Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 221 / 4 / i / Solution

The administrative data include only encounters with $M=1$. Conditioning on the stop indicator selects on the colliderwhich opens the noncausal path $D\leftrightarrow U\to Y$ and creates collider bias. The equal entries estimate only the selected risks $\mathbb{P}(Y=1\mid D=d,M=1)$. They ignore racial differences in the probability of being stopped and therefore do not identify the total causal effect of race on violence. This is also selection bias, because encounters with $M=0$ never enter the dataset.