The Effect of Omitted Variables on the Sign of Regression Coefficients

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 2019a), a widely reported robustness measure. Consequently, any time this measure is large—suggesting 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."