p.39

Least Squares, Conditional Predictions, and Estimator Properties

Wade P. Sewell

Abstract

The problem of prediction of a subset of the endogenous variables conditioned on the balance of the endogenous variables, as well as the predetermined variables, is discussed in the context of a general linear model with normal disturbances. It is shown that the conditional least-squares predictor is unbiased, correcting Srinivasan's [9] treatment of Waugh's paper [10] in a less general setting. In the course of the argument, a simple derivation of the multivariate t density is presented. Srinivasan's [9] remark that consistency of an estimator does not imply its asymptotic unbiasedness (in one of the common senses of that term) is illustrated by two examples, one with a discrete and one with a continuous distribution. They show that neither asymptotic unbiasedness nor zero asymptotic variance is necessary for consistency. The example with a continuous distribution is the two-stage least-squares estimator.