Estimating Discrimination in Sentencing: Distinguishing between Good and Bad Controls

To minimise confounding bias and disentangle warranted from unwarranted disparities, researchers examining sentencing discrimination have traditionally sought to control for as many legal factors as possible. However, over the past decade, a growing number of scholars have questioned this strategy, noting that many legal factors are themselves subject to judicial discretion and that controlling for them can introduce post-treatment bias. Here, we use directed acyclic graphs (DAGs) to provide a formal and comprehensive assessment of the different types of bias that may arise from different choices of controls. In addition, we propose a new modelling framework to facilitate the selection of controls and reflect the model uncertainty created by the trade-off inherent in judicially-defined legal factors and other factors with a similar dual causal role. We apply this framework to examine race disparities in US federal courts and gender disparities in the England and Wales magistrates’ court. We find substantial model uncertainty for gender disparities and for race disparities affecting Hispanic offenders, rendering estimates of the latter inconclusive. Disparities against black offenders are more consistent and — under specific conditions — could be interpreted as evidence of direct discrimination.