Omitted variables are a common concern in empirical research. We distinguish between two ways omitted variables can affect baseline estimates: by driving them to zero or by reversing their sign. 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. Consequently, results which are considered robust to being "explained away" by omitted variables are not necessarily robust to sign changes. We show that this behavior occurs with "Oster's delta" (Oster 2019), a commonly reported measure of regression coefficient robustness to the presence of omitted variables. Specifically, we show that 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. Relatedly, we show that selection bias adjusted estimands can be extremely sensitive to the choice of the sensitivity parameter. Specifically, researchers commonly compute a bias adjustment under the assumption that Oster's delta equals one. Under the alternative assumption that delta is very close to one, but not exactly equal to one, we show that the bias can instead be arbitrarily large. To address these concerns, we propose a modified measure of robustness that accounts for such sign changes, and discuss best practices for assessing sensitivity to omitted variables. We demonstrate this sign flipping behavior in an empirical application to social capital and the rise of the Nazi party, where we show how it can overturn conclusions about robustness, and how our proposed modifications can be used to regain robustness. We analyze three additional empirical applications as well. We implement our proposed methods in the companion Stata module regsensitivity for easy use in practice.

翻译：省略变量是实证研究中常见的问题。我们区分了省略变量影响基准估计值的两种方式：使其趋近于零或使其符号反转。研究表明，根据省略变量影响程度的衡量方式，省略变量更容易导致系数符号反转而非趋近于零。因此，那些被认为对省略变量"解释掉"结果具有稳健性的结论，未必能抵御符号反转。我们证明这种效应出现在"Oster's delta"（Oster 2019）这一常用的回归系数对省略变量稳健性度量指标中。具体而言，我们证明每当该指标值较大时——暗示省略变量可能不重要——一个更小的值就足以使目标参数符号反转。与此相关，我们证明选择偏差调整后的估计量对敏感性参数的选择极为敏感。具体而言，研究者通常假设Oster's delta等于1来计算偏差调整。若假设delta非常接近但并非精确等于1时，偏差反而可能任意大。为解决这些问题，我们提出一种考虑符号反转的改进稳健性度量指标，并讨论评估省略变量敏感性的最佳实践。我们通过社会资本与纳粹党崛起的实证应用展示这种符号翻转行为，说明它如何推翻关于稳健性的结论，以及我们提出的改进方法如何恢复稳健性。此外，我们还分析了另外三个实证应用。我们在配套Stata模块regsensitivity中实现了所提方法，便于实际应用。