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We discuss some causal estimands used to study racial discrimination inpolicing. A central challenge is that not all police-civilian encounters arerecorded in administrative datasets and available to researchers. One possiblesolution is to consider the average causal effect of race conditional on thecivilian already being detained by the police. We find that such an estimandcan be quite different from the more familiar ones in causal inference andneeds to be interpreted with caution. We propose using an estimand new for thiscontext -- the causal risk ratio, which has more transparent interpretation andrequires weaker identification assumptions. We demonstrate this through areanalysis of the NYPD Stop-and-Frisk dataset. Our reanalysis shows that thenaive estimator that ignores the post-treatment selection in administrativerecords may severely underestimate the disparity in police violence betweenminorities and whites in these and similar data.

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