Material Facts Obscured in Hansen's Modern Gauss-Markov Theorem
Methodology
2022-05-04 v1
Abstract
We show that the abstract and conclusion of Hansen's {\it Econometrica} paper, \cite{Hansen22}, entitled a modern Gauss-Markov theorem (MGMT), obscures a material fact, which in turn can confuse students. The MGMT places ordinary least squares (OLS) back on a high pedestal by bringing in the Cramer-Rao efficiency bound. We explain why linearity and unbiasedness are linked, making most nonlinear estimators biased. Hence, MGMT extends the reach of the century-old GMT by a near-empty set. It misleads students because it misdirects attention back to the unbiased OLS from beneficial shrinkage and other tools, which reduce the mean squared error (MSE) by injecting bias.
Keywords
Cite
@article{arxiv.2205.01238,
title = {Material Facts Obscured in Hansen's Modern Gauss-Markov Theorem},
author = {Hrishikesh D Vinod},
journal= {arXiv preprint arXiv:2205.01238},
year = {2022}
}