Aleksei Opacic presents Disparity Analysis: A Tale of Two Approaches

Abstract: To understand the patterns and trends of various forms of inequality, quantitative social science research has typically relied on statistical models linking the conditional mean of an outcome variable to a set of explanatory factors. A prime example of this approach is the widely used Kitagawa-Oaxaca-Blinder (KOB) method. By fitting two linear models separately for an advantaged group and a disadvantaged group, the KOB method decomposes the between-group outcome disparity into two parts: a part explained by group differences in a set of background characteristics and an unexplained part often dubbed “residual inequality.” In this paper, we explicate, contrast, and extend two distinct approaches to studying group disparities, which we term the descriptive approach, as epitomized by the KOB method and its variants, and the prescriptive approach, which focuses on how a disparity of interest would change under a hypothetical intervention to one or more manipulable treatments. For the descriptive approach, we propose a generalized nonparametric KOB decomposition that considers multiple (sets of) explanatory variables sequentially. For the prescriptive approach, we introduce a variety of stylized interventions, such as lottery-type and affirmative-action-type interventions that close between-group gaps in treatment. We illustrate the two approaches to disparity analysis by assessing the Black-White gap in college completion, how it is statistically explained by racial differences in demographic and socioeconomic background, family structure, academic performance and behavior, and college selectivity, and the extent to which it would be reduced under hypothetical reallocations of college-goers from different racial and economic backgrounds into different tiers of college --- reallocations that could be targeted by race- or class-conscious admissions policies.