Definition
The Blinder-Oaxaca decomposition is an econometric technique that splits the difference in a mean outcome between two groups into a part explained by differences in observable characteristics (the "endowments" or composition effect) and a part unexplained by them (the "coefficients" or structural effect, often interpreted as differential returns or discrimination). Developed independently by Alan Blinder and Ronald Oaxaca (1973) for wage gaps, it is now a general tool for decomposing group gaps in any continuous outcome.
Key Ideas
- Two components: the explained gap reflects differences in average characteristics (education, experience, health); the unexplained gap reflects differences in the estimated coefficients (returns to those characteristics) plus the intercept.
- Index-number / reference-group problem: the split depends on which group's coefficients are taken as the non-discriminatory benchmark; "threefold" and pooled-reference variants address this ambiguity.
- Unexplained ≠ discrimination: the residual captures coefficient differences and any omitted variables, so it bounds rather than measures discrimination.
- Nonlinear extensions: Fairlie (2005) adapts the decomposition to binary and limited-dependent-variable models (logit/probit), enabling decomposition of probabilities such as DI application or allowance rates.
How It Works
Estimate the outcome regression separately for groups A and B. The mean gap is written as YˉA−YˉB=(XˉA−XˉB)β^∗+[XˉA(β^A−β^∗)+XˉB(β^∗−β^B)], where the first term is the explained (endowment) component evaluated at reference coefficients β^∗ and the bracketed term is the unexplained (coefficient) component. For nonlinear models, Fairlie's method sequentially swaps each covariate's distribution between groups to compute its marginal contribution.
Why It Matters
- Wage and health gaps: the standard tool for decomposing race and gender wage gaps and, in this wiki, gaps in mortality by education and income and in obesity-related non-employment.
- DI applicant composition: Coe and Rutledge (2013) apply the Fairlie (2005) nonlinear extension to DI application and allowance rates across the business cycle; the large unexplained residual — gaps not accounted for by observed health and demographics — is the core finding. See DI Countercyclicality and Conditional DI Applicants.
Open Questions
- How should a large unexplained component be interpreted when key drivers (true health, local labor demand) are unobserved?
- How sensitive are conclusions to the choice of reference coefficients?
Related
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