Oaxaca Blinder Decomposition

[Theresia Verena]

Hello, everyone. Can you help me in interpreting the results of this oaxaca blinder decomposition?
(1) I would like to compare the wage decomposition between women with mental disabilities and not having this type of disability. The results show as follows:
Difference: -0.6005969
Explained: -0.013535
Unexplained: -0.5870618

(2) I would also like to compare the decomposition of young women who have mental disabilities and young women who do not have mental disabilities.
The results show as follows:
Difference:-0.7018546
Explained: 0.0357161
Unexplained: -0.7375707

Thank you in advance!

[Weiwen Ng]

Recapping another post, difference = group 1's mean - group 2's mean. The reference group is usually group 1, the focal group or group of interest is group 2. In other contexts for wages, group 1 might be men and group 2 might be women. I assume you set group 1 to be women without mental disabilities and group 2 as women with mental disabilities. Oaxaca will use whatever value of the group identifier is higher to be the focal group, so disability = 0 should be the reference and disability = 1 should be the focal group.

You have a negative difference. If I am correct about how you coded your groups above, that suggests that women with disabilities earn slightly more than women without disabilities. I am assuming the units are log wages or something like that, which I don't really know how to interpret per se. The following assumes that your coding is correct and the statement in this paragraph is true.

difference = explained + unexplained, which you can verify for yourself with a calculator or by typing:

display -0.013535 - 0.5870618

Because the difference is negative, interpretation is a little tricky. Explained is the effects of the variables you included in the regression. That is, explained accounts -0.013535 / -0.6005969 if the disparity in average wages (expressed as a proportion). Alternatively, if the groups had the same level of the observed covariates, you'd expect the difference in log wages to be larger, i.e. you would expect group 2's log wages to be difference - explained = -0.6005969 - -0.013535. (NB: double minus sign.)

Imagine the signs are flipped on the first set of results. Then it's easier to interpret. Either way, the independent variables account for only about 1/60 of the disparity in average wages, i.e. not much. You could examine the details to see more. I've been in one situation where one group of covariates is pushing the disparity one way, and a different group is pushing it the other way.

As a bonus, you requested the two-way decomp. You are assuming that the independent variables have the same effect in both groups. In analysis of wage differentials by gender, we might expect that women might have more years of education and job tenure than men, but we might also wonder if women have poorer returns to job tenure and education than men, i.e. the coefficients may differ. The three-way decomp allows that. IIRC this is a bit trickier to interpret, though, and I haven't fit a 3-way decomp in real life yet.

Here is a worked example of how to graph the results from a two-way decomp, plus you can use the output table as an example of a decomposition where the signs are all positive.

[Weiwen Ng]

(2) I would also like to compare the decomposition of young women who have mental disabilities and young women who do not have mental disabilities.
The results show as follows:
Difference:-0.7018546
Explained: 0.0357161
Unexplained: -0.7375707

Thank you in advance!

This is another interesting case. Here, group 2 has 0.70 units higher wages than group 1 (if difference were +ve, it would be group 1 has higher wages than group 2). If you gave group 2 group 1's levels of the independent variables, group 2 would have even higher wages than group 1 (if the independent variables had the same effect in group 2, which you are assuming because you did a twofold decomp).

Imagine the signs were reversed, e.g. (this is a misquote)

Difference:+0.7018546
Explained: -0.0357161
Unexplained: +0.7375707

That's group 2 earns 0.7 units less than group 1. We you equalized their observed characteristics, group 2 should earn even less than group 1 (.74 units or so). What that means in the real world is something you'll have to explain for yourself.

These situations can be tricky to describe in plain language because there are a bunch of double negatives. Just remember that difference = group 1's mean - group 2's mean and difference = explained + unexplained. Then try to work from there. If it's wages, and group 1 is men and group 2 is women, then we would expect to see a positive difference (men tend to earn more than women), with some portion explained (e.g. by education, job tenure, etc) and some portion not explained (and we expect positive values for explained and unexplained).