Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption, which states that the instrument and any confounding factor must be independent. However, if this independence condition is not met, can we still work with imperfect instrumental variables? Imperfect instruments can manifest themselves by violations of the instrumental inequalities that constrain the set of correlations in the scenario. In this paper, we establish a quantitative relationship between such violations of instrumental inequalities and the minimal amount of measurement dependence required to explain them. As a result, we provide adapted inequalities that are valid in the presence of a relaxed measurement dependence assumption in the instrumental scenario. This allows for the adaptation of existing and new lower bounds on the average causal effect for instrumental scenarios with binary outcomes. Finally, we discuss our findings in the context of quantum mechanics.
翻译:为达到这一目的,必须满足若干因果假设,其中最重要的是独立假设,其中指出文书和任何混淆因素必须是独立的;然而,如果这一独立条件没有得到满足,我们仍能用不完善的工具变量开展工作吗?不完善的文书可以表现为违反制约假设中一系列相互关系的因果不平等。在本文件中,我们在侵犯工具不平等与解释这些不平等所需的衡量依赖程度最低之间建立起一种定量关系。因此,我们提供了经调整的不平等,在工具假设中存在一种宽松的衡量依赖性假设时,这些不平等是有效的。这允许对具有双重结果的工具情景的平均因果作用调整现有和新的较低界限。最后,我们在量力力学方面讨论了我们的结论。