The bias in measuring disparity in outcomes via a dummy variable: A note

Abstract

Disparity in an outcome between two groups is often measured via the coefficient of a dummy variable in a regression that pools both groups. The dummy is interpreted as the disparity. A casual search of the literature in economics and other social sciences reviews far too many examples of this method to catalog. Unfortunately, if the impact of one (or more) of the control variables differs between the two groups, the measured disparity (i.e., the coefficient on the group dummy) will be biased. We illustrate and derive this bias. Given the bias, we believe that one is better running separate regressions for each group and then implementing decomposition methods or predicting adjusted gaps in outcome(i.e., predicting the but-for world that would exist if the two groups had identical characteristics).