  There has been considerable interest in using decomposition methods in
epidemiology (mediation analysis) and economics (Oaxaca-Blinder decomposition)
to understand how health disparities arise and how they might change upon
intervention. It has not been clear when estimates from the Oaxaca-Blinder
decomposition can be interpreted causally because its implementation does not
explicitly address potential confounding of target variables. While mediation
analysis does explicitly adjust for confounders of target variables, it does so
in a way that entails equalizing confounders across racial groups, which may
not reflect the intended intervention. Revisiting prior analyses in the
National Longitudinal Survey of Youth on disparities in wages, unemployment,
incarceration, and overall health with test scores, taken as a proxy for
educational attainment, as a target intervention, we propose and demonstrate a
novel decomposition that controls for confounders of test scores (measures of
childhood SES) while leaving their association with race intact. We compare
this decomposition with others that use standardization (to equalize childhood
SES alone), mediation analysis (to equalize test scores within levels of
childhood SES), and one that equalizes both childhood SES and test scores. We
also show how these decompositions, including our novel proposals, are
equivalent to causal implementations of the Oaxaca-Blinder decomposition.
