arXiv 1 Jul 2023 · Econometrics
arXiv:2307.00369 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Yule, G. U (1907) On the Theory of Correlation for any number of Variables, treated by a New System of Notation | 1.000 | 21 | 5 | 100% |
| 2 | Lovell, M. C (1963) Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis | 0.971 | 12 | 4 | 92% |
| 3 | Ding, P (2021) The Frisch-Waugh-Lovell theorem for standard errors | 0.961 | 9 | 3 | 89% |
| 4 | Frisch, R. and Waugh, F. V (1933) Partial Time Regressions as Compared with Individual Trends | 0.954 | 23 | 6 | 87% |
| 5 | Angrist, J. D. and Pischke, J.-S (2009) Mostly Harmless Econometrics | 0.737 | 3 | 2 | 100% |
| 6 | Greene, W. H (2012) Econometric Analysis | 0.644 | 4 | 2 | 50% |
| 7 | Krishnakumar, J (2006) Chapter 5 time invariant variables and panel data models: A generalised frisch–waugh theorem and its implications | 0.644 | 2 | 2 | 100% |
| 8 | Davidson, R. and MacKinnon, J. G (1993) Estimation and Inference in Econometrics | 0.511 | 2 | 1 | 100% |
| 9 | Agresti, A (2015) Foundations of Linear and Generalized Linear Models | 0.405 | 1 | 1 | 100% |
| 10 | Ahrens, M., Ashwin, J., Calliess, J.-P., and Nguyen, V (2021) Bayesian Topic Regression for Causal Inference | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.