Econometrica: Jan 1969, Volume 37, Issue 1
Least Squares, Conditional Predictions, and Estimator Properties
Wade P. SewellThe 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  treatment of Waugh's paper  in a less general setting. In the course of the argument, a simple derivation of the multivariate t density is presented. Srinivasan's  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.
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