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Least Squares, Conditional Predictions, and Estimator Properties

Wade P. Sewell
Econometrica
Vol. 37, No. 1 (Jan., 1969), pp. 39-43
Published by: The Econometric Society
DOI: 10.2307/1909202
Stable URL: http://www.jstor.org/stable/1909202
Page Count: 5
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Least Squares, Conditional Predictions, and Estimator Properties
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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.

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