A note on extraneous information in regression
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The Theil-Goldberger ( 196 1) exposition of combining sample and prior information is well known and appears now in standard textbooks for graduate econometrics courses. Diminishing the value of the prior relative to the sample information can be easily seen to lead to least squares in the limit, given the formula for the BLU estimator. However, it is not so obvious what happens when the converse limit is examined. Therefore, the purpose of this note is to show that as the variance of the errors on the priors approaches zero, the Theil Goldberger estimator goes to the estimator implied by exact restrictions.