Yanping Chen
arXiv 1 Sep 2026 · Econometrics
arXiv:2609.01804 · PDF · Extracted main text
Inference in linear regression commonly treats OLS residuals as proxies for unobserved errors. This approximation can fail when the regression projection is nonlocal relative to the error-dependence structure. Residualization then shifts covariance information across observations and clusters, while conventional heteroskedasticity-consistent (HC) and cluster-robust variance estimators (CRVE) retain only diagonal or within-cluster residual moments and may therefore understate sampling uncertainty. This paper develops a projection-geometry framework for robust variance estimation. The variance of the OLS estimator is represented exactly as a Riesz functional of latent covariance blocks, and observable residual moments are linked to the target through a linear operator determined by the full regression projection. This formulation reduces variance estimation to a linear inverse problem. I propose a Riesz variance estimator that combines within- and cross-cluster residual moments. Conventional HC and CRVE emerge as restricted approximations whose validity depends on negligible projection spillovers. The estimator remains well defined when cluster-specific leverage matrices are singular and is computed by an iterative algorithm that avoids explicit matrix inversion. Simulations show substantial undercoverage by conventional methods under projection spillovers, whereas the proposed estimator restores near-nominal coverage. In an application to colonial governor promotions, the correction changes the significance of four of five reported coefficients.
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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 | Cattaneo, Matias D and Jansson, Michael and Newey, Whitney K (2018) Inference in linear regression models with many covariates and heteroscedasticity | 1.000 | 11 | 5 | 100% |
| 2 | Xu, Guo (2018) The costs of patronage: Evidence from the british empire | 1.000 | 5 | 4 | 100% |
| 3 | Djogbenou, Antoine A and MacKinnon, James G and Nielsen, Morten Ørre… (2019) Asymptotic theory and wild bootstrap inference with clustered errors | 0.928 | 4 | 3 | 100% |
| 4 | Paige, Christopher C and Saunders, Michael A (1982) LSQR: An algorithm for sparse linear equations and sparse least squares | 0.811 | 4 | 2 | 100% |
| 5 | Anatolyev, Stanislav and Yaskov, Pavel (2017) Asymptotics of diagonal elements of projection matrices under many instruments/regressors | 0.737 | 3 | 2 | 100% |
| 6 | Anatolyev, Stanislav and Smirnov, Maksim (2024) Off-diagonal elements of projection matrices and dimension asymptotics | 0.644 | 2 | 2 | 100% |
| 7 | Golub, Gene and Kahan, William (1965) Calculating the singular values and pseudo-inverse of a matrix | 0.644 | 2 | 2 | 100% |
| 8 | Anatolyev, Stanislav and Ng, Cheuk Fai (2026) Many covariate and cluster robust estimation and inference | 0.585 | 3 | 1 | 100% |
| * | unmatched citation key * | 0.405 | 1 | 1 | 100% |
| 10 | Arellano, Manuel (1987) Computing robust standard errors for within-groups estimators. | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 31 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.