Rigor of Hansen (2022a) Theorems 4–7

Determine whether rigorous proofs of Theorems 4, 5, 6, and 7 in Hansen (2022a, “A Modern Gauss–Markov Theorem,” Econometrica 90, 1283–1294) can be obtained, given that their published proofs rely on Theorem 10.6 in Hansen (2022b, Probability and Statistics for Economists), which presents a non-rigorous rendition of the Cramér–Rao lower bound lacking required regularity conditions.

Background

In criticizing the proofs presented in Hansen (2022a), the authors note that these proofs depend on Theorem 10.6 in Hansen (2022b), which they argue does not state necessary regularity conditions for the Cramér–Rao bound and is therefore not rigorous as given. They observe that similar issues undermine the proof of Theorem 11.1 in Hansen (2022b).

The authors suggest the possibility that the proofs in Hansen (2022a) might be repairable but explicitly state they have not checked this in detail, thereby leaving open the question of whether rigorous proofs can be produced for those results.