# How to interpret the constant in Oaxaca Blinder decomposition?

I am currently working on an Oaxaca Blinder decomposition on wage gap between males and females. In the unexplained part, there is a constant. In my model this constant has a value of 0.6 whilst the total of the unexplained part is 0.152.

Why is the value of this constant so big and what does this constant mean in the Oaxaca Blinder model?

Here is my output:

• I don't think you are going to get much help unless you either post your code and the output (perhaps using a public dataset like the oaxaca.dta that's bundled with Stata's oaxaca command) or you show us the mathematical formula for your decomposition. As it stands, this is akin to saying I made coffee and there's something floating in it. What could it be? Commented Apr 12, 2016 at 17:03
• Thanks for your reaction! I now added a picture with my output Commented Apr 13, 2016 at 16:01

The constant is really just the difference in the intercepts from separate log wage regression for men and women. Here's a reproducible$^*$ example:

use http://fmwww.bc.edu/repec/bocode/o/oaxaca.dta
reg lnwage educ exper tenure if female==0
estimates store M
reg lnwage educ exper tenure if female==1
estimates store F
qui suest M F
lincom _b[F_mean:_cons]-_b[M_mean:_cons]
oaxaca lnwage educ exper tenure, by(female) swap pooled detail


Here I used suest to combine separate male and female regressions and constructed a difference between the female and male intercepts from those regressions using lincom.

Here's the output from the last two commands:

. lincom _b[F_mean:_cons]-_b[M_mean:_cons]

( 1)  - [M_mean]_cons + [F_mean]_cons = 0

------------------------------------------------------------------------------
|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |  -.1442439   .1624352    -0.89   0.375    -.4626112    .1741233
------------------------------------------------------------------------------

. oaxaca lnwage educ exper tenure, by(female) swap pooled detail

Blinder-Oaxaca decomposition                    Number of obs     =      1,434

1: female = 1
2: female = 0

------------------------------------------------------------------------------
|               Robust
lnwage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Differential |
Prediction_1 |   3.266761   .0218042   149.82   0.000     3.224026    3.309497
Prediction_2 |   3.440222   .0174586   197.05   0.000     3.406004     3.47444
Difference |  -.1734607   .0279325    -6.21   0.000    -.2282075    -.118714
-------------+----------------------------------------------------------------
Explained    |
educ |  -.0493404   .0113168    -4.36   0.000     -.071521   -.0271599
exper |  -.0215214   .0064081    -3.36   0.001    -.0340811   -.0089617
tenure |  -.0184852   .0051833    -3.57   0.000    -.0286443   -.0083262
Total |   -.089347   .0137531    -6.50   0.000    -.1163026   -.0623915
-------------+----------------------------------------------------------------
Unexplained  |
educ |   .0656254    .139432     0.47   0.638    -.2076564    .3389072
exper |   .0421741   .0411638     1.02   0.306    -.0385055    .1228537
tenure |  -.0476693   .0271699    -1.75   0.079    -.1009213    .0055828
_cons |  -.1442439   .1624352    -0.89   0.375    -.4626112    .1741233
Total |  -.0841137    .025333    -3.32   0.001    -.1337654    -.034462
------------------------------------------------------------------------------


As you can see, the lincom is exactly the same as _cons row in the oaxaca output.

Without knowing more about your data, it's hard to interpret your results. Presumably, it means that there's a gap in the intercepts between men and women. If that intercept is a meaningful one (i.e., doesn't correspond to the log wages of someone without any education or experience), you can take this interpretation a bit further.

Response to Questions:

1. Cut and paste the output from Stata into here, select it, and then press the {} button to format it nicely.
2. All the unexplained components sum up to the total unexplained, so your intercept component is made smaller by the negative education terms. This makes sense since your intercept is not really meaningful.
3. To make it more interpretable, I would suggest standardizing your continuous Xs (subtract the mean and perhaps also divide by the standard deviation) to make the intercept more meaningful (careful with those squared terms though). This makes the intercept correspond to the log wage of the person who has the average attributes and is in the omitted category for all the sets of dummy variables. You can also subtract salient values rather than the mean, such as 12 for years of education.
4. The unexplained part is usually attributed to discrimination, but it is important to recognize that it also captures the gender differences in unobserved (to you) variables, which will be picked up by the intercept.

$^*$Making use of standard datasets rather than providing an edited screenshot of output from data that only you have access to will make it much easier to get a good answer. But if you can't do that, pasting output and formatting it with code tags is much better than a screenshot.

• thanks for the explanation, makes it all a bit more clear to me already. How do you mean formatting it with code tags and pasting output? Would like to do that, but not sure how! I am not the best with computers :p What concerns me is that this constant term is way more bigger than the total unexplained differential. As look at the gender wage gap here, could that mean that there are other variables than the ones used in my model, that affect wage differences? As at the point of intercept, none of the variables of my model are taken into account yet, but there already is a wage difference..! Commented Apr 13, 2016 at 20:58
• @sanne See the response above, it is too long to fit in the comments. Commented Apr 13, 2016 at 21:43
• @sanne Did my answers make sense? Commented Apr 14, 2016 at 21:25
• yes it did, thanks! Sorry for the late response, was away for a while but I've got it figured out now :) thanks for your very kind help! Commented Apr 22, 2016 at 14:02
• @sanne Great!. Please select the answer by clicking on the check mark on the left. Commented Apr 22, 2016 at 14:13