# The Frisch--Waugh--Lovell Theorem for Standard Errors

arXiv: https://arxiv.org/abs/2009.06621 · HTML: https://mlsanity.com/paper/2009.06621/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Weak instrumental variables due to ignored nonlinearities in panel data: A Super Learner Control Function estimator](https://mlsanity.com/paper/2504.03228/) (2025)
- [Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes](https://mlsanity.com/paper/2410.04996/) (2024)

## Abstract (arXiv)

The Frisch--Waugh--Lovell Theorem states the equivalence of the coefficients from the full and partial regressions. I further show the equivalence between various standard errors. Applying the new result to stratified experiments reveals the discrepancy between model-based and design-based standard errors.