Omitted variables are one of the most important threats to the identification of causal effects. Several widely used approaches, including Oster (2019), assess the impact of omitted variables on empirical conclusions by comparing measures of selection on observables with measures of selection on unobservables. These approaches either (1) assume the omitted variables are uncorrelated with the included controls, an assumption that is often considered strong and implausible, or (2) use a method called residualization to avoid this assumption. In our first contribution, we develop a framework for objectively comparing sensitivity parameters. We use this framework to formally prove that the residualization method generally leads to incorrect conclusions about robustness. In our second contribution, we then provide a new approach to sensitivity analysis that avoids this critique, allows the omitted variables to be correlated with the included controls, and lets researchers calibrate sensitivity parameters by comparing the magnitude of selection on observables with the magnitude of selection on unobservables as in previous methods. We illustrate our results in an empirical study of the effect of historical American frontier life on modern cultural beliefs. Finally, we implement these methods in the companion Stata module regsensitivity for easy use in practice.

翻译：遗漏变量是因果效应识别中最关键的威胁之一。包括Oster (2019)在内的几种广泛使用的方法,通过比较可观测变量选择强度与不可观测变量选择强度来评估遗漏变量对实证结论的影响。这些方法要么(1)假设遗漏变量与包含的控制变量不相关——这一假设通常被认为过于严格且不切实际,要么(2)采用称为"残差化"的方法来规避该假设。在第一个贡献中,我们构建了一个客观比较敏感性参数的框架。利用此框架,我们严格证明了残差化方法通常会导致关于稳健性的错误结论。在第二个贡献中,我们提出了一种新的敏感性分析方法,该方法既避免了上述批评,又允许遗漏变量与包含的控制变量相关,同时使研究者能够像以往方法那样通过比较可观测变量选择强度与不可观测变量选择强度来校准敏感性参数。我们通过一项关于美国历史边疆生活对现代文化信仰影响的实证研究展示了结果。最后,我们将这些方法实现于配套的Stata模块regsensitivity中,便于实际应用。