arXiv 22 Feb 2026 · Econometrics
arXiv:2602.19384 · PDF · DOI · OpenAlex · Extracted main text
Robustness checks are routine in empirical work, but there is no standard statistical procedure to formally measure what one can learn from them. I propose a "robustness radius" measure to quantify the amount by which the robustness checks estimands differ from the main specification estimand. I do so by framing robustness checks as explicitly biased regressions, clarifying what exactly the estimands are when comparing multiple regressions with slightly different samples, and applying a test from the moment inequalities literature. The robustness radius is easily interpretable and adapts to sampling uncertainty and correlation across regressions. An application shows that, although assessing overall robustness is context-specific, the robustness radius guides those judgments and improves transparency.
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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 | Lu, Xun and White, Halbert (2014) Robustness checks and robustness tests in applied economics | 1.000 | 6 | 3 | 100% |
| 2 | Cox, Gregory and Shi, Xiaoxia (2022) Simple Adaptive Size-Exact Testing for Full-Vector and Subvector Inference in Moment Inequality Models | 0.932 | 21 | 5 | 81% |
| 3 | Paul Diegert and Matthew A. Masten and Alexandre Poirier (2023) Assessing Omitted Variable Bias when the Controls are Endogenous | 0.874 | 6 | 2 | 100% |
| 4 | Bei, Xinyue (2024) Inference on Union Bounds | 0.843 | 3 | 3 | 100% |
| 5 | Massenkoff, Maxim and Wilmers, Nathan (2023) Wage Stagnation and the Decline of Standardized Pay Rates, 1974–1991 | 0.737 | 3 | 2 | 100% |
| 6 | Altonji, Joseph G. and Elder, Todd E. and Taber, Christopher R (2005) Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools | 0.644 | 2 | 2 | 100% |
| 7 | Chernozhukov, Victor and others (2024) Long Story Short: Omitted Variable Bias in Causal Machine Learning | 0.644 | 2 | 2 | 100% |
| 8 | Cinelli, Carlos and Hazlett, Chad (2020) Making sense of sensitivity: Extending omitted variable bias | 0.644 | 2 | 2 | 100% |
| 9 | Oster, Emily (2019) Unobservable selection and coefficient stability: Theory and evidence | 0.644 | 2 | 2 | 100% |
| 10 | Hansen, B (2022) Econometrics | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 22 scored citations.