1.3.3.md

Solution to Review Question

by Qiang Gao, updated at Apr 23, 2017

---

Chapter 1 Finite-Sample Properties of OLS

Section 3 Finite-Sample Properties of OLS

...

Review Question 1.3.3 (What Gauss-Markov does not mean)

Under Assumptions 1.1–1.4, does there exist a linear, but not necessarily unbiased, estimator of $$ \boldsymbol{\beta} $$ that has a variance smaller than that of the OLS estimator? If so, how small can the variance be?

Solution

If an estimator of $$ \boldsymbol{\beta} $$ is a constant, then the estimator is trivially linear in $$ \mathbf{y} $$.

---

Copyright ©2017 by Qiang Gao