2023/07/01 by Deepankar Basu, Basu, Deepankar · 1 citation
Mathematics · #Advanced Statistical Methods and Models #Econometrics (econ.EM) #FOS: Economics and business
paper · pdf · doi:10.48550/arxiv.2307.00369
openalex publication_date 2023/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper traces the historical and analytical development of what is known in the econometrics literature as the Frisch-Waugh-Lovell theorem. This theorem demonstrates that the coefficients on any subset of covariates in a multiple regression is equal to the coefficients in a regression of the residualized outcome variable on the residualized subset of covariates, where residualization uses the complement of the subset of covariates of interest. In this paper, I suggest that the theorem should be renamed as the Yule-Frisch-Waugh-Lovell (YFWL) theorem to recognize the pioneering contribution of the statistician G. Udny Yule in its development. Second, I highlight recent work by the statistician, P. Ding, which has extended the YFWL theorem to a comparison of estimated covariance matrices of coefficients from multiple and partial, i.e. residualized regressions. Third, I show that, in cases where Ding's results do not apply, one can still resort to a computational method to conduct statistical inference about coefficients in multiple regressions using information from partial regressions.