Oaxaca Blinder Decomposition

The Oaxaca-Blinder decomposition is a statistical method for decomposing a group difference into the effect of an independent variable, which in turn has a corresponding group difference, and into a residual difference that cannot be predicted by the independent variable. The process was presented by Ronald Oaxaca in 1973 in a study on the gender pay gap . The name also refers to the economist Alan Blinder , who submitted a methodologically similar work in the same year.

Procedure

A linear regression model is given :

${\displaystyle \mathbf {y} =\beta _{0}+\mathbf {X} \mathbf {\beta } +{\boldsymbol {\varepsilon }}}$

Here stands for the dependent variable, is the regression constant, is a vector of independent variables and a vector of corresponding regression coefficients. is the error term. ${\displaystyle \mathbf {y} }$ ${\displaystyle \beta _{0}}$ ${\displaystyle \mathbf {X} }$ ${\displaystyle \beta }$ ${\displaystyle {\boldsymbol {\varepsilon }}}$

If this model is estimated in two different groups, the result is for group or for group , where the empirically estimated value is for . Then the group difference under investigation is . To determine this, the group mean values ​​of the variables are first inserted into the two regression equations. Since the mean of the error term vanishes, we get: ${\displaystyle \mathbf {y} _{A}=b_{A0}+\mathbf {x} _{A}b_{A}}$ ${\displaystyle A}$ ${\displaystyle \mathbf {y} _{B}=b_{B0}+\mathbf {x} _{B}b_{B}}$ ${\displaystyle B}$ ${\displaystyle b}$ ${\displaystyle \beta }$ ${\displaystyle \mathbf {\bar {y}} _{B}-\mathbf {\bar {y}} _{A}}$ ${\displaystyle {\boldsymbol {\varepsilon }}}$

${\displaystyle \mathbf {\bar {y}} _{A}=b_{A0}+\mathbf {\bar {x}} _{A}{b}_{A}}$ or. ${\displaystyle \mathbf {\bar {y}} _{B}=b_{B0}+\mathbf {\bar {x}} _{B}{b}_{B}}$

Then the difference is formed by subtraction:

${\displaystyle \mathbf {\bar {y}} _{B}-\mathbf {\bar {y}} _{A}=(b_{B0}+\mathbf {\bar {x}} _{B}{b}_{B})-(b_{A0}+\mathbf {\bar {x}} _{A}{b}_{A})}$

This difference can now be broken down into several components:

${\displaystyle \mathbf {\bar {y}} _{B}-\mathbf {\bar {y}} _{A}=(b_{B0}-b_{A0})+(\mathbf {\bar {x}} _{B}-\mathbf {\bar {x}} _{A})b_{A}+(b_{B}-b_{A})\mathbf {\bar {x}} _{B}}$

The first part of the right-hand side of this equation now stands for the unexplained (that is, the group difference in . The second part represents the equipment difference assuming the coefficient of group A. The third part represents the difference in the coefficients assuming the same group mean values ​​(namely the empirical mean value of group B). ${\displaystyle {\bar {\mathbf {x} }}}$ ${\displaystyle {\bar {\mathbf {y} }}}$

There is a twofold and a threefold decomposition. The standard procedure is to break it down into three components.

Application in inequality research

For Oaxaca, this process plays a central role in quantifying discrimination in the labor market . It was introduced for the purpose of calculating a so-called discrimination coefficient, which is defined as

${\displaystyle D={{{W_{m}/W_{f}}-(W_{m}/W_{f})_{0}} \over {(W_{m}/W_{f})_{0}}}}$,

where is the empirical ratio of wages for male and female employees and the hypothetical ratio in the absence of discrimination, ie when wage differences can be fully explained by differences in independent variables such as qualifications. In order to be able to calculate this value, the decomposition described above is necessary beforehand. The missing quotient is then given by ${\displaystyle W_{m}/W_{f}}$ ${\displaystyle (W_{m}/W_{f})_{0}}$

${\displaystyle (W_{m}/W_{f})_{0}=(\mathbf {\bar {x}} _{B}-\mathbf {\bar {x}} _{A})b_{A}}$.

criticism

The method has been criticized from various perspectives. Elder et al. (2009) come to the conclusion that the Oaxaca decomposition has some useful applications, but a pooled multiple regression analysis with a dummy variable for group membership is more suitable for decomposing the effects of independent variables and unexplained group differences .

literature

Original contributions

• Oaxaca, Ronald (1973): Male-Female Wage Differentials in Urban Labor Markets, in International Economic Review . 14 (3), pp. 693-709
• Blinder, AS (1973): Wage Discrimination: Reduced Form and Structural Estimates, in Journal of Human Resources 8 (4), pp. 436-455

Individual evidence

1. ↑ Olaf Hübler: Gender-specific wage differences. (No longer available online.) In: Mitteilungen aus der Arbeitsmarkt - und Berufsforschung 36. Archived from the original on August 10, 2017 ; accessed on August 10, 2017 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
2. ↑ Hlavac, M. (2014). oaxaca: Blinder-Oaxaca decomposition in R. Available at SSRN 2528391.
3. ↑ Pierdzioch, C., & Stadtmann, G. (2019). Who "deserves" what and why? The Oaxaca / Blinder Decomposition Procedure for Analyzing the Gender Pay Gap (No. 408). Discussion paper.
4. ↑ Ronald Oaxaca: Male-Female Wage Differentials in Urban Labor Markets . In: International Economic Review . tape 14 , no. 3 , p. 696 .
5. ↑ Elder, Todd. E / Goddeeris, John H. / Haider, Steven J. (2009): Unexplained Gaps and Oaxaca-Blinder Decompositions (IZA DP No. 4159), online at http://ftp.iza.org/dp4159.pdf