Whether racial disparities in enrollment in advanced high school coursework
can be attributed to differences in prior academic preparation is a central
empirical question in sociological research, with important implications for
education policy. However, the regression-based approaches to this question
that are predominant in the literature suffer significant methodological
limitations by implicitly assuming that students are similarly prepared if and
only if they have similar values on a selected set of academic background
measures. Here, we provide a general technique to estimate enrollment
disparities in advanced coursework between similarly-prepared students of
different races that is less vulnerable to these limitations. We introduce a
novel measure of academic preparedness, a student's ex-ante probability of
"success" in the course, directly adjust for this single measure in a
regression model of enrollment on race, and assess the robustness of estimated
disparities to potential unmeasured confounding. We illustrate this approach by
analyzing Black-White disparities in AP mathematics enrollment in a large,
urban, public school system in the United States. We find that preexisting
differences in academic preparation do not fully explain the
under-representation of Black students relative to White students in AP
mathematics, and contrast our results with those from traditional approaches