Oaxaca decomposition interpretation - pooled method and reference category

[Sherry Ahmed]

Hello,

I'm using the Blinder-Oaxaca decomposition to study the wage differentials between males and females. I used logarithm or hourly wages to do that and reported the pooled method. I read a lot of research papers including Jann's paper and I feel like I understand 100% what the decomposition equations mean. However, I'm a little confused if 1) my results make sense; 2) how to make interpretations for these coefficients and 3) will I need to pick a reference category (because I thought we are always comparing same category between males and females so for example, looking at the married variable, I'm comparing married females to married males.. so won't married males be automatically considered the reference here for me.. same for educational attainment, when reporting a female with a bachelor degree, isn't a male with a bachelor degree considered automatically to be the reference group). Looking at one of my results below, I would make these conclusions but I'm not sure if that's the right way to do it... am I using percentage points versus percent correctly?

1- The total gender pay gap in 2001, calculated with hourly wages was 28 percentage points.

2- Differences in the characteristics of males and females explains less than half of the total gap. (E.g. 0.0775254/0.2759044 = 28 percent)

3- Age is estimated to explain 0.15808 percentage points of the total wage gap of 0.2759044 or 57.6% of the total gap. However, the effect of age tapper over time (looking at age square having a negative sign

4- Having a high school degree (a female with a high school compared to a male with high school) is also contributing to an increase in the gender wage gap by 0.0002263 percentage points (or 0.0002263/0.2759044 = 0.08 percent)

5- Completing a bachelor’s degree (a female with a bachelor degree compared to a male with bachelor degree) will reduce the gender wage gap by 4 percent (-0.113391/0.2759044)

6- can do the same with single females/single males, and married females/married males? right

7- Looking at working full time (FTW), is this coefficients comparing females working full time versus males working full time? or females working full time versus females working part time (which I think would be wrong)?. how would this be interpreted?




Blinder-Oaxaca decomposition Number of obs = 30,330
Model = linear
Group 1: female = 0 N of obs 1 = 15540
Group 2: female = 1 N of obs 2 = 14790

------------------------------------------------------------------------------
| Robust
lnHwages | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
overall |
group_1 | 10.28898 .0040482 2541.60 0.000 10.28105 10.29692
group_2 | 10.01308 .0041629 2405.33 0.000 10.00492 10.02124
difference | .2759044 .0058067 47.51 0.000 .2645235 .2872853
explained | .0775254 .0030875 25.11 0.000 .0714741 .0835767
unexplained | .198379 .0054102 36.67 0.000 .1877752 .2089828
-------------+----------------------------------------------------------------
explained |
hschool | .0002263 .0001441 1.57 0.116 -.000056 .0005087
Bachdegree | -.0113391 .0009713 -11.67 0.000 -.0132429 -.0094353
Married | .0078862 .0011745 6.71 0.000 .0055842 .0101881
Single | -.0018602 .0005965 -3.12 0.002 -.0030293 -.0006911
kid | -.0003125 .0001162 -2.69 0.007 -.0005403 -.0000848
age | .15808 .0074566 21.20 0.000 .1434652 .1726947
age2 | -.145693 .0064581 -22.56 0.000 -.1583506 -.1330354
FTW | .0652989 .0015793 41.35 0.000 .0622035 .0683942
-------------+----------------------------------------------------------------
unexplained |
hschool | .0234703 .0026166 8.97 0.000 .0183419 .0285987
Bachdegree | .0008703 .0014974 0.58 0.561 -.0020646 .0038053
Married | .0462083 .0435611 1.06 0.289 -.0391699 .1315866
Single | .0074362 .0052602 1.41 0.157 -.0028736 .017746
kid | .0080418 .007342 1.10 0.273 -.0063482 .0224318
age | .4657228 .1505767 3.09 0.002 .1705979 .7608478
age2 | -.0623104 .0809454 -0.77 0.441 -.2209605 .0963397
FTW | .1212236 .016439 7.37 0.000 .0890037 .1534436
_cons | -.3995266 .0858276 -4.65 0.000 -.5677457 -.2313076

------------------------------------------------------------------------------

Any help will be greatly appreciated

Thank you

[Sherry Ahmed]

I would really appreciate any help with my questions? especially about how to figure out the reference category for the oaxaca decomposition. Thank you

[Sherry Ahmed]

Another couple of questions please:

1- when trying to get the female and male wage equations in STATA. Is it just a regular regression such as: by gender: regress lnhwages education marital status children full time work

2- I'm looking to get the average hourly wages for men versus the average hourly wages for women so I use: sum wage if gender==1 and sum wage if gender==0. So let's say I get a ratio of $15/$30= 50 percent. Is that called the wage gap too??? because when I run the oaxaca decomposition, the difference (explained + unexplained) I'm getting is not the same as 50% (usually less)? does that make sense? or I'm doing something wrong.


