The Blinder-Oaxaca decomposition for linear regression models

The counterfactual decomposition technique popularized by Blinder (1973, Journal of Human Resources, 436–455) and Oaxaca (1973, International Economic Review, 693–709) is widely used to study mean outcome differences between groups. For example, the technique is often used to analyze wage gaps by sex or race. This article summarizes the technique and addresses several complications, such as the identification of effects of categorical predictors in the detailed decomposition or the estimation of standard errors. A new command called oaxaca is introduced, and examples illustrating its usage are given.

Standard Errors for the Blinder-Oaxaca Decomposition

The decomposition technique introduced by Blinder (1973) and Oaxaca (1973) is widely used to study outcome differences between groups. For example, the technique is commonly applied to the analysis of the gender wage gap. However, despite the procedure's frequent use, very little attention has been paid to the issue of estimating the sampling variances of the decomposition components. We therefore suggest an approach that introduces consistent variance estimators for several variants of the decomposition. The accuracy of the new estimators under ideal conditions is illustrated with the results of a Monte Carlo simulation. As a second check, the estimators are compared to bootstrap results obtained using real data. In contrast to previously proposed statistics, the new method takes into account the extra variation imposed by stochastic regressors.

OAXACA: Stata module to compute the Blinder-Oaxaca decomposition

-oaxaca- computes the so-called Blinder-Oaxaca decomposition, which is often used to analyze wage gaps by sex or race. Older versions of this routine are available as -oaxaca9- and -oaxaca8-.

A Stata implementation of the Blinder-Oaxaca decomposition

The counterfactual decomposition technique popularized by Blinder (1973) and Oaxaca (1973) is widely used to study mean outcome differences between groups. For example, the technique is often used to analyze wage gaps by sex or race. The present paper summarizes the technique and addresses a number of complications such as the identification of effects of categorical predictors in the detailed decomposition or the estimation of standard errors. A new Stata command called -oaxaca- is introduced and examples illustrating its usage are given.

DEVCON: Stata module to apply the deviation contrast transform to estimation results

devcon transforms the coefficients of 0/1 dummy variables so that they reflect deviations from the "grand mean" rather than deviations from the reference category (the transformed coefficients are equivalent to those obtained by the so called "effects coding") and adds the coefficient for the reference category. The variance-covariance matrix of the estimates is transformed accordingly. The transformed estimated can be used with post estimation procedures. In particular, devcon can be used to solve the identification problem for dummy variable effects in the so-called Blinder-Oaxaca decomposition (see the oaxaca package).