A Modern Gauss-Markov Theorem? Really?

TL;DR

This paper critically examines recent econometric theorems claiming to be modern versions of classical results, showing most are not new and some are incorrect, clarifying their relation to established theorems.

Contribution

It clarifies the relationship between recent theorems in Hansen's work and classical Gauss-Markov and Aitken theorems, correcting inaccuracies and highlighting when assumptions are extraneous.

Findings

Most recent theorems coincide with classical results

One theorem in Hansen (2021a) is incorrect

Hansen (2021b) corrects the erroneous theorem

Abstract

We show that the theorems in Hansen (2021a) (the version accepted by Econometrica), except for one, are not new as they coincide with classical theorems like the good old Gauss-Markov or Aitken Theorem, respectively; the exceptional theorem is incorrect. Hansen (2021b) corrects this theorem. As a result, all theorems in the latter version coincide with the above mentioned classical theorems. Furthermore, we also show that the theorems in Hansen (2022) (the version published in Econometrica) either coincide with the classical theorems just mentioned, or contain extra assumptions that are alien to the Gauss-Markov or Aitken Theorem.