Causal inference with imperfect instrumental variables
This work addresses a fundamental limitation in causal inference for researchers dealing with imperfect data, though it is incremental as it builds on existing instrumental variable methods.
The paper tackles the problem of causal inference with imperfect instrumental variables that violate independence assumptions, establishing a quantitative link between violations of instrumental inequalities and the minimal measurement dependence needed, and provides adapted inequalities for binary outcomes.
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.