Common mistake 1 with Oaxaca–Blinder decomposition

Calling the unexplained part "discrimination". It is a residual and it also absorbs every variable you omitted.

Common mistake 2 with Oaxaca–Blinder decomposition

Ignoring how sensitive the split is to the reference structure. Report more than one.

Common mistake 3 with Oaxaca–Blinder decomposition

Controlling for occupation and then wondering why the gap shrank - occupation may itself be an outcome of discrimination.

Common mistake 4 with Oaxaca–Blinder decomposition

Decomposing a gap that is not statistically distinguishable from zero. The components will still sum to it and still look substantial, and none of it is evidence of anything.

EconStatsCraft › Oaxaca–Blinder decomposition

Oaxaca–Blinder decomposition

Decomposes the gap in an outcome between two groups into the part explained by different characteristics and the part explained by different returns to those characteristics.

What it needs

Outcome
Group (two categories)
Explanatory variables

The intuition

Men earn more than women. Some of that is because the two groups differ in measured characteristics - experience, occupation, hours. The rest is because the same characteristic buys a different wage depending on which group you are in. Oaxaca–Blinder separates the two, and the second part is what discrimination research is about - while being careful that it is a residual, not a measurement.

When to use it

Studying gaps between groups: gender or ethnic wage gaps, urban–rural differences, public–private sector pay.

Where the estimator comes from

Estimate separate regressions \bar{y}_A=\bar{x}_A'\hat{\beta}_A and \bar{y}_B=\bar{x}_B'\hat{\beta}_B. Then \bar{y}_A-\bar{y}_B=(\bar{x}_A-\bar{x}_B)'\beta^{}+\left[\bar{x}_A'(\hat{\beta}_A-\beta^{})+\bar{x}_B'(\beta^{}-\hat{\beta}_B)\right]. The first term is the endowment (explained) component, the second the coefficient (unexplained) component. \beta^{} is the reference structure: Oaxaca originally used \beta_A or \beta_B, Neumark (1988) the pooled estimate, Cotton (1988) a weighted average. The choice is not innocuous and the split moves with it.

The model

\bar{y}_A-\bar{y}_B=\underbrace{(\bar{\mathbf{x}}_A-\bar{\mathbf{x}}_B)^{\prime}\boldsymbol{\beta}^{*}}_{\text{explained}}+\underbrace{\bar{\mathbf{x}}_A^{\prime}(\boldsymbol{\beta}_A-\boldsymbol{\beta}^{*})+\bar{\mathbf{x}}_B^{\prime}(\boldsymbol{\beta}^{*}-\boldsymbol{\beta}_B)}_{\text{unexplained}}

What it assumes

The regression is correctly specified for both groups.
The chosen reference coefficient structure is the "non-discriminatory" one - a genuinely contestable choice.
No selection into the groups on unobservables.
The two groups face the same functional form, not merely the same variables. If returns to experience are concave for one group and linear for the other, a linear decomposition attributes the difference in curvature to the unexplained component.

Statistical properties

The decomposition is exact and additive at the means by construction.
It is NOT invariant to the reference structure, which is the index-number problem at the heart of the method.
The detailed per-variable decomposition of the unexplained part depends on the base category for any dummy variables - an arbitrary choice with non-arbitrary consequences.
It decomposes only at the MEAN; use Machado–Mata or RIF regressions for the whole distribution.
The unexplained component absorbs every omitted variable, so it bounds discrimination from above at best.

How to read the output

Explained: the part due to differing characteristics.
Unexplained: the part due to differing returns to those characteristics.
The per-variable table shows which characteristic drives most of the gap.
The split depends on the reference coefficients, and there is no neutral choice. Pooled, group-A and group-B references give three different answers, and the honest report gives the range rather than one of them.

A worked reading

Mean log wage is 2.2538 for group 1 and 2.4681 for group 0, a raw gap of -0.2144. The threefold decomposition puts the explained part - differences in education, experience and union status - at 0.0032, which is -1.5% of the gap, and the unexplained part at -0.2176, or 101.5%. In other words essentially NONE of the gap is accounted for by the characteristics measured here: the two groups have almost identical average schooling (12.95 against 12.87 years) and experience (15.8 against 15.9 years), and are paid differently anyway. That is consistent with unequal returns to the same characteristics, and equally consistent with an omitted variable - hours, occupation, continuity of employment - that is simply not in this dataset. The decomposition cannot separate those two readings, and any write-up that calls the unexplained share "discrimination" without saying so is overstating what the arithmetic delivers.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Unexplained share is very large	Either real differential treatment, or important omitted variables	Say plainly what you could not measure
Split changes a lot with the reference structure	Index-number problem	Report under more than one reference
Controlling for occupation shrinks the gap sharply	Occupation may itself be an outcome of discrimination	Report both with and without - and discuss
Groups have very different characteristic distributions	Limited common support	Consider a matching-based decomposition

Common mistakes

Calling the unexplained part "discrimination". It is a residual and it also absorbs every variable you omitted.
Ignoring how sensitive the split is to the reference structure. Report more than one.
Controlling for occupation and then wondering why the gap shrank - occupation may itself be an outcome of discrimination.
Decomposing a gap that is not statistically distinguishable from zero. The components will still sum to it and still look substantial, and none of it is evidence of anything.

Where to read this properly

Oaxaca (1973); Blinder (1973)
Neumark (1988); Cotton (1988) - the reference-structure problem
Fortin, Lemieux & Firpo (2011) - decomposition methods, Handbook of Labor Economics
Jann (2008) - the Stata implementation and its pitfalls

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Oaxaca–Blinder decomposition

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

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