📌 The Measurement Problem

Not all police–civilian encounters appear in administrative datasets available to researchers. One common workaround is to measure the effect of race only among civilians who have already been detained by police, but this selection is made after the treatment (race) and so can distort causal conclusions.

🧾 What This Choice Actually Estimates

• Considering the average causal effect of race conditional on being detained is a distinct estimand from the more familiar unconditional causal measures and can lead to different conclusions.
• Such a post-treatment conditional estimand must be interpreted with caution because the sample of recorded encounters is itself affected by race and policing decisions.

🔍 A Better Estimand and How It Helps

• The causal risk ratio is proposed as an alternative estimand for this context.
• The causal risk ratio offers a more transparent interpretation of disparities and requires weaker identification assumptions than the post-treatment conditional average effect.

🧾 Reanalysis of Stop-and-Frisk Records

• The NYPD Stop-and-Frisk dataset is reanalyzed to illustrate these points.
• The reanalysis shows that a naive estimator that ignores post-treatment selection in administrative records can severely underestimate disparities in police violence between minorities and whites.

⚖️ Why It Matters

• Studies that condition on detention without accounting for selection may understate racial disparities in policing outcomes.
• Using the causal risk ratio or similar estimands gives clearer, more robust assessments of racial disparities when working with incomplete administrative records.