The Exact Distribution of a Simple Pre-Test Estimator* *An earlier version of this paper was presented to the 1988 Australasian Meeting of the Econometric Society. I am grateful to Robert Davies for supplying FORTRAN code for his algorithm AS155 and to Judith Giles for several valuable discussions, and for preparing the figures. I would also like to thank Chien-Pai Han, Mary Ellen Bock, Chris Skeels, Murray Smith and participants in seminars at McMaster University, the University of Guelph and the University of Western Ontario for their helpful comments.