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：遗漏变量是识别因果效应时最重要威胁之一。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程度与不可观测变量选择程度来评估遗漏变量对经验结论的影响。这些方法要么（1）假设遗漏变量与已纳入的控制变量不相关——这一假设通常被认为过于严格且不切实际，要么（2）采用一种称为残差化的方法来避免该假设。在本文的第一个贡献中，我们构建了一个用于客观比较敏感性参数的框架。利用该框架，我们正式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，该方法避免了上述批评，允许遗漏变量与已纳入的控制变量相关，并使研究者能够像以往方法一样通过比较可观测变量选择程度与不可观测变量选择程度来校准敏感性参数。我们通过对美国历史边疆生活对现代文化信仰影响的一项实证研究来展示研究结果。最后，我们将这些方法实现于配套的Stata模块regsensitivity中，以便于实际应用。