Estimating Racial Disparities When Race is Not Observed

The estimation of racial disparities in health care, financial services, voting, and other contexts is often hampered by the lack of individual-level racial information in administrative records. In many cases, the law prohibits the collection of such information to prevent direct racial discrimination. As a result, many analysts have adopted Bayesian Improved Surname Geocoding (BISG), which combines individual names and addresses with the Census data to predict race. Although BISG tends to produce well-calibrated racial predictions, its residuals are often correlated with the outcomes of interest, yielding biased estimates of racial disparities. We propose an alternative identification strategy that corrects this bias. The proposed strategy is applicable whenever one's surname is conditionally independent of the outcome given their (unobserved) race, residence location, and other observed characteristics. Leveraging this identification strategy, we introduce a new class of models, Bayesian Instrumental Regression for Disparity Estimation (BIRDiE), that estimate racial disparities by using surnames as a high-dimensional instrumental variable for race. Our estimation method is scalable, making it possible to analyze large-scale administrative data. We also show how to address potential violations of the key identification assumptions. A validation study based on the North Carolina voter file shows that BIRDiE reduces error by up to 84% in comparison to the standard approaches for estimating racial differences in party registration. Open-source software is available which implements the proposed methodology.