Oaxaca-Blinder Health Decomposition

The explained (composition) component is the part of the mean health gap that would remain if the two groups had identical returns to their characteristics but kept their actual differences in those characteristics, for example differing average income, age, smoking, or insurance. The unexplained (coefficient) component is the part that would remain if the groups had identical covariate distributions but kept their different coefficients, meaning the same exposure maps to different health. In health research the unexplained part is often interpreted as reflecting discrimination, chronic stress, or unmeasured exposures, but because it also absorbs omitted-variable bias it should not be read as a clean causal quantity.

The decomposition requires a reference coefficient vector against which to measure both composition and returns, and there is no uniquely correct choice, this is the classic index-number problem. Using group A's coefficients, group B's coefficients, or a pooled estimate shifts how much of the gap is labeled explained versus unexplained. A common modern practice is to use coefficients from a pooled model that includes a group indicator, but the right answer is to report results under more than one reference and treat the partition as a range rather than a single number. Transparency about the weighting is essential for honest interpretation.

Not with the plain linear identity, because for nonlinear models the mean outcome is not simply mean covariates times coefficients and the exact algebraic split no longer holds. Fairlie's 2005 extension handles this by working with average predicted probabilities from a logit or probit model: the explained part is the change in mean predicted probability when one group's covariate distribution is passed through the other group's coefficients, and the unexplained part is the change from swapping the coefficients. This preserves the explained-unexplained logic for binary and count health outcomes, though results can depend on the order of substitution and how observations are paired across groups.