The Problem of Infra-marginality in Outcome Tests for Discrimination

TL;DR

This paper introduces the threshold test, a new statistical method that improves discrimination detection in decision-making by addressing infra-marginality, demonstrated through analysis of North Carolina police stop data.

Contribution

The paper develops a hierarchical Bayesian threshold test that jointly estimates decision thresholds and risk distributions to better detect discrimination.

Findings

Infra-marginality significantly affects outcome test accuracy.

The threshold test reveals more accurate discrimination signals.

Infra-marginality can cause outcome tests to mislead in real-world data.

Abstract

Outcome tests are a popular method for detecting bias in lending, hiring, and policing decisions. These tests operate by comparing the success rate of decisions across groups. For example, if loans made to minority applicants are observed to be repaid more often than loans made to whites, it suggests that only exceptionally qualified minorities are granted loans, indicating discrimination. Outcome tests, however, are known to suffer from the problem of infra-marginality: even absent discrimination, the repayment rates for minority and white loan recipients might differ if the two groups have different risk distributions. Thus, at least in theory, outcome tests can fail to accurately detect discrimination. We develop a new statistical test of discrimination---the threshold test---that mitigates the problem of infra-marginality by jointly estimating decision thresholds and risk distributions via a hierarchical Bayesian latent variable model. Applying our test to a dataset of 4.5 million police stops in North Carolina, we find that the problem of infra-marginality is more than a theoretical possibility, and can cause the outcome test to yield misleading results in practice.