This paper investigates the exact sampling distribution of the least squares estimator of @b in the model y"t = @m + @by"t"-"1 + @u"t where the @u"t are independently N(0, @s^2). The distribution is calculated for the case where y"0 is a known constant and where y"0 is a random variable. Given y"0 is a constant we prove a small @s asymptotic result and compute the exact powers of nonsimilar tests of the random-walk hypothesis @b = 1 and of the stability hypothesis @b = 0.9. The exact powers of a test of the stability hypothesis are calculated for the case where y"0 is random. The accuracy of the standard normal approximation is examined for both start-up regimes.