to examine the small sample properties of five alternative estimators of a set of linear regression equations with mutually correlated disturbances. The estimators considered are ordinary least squares, Zellners two-stage Aitken, Zellners iterative Aitken, Telsers iterative, and maximum likelihood. The experiment, based on 100 samples, provides approximate sampling distributions for samples of size 10, 20 and 100 for various model specifications. The results show that three of the five estimation methods lead to identical estimates for any sample size, that in many cases the two-stage Aitken estimator performs as well as or better than the other estimators, and that most of the asymptotic properties of this estimator tend to hold in small samples as well.

Estimation of Seemingly Unrelated Regressions with Autoregressive Disturbances

Abstract Joint estimation of a system of linear regression equations with mutually correlated disturbances leads, in general, to more efficient estimates than estimation of each equation separately. A method of joint estimation developed by Arnold Zeller on the assumption that the disturbances are non-autocorrelated has recently been adapted by Richard Parks for the case in which this assumption does not hold. In the present article we develop several alternative estimators and compare their small-sample efficiency. The comparison is done with the help of a sampling experiment applied to various model specifications.