  The estimation of racial disparities in various fields is often hampered by
the lack of individual-level racial information. In many cases, the law
prohibits the collection of such information to prevent direct racial
discrimination. As a result, analysts have frequently adopted Bayesian Improved
Surname Geocoding (BISG) and its variants, which combine individual names and
addresses with Census data to predict race. Unfortunately, the residuals of
BISG are often correlated with the outcomes of interest, generally attenuating
estimates of racial disparities. To correct this bias, we propose an
alternative identification strategy under the assumption that surname is
conditionally independent of the outcome given (unobserved) race, residence
location, and other observed characteristics. We introduce a new class of
models, Bayesian Instrumental Regression for Disparity Estimation (BIRDiE),
that take BISG probabilities as inputs and produce racial disparity estimates
by using surnames as an 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 BISG+BIRDiE reduces error by up to 84% when estimating racial differences
in party registration. Finally, we apply the proposed methodology to estimate
racial differences in who benefits from the home mortgage interest deduction
using individual-level tax data from the U.S. Internal Revenue Service.
Open-source software is available which implements the proposed methodology.
