Average gaps and Oaxaca-Blinder decompositions : a cautionary tale about regression estimates of racial differences in labor market outcomes

In this paper I demonstrate, both theoretically and empirically, that the interpretation of regression estimates of between-group differences in economic outcomes depends on the relative sizes of subpopulations under study. When the disadvantaged group is small, regression estimates are similar to its average loss. When this group is instead a numerical majority, regression estimates are similar to the average gain for advantaged individuals. I analyze black-white test score gaps using ECLS-K data and black-white wage gaps using CPS, NLSY79, and NSW data, documenting that the interpretation of regression estimates varies dramatically across applications. Methodologically, I also develop a new version of the Oaxaca-Blinder decomposition whose unexplained component recovers a parameter referred to as the average outcome gap. Under a particular conditional independence assumption, this estimand is equivalent to the average treatment effect (ATE). Finally, I provide treatment-effects reinterpretations of the Reimers, Cotton, and Fortin decompositions.