A note on post-treatment selection in studying racial discrimination in policing

TL;DR

This paper examines how post-treatment selection affects the measurement of racial discrimination in policing, proposing a new causal estimand and reanalyzing NYPD data to reveal potential underestimation of disparities.

Contribution

It introduces the causal risk ratio as a more interpretable estimand for studying racial disparities in police encounters, accounting for post-treatment selection.

Findings

Naive estimators can underestimate racial disparities.

The causal risk ratio offers clearer interpretation with weaker assumptions.

Reanalysis of NYPD data shows larger disparities than previously estimated.

Abstract

We discuss some causal estimands used to study racial discrimination in policing. A central challenge is that not all police-civilian encounters are recorded in administrative datasets and available to researchers. One possible solution is to consider the average causal effect of race conditional on the civilian already being detained by the police. We find that such an estimand can be quite different from the more familiar ones in causal inference and needs to be interpreted with caution. We propose using an estimand new for this context -- the causal risk ratio, which has more transparent interpretation and requires weaker identification assumptions. We demonstrate this through a reanalysis of the NYPD Stop-and-Frisk dataset. Our reanalysis shows that the naive estimator that ignores the post-treatment selection in administrative records may severely underestimate the disparity in police violence between minorities and whites in these and similar data.