Assessing Threats to Inference with Simultaneous Sensitivity Analysis: The Case of US Supreme Court Oral Arguments

Political scientists relying on observational data face substantial challenges in drawing causal inferences. A particularly problematic threat to inference is the unobserved confounder. As a means to assess this threat, we introduce simultaneous sensitivity analysis to the political science literature. As an application, we consider the potentially confounded relationship between Supreme Court justice voting and oral argument quality. We demonstrate that this relationship is sensitive to the presence of a confounder, to a degree that threatens inference, and explore the confounder both theoretically and empirically. More generally, we show how sensitivity analysis can guide inquiry related to a covariate that cannot be directly measured.