Many methods are available for assessing the importance of omitted variables in linear regression. These methods typically make different, non-falsifiable assumptions. Hence the data alone cannot tell us which method is most appropriate. Since it is unreasonable to expect results to be robust against all possible robustness checks, researchers often use methods deemed ``interpretable,'' a subjective criterion with no formal definition. In contrast, we develop the first formal, axiomatic framework for comparing and selecting among these methods. Our framework is analogous to the standard approach for comparing estimators based on their sampling distributions. We propose that sensitivity parameters be selected based on their covariate sampling distributions, a design distribution of parameter values induced by an assumption on how covariates are assigned to be observed or unobserved. Using this idea, we define new concepts of parameter consistency and monotonicity, and argue that a reasonable sensitivity parameter should satisfy both properties. We prove that the literature's most popular approach is inconsistent and non-monotonic, while several alternatives satisfy both.

翻译：在线性回归中，评估遗漏变量重要性的方法众多。这些方法通常基于不同且无法证伪的假设，因此仅凭数据本身无法判断哪种方法最为适用。由于期望结果对所有可能的稳健性检验均保持稳健并不现实，研究者常采用被认为具有“可解释性”的方法——这一主观标准缺乏正式定义。与此不同，我们首次建立了用于比较和选择这些方法的正式公理化框架。该框架类似于基于抽样分布比较估计量的标准方法。我们提出，敏感性参数应根据其协变量抽样分布进行选择，该分布是由关于协变量被设定为观测或未观测状态的假设所诱导的参数值设计分布。基于这一思想，我们定义了参数一致性与单调性的新概念，并论证合理的敏感性参数应同时满足这两条性质。我们证明文献中最主流的方法既不满足一致性也不满足单调性，而若干替代方法则能同时满足两者。