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.
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Thomas D. Wallace
James B. Duke Distinguished Professor Emeritus of Economics
Professor Wallace’s most recent endeavor was the completion of a textbook covering general knowledge within his field. The book was Econometrics: An Introduction, written in collaboration with his former student, Lew Silver. As a researcher, his investigations explored such variables as human capital accumulation, linear restrictions in regression, time series data, multicollinearity and low-order moments in stable lag distribution, fertility and replacement, full time schooling, the mean squa
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