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

2026-03-31

AI Summary

This study investigates whether the choice of reference group in Oaxaca-Blinder decomposition can lead to substantively opposite conclusions about the sources of group disparities. Through theoretical derivation, simulation experiments, and empirical analysis, it systematically demonstrates for the first time that conclusion reversals can occur across as much as half of the parameter space when different reference groups are used. However, such reversals are rare in real-world data, as empirical data-generating processes tend to produce structurally stable parameter configurations. The paper not only rigorously characterizes the conditions under which decomposition results become unstable but also explains why this instability seldom manifests in practice, thereby offering both theoretical grounding and empirical guidance for the appropriate application and interpretation of decomposition methods.

Abstract

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.

Problem

• Oaxaca-Blinder decomposition
• reference group
• substantive conclusions
• group differences
• covariates

Innovation

• Oaxaca-Blinder decomposition
• reference group choice
• causal interpretation
• parameter space analysis
• empirical robustness