A Modern Gauss–Markov Theorem. Issue 3 (27th May 2022)

• Record Type: Journal Article
• Authors: Hansen, Bruce E.
• Is Part Of: Econometrica. Volume 90:Issue 3(2022)
• Page Start: 1283
• Page End: 1294
• Publication Date: 2022-05-27
• Subjects: Gauss‐Markov -- BLUE -- efficient estimation -- least squares -- linear estimators -- unbiasedness; Econometrics -- Periodicals; Economics, Mathematical -- Periodicals; Economics -- Periodicals; Économétrie -- Périodiques; Mathématiques économiques -- Périodiques; Économie politique -- Périodiques; 330.05
• DOI: 10.3982/ECTA19255
• Languages: English
• ISSNs: 0012-9682

Abstract

Abstract : This paper presents finite‐sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss–Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label "linear estimator" from the pedagogy of the Gauss–Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators).