Do covariates explain why these groups differ? The choice of reference group can reverse conclusions in the Oaxaca-Blinder decomposition
This addresses a methodological issue for researchers using OBD in fields like social sciences and healthcare, but it is incremental as it builds on known limitations of the method.
The paper investigates how the choice of reference group in the Oaxaca-Blinder decomposition (OBD) can lead to substantively different conclusions about whether covariates explain group differences, finding that this occurs in up to half of the parameter space in theory but is rare in real-world data analyses.
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. To the best of our knowledge, there has not been a systematic investigation into whether the choice of OBD reference can yield different substantive conclusions and how common this issue is. In the present paper, we give existence proofs in real and simulated data that the OBD references can yield substantively different conclusions and that these differences are not entirely driven by model misspecification or small data. We prove that substantively different conclusions occur in up to half of the parameter space, but find these discrepancies rare in the real-data analyses we study. We explain this empirical rarity by examining how realistic data-generating processes can be biased towards parameters that do not change conclusions under the OBD.