Do covariates explain why these groups differ? The choice of reference group can reverse conclusions in the Oaxaca-Blinder decomposition

ArXi:2603.29972v1 Announce Type: cross Scientists often want to explain why an outcome is different in two groups. For instance, differences in patient mortality rates across two hospitals could be due to differences in the patients themselves (covariates) or differences in medical care (outcomes given covariates). The Oaxaca--Blinder decomposition (OBD) is a standard tool to tease apart these factors. It is well known that the OBD requires choosing one of the groups as a reference, and the numerical answer can vary with the reference.