Oaxaca-Blinder decomposition: percentage greater than 100

[Hinaaa Khalid]

Dear all,

I'm currently running the Oaxaca-Blinder Decomposition on a binary outcome variable, stunting. I'm using the following command:

xi: oaxaca stunting i.sex i.feeding i.environment i.other-categorical-variables (iw=weight) , by (year) logit cluster(hh)

I calculate percentage of explained contribution for each significant variable using the following formula:
(endowment for individual variable/ overall endowments) *100.

However, the problem I'm running into is that the sum of the explained contributions i.e. when I added percentages for sex (50%), feeding (40%), and environment (40%) etc is greater than 100%. This does not make sense.

Is there something wrong with my code? Please guide. I will be very thankful for any assistance. Thank you so much!

Best wishes,
Hina.

[FernandoRios]

Hi Hinaaa,
so, first of all, there is nothing wrong with the code.
Second, the results may seem strange, but they are not. There is nothing in the OB decomposition that says that the explained and unexplained contributions have to be smaller than 100%.
consider the following example
Assume im analyzing wages for men and women, and they are a function only of education:

wg=2+5*educ for men
wg=2+2*educ for women

But say that men have in average only 2 years of education, whereas women have 5. In average the RAW wage gap between men and women is Zero.
The gap because of differences in education will be negative (in favor of women because they have more education), but the gap because of coefficients will be positive (men get paid more for each year of education).
If you calculate the relative gap, it will be infinite! (x/e, if e -> 0, goes to infinity)

Bottom line, relative contributions are not always intuitive, if the coefficients and endowoment effects have different signs. So you may want to refer to the actual gaps only.

HTH
Fernando

[Hinaaa Khalid]

Hi Fernando,

Thank you so much! This was really, really helpful.

1. So, just to be crystal clear: If I'm trying to decompose what factors contributed to a reduction in stunting between two years, and their endowments add up to greater than 100 percent (for eg: education + feeding + environment + sex ) according to your explanation this is not inaccurate.

2. If an individual explained component [(endowment for individual variable/ overall endowments) *100] has a negative sign, that is okay too. So, for example if the explained contribution of environment is -40% then that just means the overall difference on the outcome, stunting, would be larger if average environment condition would be the same across the grouping variable (year). So, in this situation, is it okay to report the contribution of environment as 40 percent (i.e. exclude the negative sign).

Really appreciate the help.

Best wishes,
Hina.

[FernandoRios]

yes, finding that the explained or unexplained gap larger than 100% is not wrong. It is just unexpected, and as you already experienced, hard to explain.
Regarding the contribution....While I think what you say is technically correct, you will need to write it carefully, because it can be confusing.
HTH
Fernando

[Hinaaa Khalid]

Thank you! Really appreciate the response/insights.

[Matthew Williams]

yes, finding that the explained or unexplained gap larger than 100% is not wrong. It is just unexpected, and as you already experienced, hard to explain.
Regarding the contribution....While I think what you say is technically correct, you will need to write it carefully, because it can be confusing.
HTH
Fernando

Hi FernandoRios,

Considering your expertise on decomposition analysis, especially Oaxaca-Blinder decomposition, I would be highly appreciated if you can take a look at my post and give me advice on how to interpret the Oaxaca-Blinder results.

My post can be accessed at: https://www.statalist.org/forums/for...sition-results

Thank you.