arXiv 3 Jul 2026 · Econometrics
arXiv:2607.03331 · PDF · DOI · OpenAlex · Extracted main text
Conventional heteroskedasticity diagnostics ask whether the conditional variance of the regression disturbance varies with covariates. This paper asks a different question: when does that variation matter for inference on the estimand of interest? The paper develops a contrast-specific theory characterizing when covariance perturbations are inferentially relevant. We show that, for any linear contrast $a'β$ in a linear regression, the difference between the heteroskedasticity-robust variance and the pooled fixed-design variance is governed by the empirical covariance between conditional error variance and a contrast-specific leverage score. Thus, heteroskedasticity may be present in the model yet first-order irrelevant for a particular coefficient or linear combination. Conversely, modest heteroskedasticity may have a large inferential effect if it is concentrated on observations that are highly informative for the contrast of interest. We characterize the effect exactly through a heteroskedasticity relevance ratio and a standard-error inflation factor, relate the result to pairs and residual bootstrap procedures, and extend the decomposition to general covariance structures, where off-diagonal dependence contributes a separate contrast-specific term. The results provide a unified way to understand why robust, clustered, and bootstrap standard errors can differ across coefficients in the same regression.
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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 | King, Gary and Roberts, Margaret E (2015) How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It | 0.928 | 4 | 3 | 100% |
| 2 | Harrison, David and Rubinfeld, Daniel L (1978) Hedonic Housing Prices and the Demand for Clean Air | 0.737 | 3 | 2 | 100% |
| 3 | Chesher, Andrew and Austin, Guy (1991) The finite-sample distributions of heteroskedasticity robust Wald statistics | 0.644 | 2 | 2 | 100% |
| 4 | White, Halbert (1980) A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity | 0.644 | 2 | 2 | 100% |
| 5 | Patrick Billingsley (1995) Probability and Measure | 0.511 | 2 | 2 | 50% |
| 6 | Breusch, Trevor S. and Pagan, Adrian R (1979) A Simple Test for Heteroscedasticity and Random Coefficient Variation | 0.511 | 2 | 1 | 100% |
| 7 | MacKinnon, James G (2013) Thirty Years of Heteroskedasticity-Robust Inference | 0.511 | 2 | 1 | 100% |
| 8 | Andrews, Donald W. K (1991) Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation | 0.405 | 1 | 1 | 100% |
| 9 | Arellano, Manuel (1987) Computing Robust Standard Errors for Within-Groups Estimators | 0.405 | 1 | 1 | 100% |
| 10 | Belsley, David A. and Kuh, Edwin and Welsch, Roy E (1980) Regression Diagnostics: Identifying Influential Data and Sources of Collinearity | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 29 scored citations.