Primary Submission Category: Sensitivity Analysis
Bounding Disparities under Selective Reporting
Authors: Elsa Palumbo, Edward Kennedy, Leah Jacobs,
Presenting Author: Elsa Palumbo*
Understanding disparities in outcomes across subpopulations is a central problem in the social sciences. However, accurately quantifying the magnitude of a disparity is challenging when the observed data are unrepresentative. The case of selective reporting is especially difficult, since standard biased sampling tools do not apply. In this paper, we develop a nonparametric sensitivity model to address this challenge. We derive tight bounds on the conditional mean outcome for each treatment group and, from those, bounds on the covariate-adjusted mean outcome as well. Using this result, we provide doubly robust estimators for the covariate-adjusted bounds, assuming the margin condition in order to handle the non-smoothness of our target parameters. Finally, we implement our sensitivity analysis framework on traffic stop data from the Racial and Identity Profiling Act (RIPA), bounding the relative risk of police use of force against civilians with and without perceived mental illness. At 5% missing records, we predict a three to four times higher risk for those with perceived mental illness. The existence of a disparity is robust to substantial missingness, allowing up to 35% unrecorded traffic stops.