Just want to mention that I do not have my results for the above because, due to privacy reason, the university won't let me take any of my results out until they get vetted first (a long process). I would appreciate any help. Thank you

[Sherry Ahmed]

Hello, I still did not get any reply and I would really appreciate any help. I got my results now (below) and I was hoping if I can get help in interpreting the decomposition (wage gap between females and males). This is what I have

-An indicator variable for education is set equal to 1 if the individual has a bachelor degree (Ibach_1) or higher and 0 if the individual has an education lower than a bachelor degree
- An indicator variable for marital status is set equal to 1 (Imar_1) if the individual is married and set equal to 0 otherwise.
- For the presence of children, an indicator variable is set to 1 if there is children (Ichild_1) in the house and set to 0 otherwise.
- An indicator variable is set to 1if an individual is working full time (Iwork_1) (30 hours or more per week) and 0 otherwise.

I think that the interpretation would be for example,

- Being married explain 0.0016 of the total 0.527 log wage differential between males and females (is that correct?). What is confusing me here is: does that mean that we are comparing a married female with a married male or are we comparing being married in general (male or female) to my reference group (0 = otherwise).

- Same with working full time, will the interpretation be something like: working full time explains 0.156 of the 0.527 (meaning that I'm comparing a female working full time with a male working full time) OR am I comparing working full time versus working part time?

- The variable age square is negative which, from my understanding, means that the effect of age tapper over time. Does that mean that the gender wage gap will decrease as females and males get older??? so the gap between lets say a 45 years old male and a 45 years old female will be lower than the gap between males and females who are for example 30 years old? and if that's correct, how would I interpret the -0.1007 coefficient.


I would really appreciate if I can get any help.

Thank you
------------------------------------------------------------------------------
| Robust
lnhwages | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
overall |
group_1 | 2.44436 .003485 701.39 0.000 2.437529 2.45119
group_2 | 1.917152 .0040444 474.03 0.000 1.909226 1.925079
difference | .5272072 .0053388 98.75 0.000 .5167433 .537671
explained | .1402948 .0027205 51.57 0.000 .1349627 .1456269
unexplained | .3869123 .0048965 79.02 0.000 .3773153 .3965094
-------------+----------------------------------------------------------------
explained |
age | .0990073 .0052733 18.78 0.000 .0886719 .1093427
age2 | -.1007936 .005107 -19.74 0.000 -.1108031 -.0907841
_Imar_1 | .0016793 .0003274 5.13 0.000 .0010376 .0023209
_Ibach_1 | -.0152759 .0011953 -12.78 0.000 -.0176185 -.0129332
_Ichild_1 | -.0009208 .0002129 -4.32 0.000 -.0013381 -.0005034
_Iwork_1 | .1565985 .0022097 70.87 0.000 .1522675 .1609294
-------------+----------------------------------------------------------------
unexplained |
age | -.0424122 .2000427 -0.21 0.832 -.4344887 .3496642
age2 | .0592419 .1034631 0.57 0.567 -.1435421 .2620259
_Imar_1 | .168149 .0087593 19.20 0.000 .1509812 .1853169
_Ibach_1 | -.0275075 .0017457 -15.76 0.000 -.030929 -.0240859
_Ichild_1 | .0226635 .0068612 3.30 0.001 .0092157 .0361112
_Iwork_1 | .0283806 .016019 1.77 0.076 -.0030161 .0597772
_cons | .1783971 .0967319 1.84 0.065 -.0111939 .3679881
------------------------------------------------------------------------------

[Sherry Ahmed]

Any help please?

[Sherry Ahmed]

.

[Sven-Kristjan Bormann]

You probably don't get answers here, because your questions have little to do with Stata per see. Regarding the base category problem, you can re-read the oaxaca helpfile section about the normalisation of categorical variables

help oaxaca##norm

In my interpretation, it means that getting the coefficients for categorical variables correct is tricky. What you get is

... "normalized" effects, i.e. effects that are expressed as deviation contrasts from the grand mean ...

Overall, I think that your interpretations are correct.

What is confusing me here is: does that mean that we are comparing a married female with a married male ...

Remember how dummy variables work in regressions. They are constants like the intercept, so your first idea should be correct.

1 - when trying to get the female and male wage equations in STATA. Is it just a regular regression such as: by gender: regress lnhwages education marital status children full time work

When you look at the code for the oaxaca command, then you should see that instead of

by gender: regress lnhwages education marital status children full time work

It is rather

forvalues g=1/2{
regress lnhwages education marital status children full time work if gender==`g'
}

2- I'm looking to get the average hourly wages for men versus the average hourly wages for women so I use: sum wage if gender==1 and sum wage if gender==0. So let's say I get a ratio of $15/$30= 50 percent. Is that called the wage gap too??? because when I run the oaxaca decomposition, the difference (explained + unexplained) I'm getting is not the same as 50% (usually less)? does that make sense? or I'm doing something wrong.

You should get roughly the same result when you condition on all the variables in your regression.

bysort gender: sum wage if !missing(education, marital status, children, full time work)

[Sherry Ahmed]

Thank you so much. Really appreciate it.