Paul Diegert, Matthew A. Masten, Alexandre Poirier
arXiv 29 Apr 2025 · Econometrics
arXiv:2504.21106 · PDF · DOI · OpenAlex · Extracted main text
Many methods are available for assessing the importance of omitted variables. These methods typically make different, non-falsifiable assumptions. Hence the data alone cannot tell us which method is most appropriate. Since it is unreasonable to expect results to be robust against all possible robustness checks, researchers often use methods deemed "interpretable", a subjective criterion with no formal definition. In contrast, we develop the first formal, axiomatic framework for comparing and selecting among these methods. Our framework is analogous to the standard approach for comparing estimators based on their sampling distributions. We propose that sensitivity parameters be selected based on their covariate sampling distributions, a design distribution of parameter values induced by an assumption on how covariates are assigned to be observed or unobserved. Using this idea, we define a new concept of parameter consistency, and argue that a reasonable sensitivity parameter should be consistent. We prove that the literature's most popular approach is inconsistent, while several alternatives are consistent.
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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 | Altonji, J. G., T. E. Elder, and C. R. Taber (2005) Selection on observed and unobserved variables: Assessing the effectiveness of Catholic schools | 1.000 | 16 | 4 | 100% |
| 2 | Diegert, P., M. A. Masten, and A. Poirier (2025) Assessing omitted variable bias when the controls are endogenous self | 1.000 | 8 | 4 | 100% |
| 3 | Cinelli, C. and C. Hazlett (2020) Making sense of sensitivity: Extending omitted variable bias | 1.000 | 8 | 3 | 100% |
| 4 | Altonji, J. G., T. Conley, T. E. Elder, and C. R. Taber (2019) Methods for using selection on observed variables to address selection on unobserved variables | 1.000 | 7 | 3 | 100% |
| 5 | Oster, E (2019) Unobservable selection and coefficient stability: Theory and evidence | 0.874 | 12 | 2 | 100% |
| 6 | Bazzi, S., M. Fiszbein, and M. Gebresilasse (2020) Frontier culture: The roots and persistence of “rugged individualism” in the United States | 0.737 | 3 | 2 | 100% |
| 7 | Masten, M. A. and A. Poirier (2025) The effect of omitted variables on the sign of regression coefficients self | 0.737 | 3 | 2 | 100% |
| 8 | Abadie, A., S. Athey, G. W. Imbens, and J. M. Wooldridge (2020) Sampling-based versus design-based uncertainty in regression analysis | 0.644 | 2 | 2 | 100% |
| 9 | Krauth, B (2016) Bounding a linear causal effect using relative correlation restrictions | 0.644 | 2 | 2 | 100% |
| 10 | Aizer, A., N. Early, S. Eli, G. Imbens, K. Lee, A. Lleras-Muney, and… (2024) The Lifetime Impacts of the New Deal's Youth Employment Program | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 23 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Assessing Omitted Variable Bias when the Controls are Endogenous | 1.000 | 9 | 3 |