Omitted and Included Variable Bias in Tests for Disparate Impact
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Policymakers often seek to gauge discrimination against groups defined by race, gender, and other protected attributes. One popular strategy is to estimate disparities after controlling for observed covariates, typically with a regression model. This approach, however, suffers from two statistical challenges. First, omitted-variable bias can skew results if the model does not control for all relevant factors; second, and conversely, included-variable bias can skew results if the set of controls includes irrelevant factors. Here we introduce a simple three-step strategy---which we call risk-adjusted regression---that addresses both concerns in settings where decision makers have clearly measurable objectives. In the first step, we use all available covariates to estimate the utility of possible decisions. In the second step, we measure disparities after controlling for these utility estimates alone, mitigating the problem of included-variable bias. Finally, in the third step, we examine the sensitivity of results to unmeasured confounding, addressing concerns about omitted-variable bias. We demonstrate this method on a detailed dataset of 2.2 million police stops of pedestrians in New York City, and show that traditional statistical tests of discrimination can yield misleading results. We conclude by discussing implications of our statistical approach for questions of law and policy.
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