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The Effect of Omitted Variables on the Sign of Regression Coefficients

Matthew A. Masten, Alexandre Poirier

arXiv 1 Aug 2022 · Econometrics

arXiv:2208.00552 · PDF · Extracted main text

Abstract

We show that, depending on how the impact of omitted variables is measured, it can be substantially easier for omitted variables to flip coefficient signs than to drive them to zero. This behavior occurs with "Oster's delta" (Oster 2019), a widely reported robustness measure. Consequently, any time this measure is large -- suggesting that omitted variables may be unimportant -- a much smaller value reverses the sign of the parameter of interest. We propose a modified measure of robustness to address this concern. We illustrate our results in four empirical applications and two meta-analyses. We implement our methods in the companion Stata module regsensitivity.

Citation extraction

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in-text mentions
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distinct cited
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main-text words

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
Oster2019unmatched citation key Oster20190.0002340%
SatyanathVoigtlanderVoth2017unmatched citation key SatyanathVoigtlanderVoth20170.0001020%
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BlandholEtAl2022unmatched citation key BlandholEtAl20220.000210%
8Abaluck, J., M. Caceres Bravo, P. Hull, and A. Starc (2021) Mortality effects and choice across private health insurance plans0.000110%
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Showing the top 10 of 39 scored citations. 3 of these could not be matched to a bibliography entry, so only the citation key is shown.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1An Axiomatic Approach to Comparing Sensitivity Parameters0.73732
2Assessing Omitted Variable Bias when the Controls are Endogenous0.58531
3Robustness to Missing Data: Breakdown Point Analysis0.40511