When we try to measure gaps in outcomes between groups, we often turn to an approach called a Blinder-Oaxaca Decomposition. I’m all for identifying discriminatory gaps, but we need to be careful that we don’t discount certain kinds of discrimination from our data calculations just because it isn’t our discrimination.

Ok, so what is the Blinder-Oaxaca Decomposition? There are many, many free resources explaining this in great detail, with mathematical formulas and examples of it being applied across subject matter and sectors. If you want to get a real handle on this, definitely seek them out. For our purposes, we’re going to use a very simplistic and commonly used example: looking at differences between wages and workers.

###### HOLD UP:

I’ve been calling this the “Blinder-Oaxaca Decomposition” because that’s how I learned about it in school, and that’s a useful way to look it up online, but really, we should be calling it the Kitagawa-Blinder-Oaxaca Decomposition.

Nearly twenty years before Alan Blinder and Ronald Oaxaca wrote their respective papers on the subject (1973) an incredible sociologist and demographer named Evelyn M. Kitagawa developed the method in a 1955 published piece titled: “Components of a Difference Between Two Rates”. Neither Blinder nor Oaxaca cited her work in their papers. Look her up, she’s amazing.

Let’s say that we run a company with a few hundred employees. We want to see if we’re discriminating against our female employees by paying them less. For the sake of our example, we’re going to say that the only legitimate thing we base wages on is how many years of schooling an employee has. Obviously, in a real-world example, there would be many factors that we might consider “legitimate” in why one employee gets paid more than another. For now, let’s stick with one.

If we want to separate this out by “men” and “women” (not by any means the only way to break it out, or even the only genders/sexes you may want to consider) we get two equations:

Wm = 500 + 17S

Ww = 200 + 8S

And another vital piece of information: that the average male employee has 9 years of schooling and the average female employee has 2.

What do these mean?

This means that men are being paid $500 plus $17 per year of schooling that they have, whereas women are being paid $200 plus $8 per year of schooling that they have.

*Math notes: The simple numbers (500 and 200) are called intercepts. They reflect the theoretical amount that would be earned if the employee had 0 years of schooling. This isn’t very useful to think about in the reality of our example as likely no employees would be hired with 0 years of schooling, but it does point us towards an obvious disparity between the $500 baseline that men are enjoying vs the $200 that women are getting.*

*The other terms, 17 x S and 8 x S are called coefficients and they simply represent the average amount that men and women make per year of schooling (S). This would be calculated with regressions. Essentially we would count up all our male and female employees and calculate an average for how much they were making vs how many years of schooling they had.*

The two big takeaways from these equations are that they are different and that the Ww is lower. Right away, that means that we’ve got an illegitimate or discriminatory difference going on, based on our own definition. We want people’s wages to be determined by how many years of school they have, but in reality, it turns out that we’ve been valuing women’s schooling at $8 per year of schooling and men’s at $17 per year of schooling.

The great part of the Kitagawa-Blinder-Oaxaca approach is that we can easily see the practical difference between these two groups. We simply plug in the average years of schooling for each group into their appropriate formulas:

Wm = $500 + ($17×9)

Ww = $200 + ($8×2)

We get these results:

Wm = $653

Ww = $216

The average man is getting $653 in wages, while the average woman is getting $216.

If we subtract $216 from $653 we get a difference of $437. “But hold on!”, say Kitagawa, Blinder and Oaxaca, “Some of that difference is discrimination, sure, but some of it is because the average man at our company has more years of schooling (9) than the women (5). How much of the $437 gap is due to how we value a year of schooling for women vs men (discrimination) and how much is based on the difference in amount of schooling – what we consider a legitimate reason to pay an employee more?”

We simply have to make a formula that shows what the average woman would make if we valued their years of schooling at the same rate.

We will take the Wm formula (a mathematical representation of how our company values men) and instead of putting in the average schooling years of men, we’ll put in the average from women. Then, we’ll subtract from that the current reality for women.

$500 + ($17×2) – $200 + ($8×2)

$534 – $216 = $318

So, by seeing what we would be paying the average woman who has 5 years of schooling if we valued them the same, we see that $318 of the $437 gap is due to our discrimination. This is super useful! We might decide as a company to increase the wages of women by $318 to make up the gap, problem solved!

But… there’s something dangerous going on here. What about the other $119 difference? There’s a total pay gap of $437 between men and women, and we’ve essentially said to our female employees: “Ok, $318 of that gap is discrimination, we’re going to adjust for that, but the remaining $119 is just a legitimate difference between you and your average male colleagues.”

The Kitagawa-Blinder-Oaxaca decomposition typically divides a pay gap between “legitimate” and “discriminatory” piles. The legitimate difference exists because even if we value years of schooling the same for both groups, men on average still have more years of schooling. What about the discrimination that led to that gap?

We should talk about the results of a K.B.O. Decomposition as the direct discrimination gap, the indirect discrimination gap, and the legitimate gap. In our example, we’ve got a total gap of $437, a direct discrimination gap of $318 and a remaining $119 which depending on your worldview is some combination of legitimate differences and indirect discrimination. How much of a role does being a woman have in the gap between their average of 2 schooling years and men’s 9? In many societies and countries, gender basically is that difference. Yes, this discrimination happened before the company started paying them. Yes, the company isn’t directly responsible for equity in the education rates of women. Yes, there may also be non-discriminatory reasons that women have on average fewer years of schooling.

Regardless, as a company, we will have to decide how to account for the remaining $119 difference. Some companies actively try to even out inequalities and discriminations that happened “pre-market”, i.e. before their sphere of influence, by valuing a woman’s year of schooling higher than a man’s, reflecting the increased difficulty in achieving the same years of schooling as their male peers. Others say, “well, we’re only going to make up for the gap that we are directly responsible for, but we acknowledge that there is another part of the gap that may be a broader societal issue, here’s how much it is…”.

The problem with just saying “there’s a $318 gap” to your women employees is that A) there’s actually a larger gap ($437), you’ve just decided that the $119 remainder is fine, and B) it doesn’t even point those women (and their allies!) towards the root of the problem – like educational inequalities – that they could try to overcome for individually or fight for as a group.

Just because an inequity exists before you encountered someone doesn’t mean it doesn’t exist. I totally get that companies, or schools, or hospitals, don’t have the capabilities to solve or even measure large, abstract and sometimes unquantifiable societal inequalities, but they can acknowledge them in the math. Plus, many of these gaps have been measured, we just need to look them up.

Women getting paid less, or kids getting the short end of an education system designed for someone else, or people of color getting worse healthcare through no fault of their own can feel the full extent of these gaps. They live them in their entirety. Let’s not accidentally place any part of those gaps in the “legitimate” pile unless we feel really sure that they are. Just because a problem isn’t our fault, doesn’t mean we should say it’s not a problem at all.