Journal of Econometrics 54 (1992) 321-334. North-Holland Properties of ordinary least squares estimators in regression models with nonspherical disturbances* Denzil G. Fiebig zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG University of Sydney, Sydney, NSW 2006, Australia Michael McAleer Vniuersity of W estern Australia, Nedlands, W A 600!9, Australia Robert Bartels University of Bonn, Bonn, Germany University of Sydney, Sydney, NSW 2006, Australia Received October 1989, final version received November 1991 A general discussion is presented of the properties of the OLS estimator in regression models where the disturbances do not have a scalar identity covariance matrix. Several new and interesting characterizations are provided together with a synthesis of existing results. A distinguishing feature of the paper is the unified treatment of the issues of efficiency and inference. The theoretical material is illustrated by examples covering a wide range of models of interest to applied econometricians. ‘It is just these very simple things which are extremely liable to be overlooked.’ Sherlock Holmes to Dr. Watson in The Sign of zyxwvutsrqponmlkjihgfedcbaZYXWVUT Four by A. Conan Doyle zyxwvutsrqponmlkjihgfed 1. Introduction There are two primary implications for the ordinary least squares (OLS) estimator in a linear model with nonspherical errors: first, OLS will be *The authors wish to thank Trevor Breusch, Colin McKenzie, Hashem Pesaran, Peter Phillips, Hans Joachim Werner, and seminar participants at Kyoto, Osaka, Sydney, and Tilburg Universi- ties for helpful discussions. The helpful comments of two referees, an Associate Editor, and Arnold Zellner led to improvements in the presentation of this paper. McAleer wishes to acknowledge the financial support of the Australian Research Council and Japanese Govern- ment Foreign Research Fellowships at Kyoto and Osaka Universities, while Bartels acknowl- edges the financial support of the Von Humboldt Foundation. 0304-4076/92/$05.00 0 1992-Elsevier Science Publishers B.V. All rights reserved