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The Effect of Omitted Variables on the Sign of Regression Coefficients
(Forthcoming Article) - 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 2019b), 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.
