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“We find that stopped black and Hispanic pedestrians had about twice the odds of being frisked than white pedestrians who were equally likely to be carrying a weapon… Further, the risk-adjusted disparities are in fact greater than the raw disparities in frisk rates, a finding consistent with the fact that stopped whites are, on average, more likely to be carrying a weapon than stopped minorities."

Omitted and Included Variable Bias in Tests for Disparate Impact Omitted and Included Variable Bias in Tests for Disparate Impact Figure 3: Different estimates of racially disparate impacts of frisk decisions, where the y-axis is the odds of being frisked for each race group relative to white individuals. The left-most panel shows the raw disparities in frisk rates. As a measure of discrimination, raw disparities suffer from omitted-variable bias: there may be legitimate reasons why black and Hispanic pedestrians are more likely to be frisked. The second panel shows the estimated race effects in a kitchen-sink regression, controlling for all pre-frisk covariates. These estimates suffer from included-variable bias because they control for features that are correlated with race but unrelated to risk. The right two panels show the results of our risk-adjusted regression, controlling for risk only, and for risk and location. The measured disparities are robust to different specifications of the risk transformation g, and 95% bootstrap confidence intervals are shown for each estimate. Figure 3: Different estimates of racially disparate impacts of frisk decisions, where the y-axis is the odds of being frisked for each race group relative to white individuals. The left-most panel shows the raw disparities in frisk rates. As a measure of discrimination, raw disparities suffer from omitted-variable bias: there may be legitimate reasons why black and Hispanic pedestrians are more likely to be frisked. The second panel shows the estimated race effects in a kitchen-sink regression, controlling for all pre-frisk covariates. These estimates suffer from included-variable bias because they control for features that are correlated with race but unrelated to risk. The right two panels show the results of our risk-adjusted regression, controlling for risk only, and for risk and location. The measured disparities are robust to different specifications of the risk transformation g, and 95% bootstrap confidence intervals are shown for each estimate.
Omitted and Included Variable Bias in Tests for Disparate Impact
working paper
Jung, Jongbin / Corbett-Davies, Sam / Shroff, Ravi / Goel, Sharad
29 August 2019
https://scholar.stanford.edu/papers/included-variable-bias.pdf
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