Aug 25 JDN 2460548

For concreteness, I’ll use men and women as my example, though the same principles would apply for race, sexual orientation, and so on. Suppose we find that there are more men than women in a given profession; does this mean that women are being discriminated against?

Not necessarily. Maybe women are less interested in that kind of work, or innately less qualified. Is there a way we can determine empirically that it really is discrimination?

It turns out that there is. All we need is a reliable measure of performance in that profession. Then, we compare performance between men and women, and that comparison can tell us whether discrimination is happening or not. The key insight is that workers in a job are not a random sample; they are a selected sample. The results of that selection can tell us whether discrimination is happening.

Here’s a simple model to show how this works.

Suppose there are five different skill levels in the job, from 1 to 5 where 5 is the most skilled. And suppose there are 5 women and 5 men in the population.

1. Baseline

The baseline case to consider is when innate talents are equal and there is no discrimination. In that case, we should expect men and women to be equally represented in the profession.

For the simplest case, let’s say that there is one person at each skill level:

Men	Women
1	1
2	2
3	3
4	4
5	5

Now suppose that everyone above a certain skill threshold gets hired. Since we’re assuming no discrimination, the threshold should be the same for men and women. Let’s say it’s 3; then these are the people who get hired:

Hired Men	Hired Women
3	3
4	4
5	5

The result is that not only are there the same number of men and women in the job, their skill levels are also the same. There are just as many highly-competent men as highly-competent women.

2. Innate Differences

Now, suppose there is some innate difference in talent between men and women for this job. For most jobs this seems suspicious, but consider pro sports: Men really are better at basketball, in general, than women, and this is pretty clearly genetic. So it’s not absurd to suppose that for at least some jobs, there might be some innate differences. What would that look like?

Again suppose a population of 5 men and 5 women, but now the women are a bit less qualified: There are two 1s and no 5s among the women.

Men	Women
1	1
2	1
3	2
4	3
5	4

Then, this is the group that will get hired:

Hired Men	Hired Women
3	3
4	4
5

The result will be fewer women who are on average less qualified. The most highly-qualified individuals at that job will be almost entirely men. (In this simple model, entirely men; but you can easily extend it so that there are a few top-qualified women.)

This is in fact what we see for a lot of pro sports; in a head-to-head match, even the best WNBA teams would generally lose against most NBA teams. That’s what it looks like when there are real innate differences.

But it’s hard to find clear examples outside of sports. The genuine, large differences in size and physical strength between the sexes just don’t seem to be associated with similar differences in mental capabilities or even personality. You can find some subtler effects, but nothing very large—and certainly nothing large enough to explain the huge gender gaps in various industries.

3. Discrimination

What does it look like when there is discrimination?

Now assume that men and women are equally qualified, but it’s harder for women to get hired, because of discrimination. The key insight here is that this amounts to women facing a higher threshold. Where men only need to have level 3 competence to get hired, women need level 4.

So if the population looks like this:

Men	Women
1	1
2	2
3	3
4	4
5	5

The hired employees will look like this:

Hired Men	Hired Women
3
4	4
5	5

Once again we’ll have fewer women in the profession, but they will be on average more qualified. The top-performing individuals will be as likely to be women as they are to be men, while the lowest-performing individuals will be almost entirely men.

This is the kind of pattern we observe when there is discrimination. Do we see it in real life?

Yes, we see it all the time.

Corporations with women CEOs are more profitable.

Women doctors have better patient outcomes.

Startups led by women are more likely to succeed.

This shows that there is some discrimination happening, somewhere in the process. Does it mean that individual firms are actively discriminating in their hiring process? No, it doesn’t. The discrimination could be happening somewhere else; maybe it happens during education, or once women get hired. Maybe it’s a product of sexism in society as a whole, that isn’t directly under the control of employers. But it must be in there somewhere. If women are both rarer and more competent, there must be some discrimination going on.

What if there is also innate difference? We can detect that too!

4. Both

Suppose now that men are on average more talented, but there is also discrimination against women. Then the population might look like this:

Men	Women
1	1
2	1
3	2
4	3
5	4

And the hired employees might look like this:

Hired Men	Hired Women
3
4
5	4

In such a scenario, you’ll see a large gender imbalance, but there may not be a clear difference in competence. The tiny fraction of women who get hired will perform about as well as the men, on average.

Of course, this assumes that the two effects are of equal strength. In reality, we might see a whole spectrum of possibilities, from very strong discrimination with no innate differences, all the way to very large innate differences with no discrimination. The outcomes will then be similarly along a spectrum: When discrimination is much larger than innate difference, women will be rare but more competent. When innate difference is much larger than discrimination, women will be rare and less competent. And when there is a mix of both, women will be rare but won’t show as much difference in competence.

Moreover, if you look closer at the distribution of performance, you can still detect the two effects independently. If the lowest-performing workers are almost all men, that’s evidence of discrimination against women; while if the highest-performing workers are almost all men, that’s evidence of innate difference. And if you look at the table above, that’s exactly what we see: Both the 3 and the 5 are men, indicating the presence of both effects.

What does affirmative action do?

Effectively, affirmative action lowers the threshold for hiring women (or minorities) in order to equalize representation in the workplace. In the presence of discrimination raising that threshold, this is exactly what we need! It can take us from case 3 (discrimination) to case 1 (equality), or from case 4 (both discrimination and innate difference) to case 2 (innate difference only).

Of course, it’s possible for us to overshoot, using more affirmative action than we should have. If we achieve better representation of women, but the lowest performers at the job are women, then we have overshot, effectively now discriminating against men. Fortunately, there is very little evidence of this in practice. In general, even with affirmative action programs in place, we tend to find that the lowest performers are still men—so there is still discrimination against women that we’ve failed to compensate for.

What if we can’t measure competence?

Of course, it’s possible that we don’t have good measures of competence in a given industry. (One must wonder how firms decide who to hire, but frankly I’m prepared to believe they’re just really bad at it.) Then we can’t observe discrimination statistically in this way. What do we do then?

Well, there is at least one avenue left for us to detect discrimination: We can do direct experiments comparing resumes with male names versus female names. These sorts of experiments typically don’t find very much, though—at least for women. For different races, they absolutely do find strong results. They also find evidence of discrimination against people with disabilities, older people, and people who are physically unattractive. There’s also evidence of intersectional effects, where women of particular ethnic groups get discriminated against even when women in general don’t.

But this will only pick up discrimination if it occurs during the hiring process. The advantage of having a competence measure is that it can detect discrimination that occurs anywhere—even outside employer control. Of course, if we don’t know where the discrimination is happening, that makes it very hard to fix; so the two approaches are complementary.

And there is room for new methods too; right now we don’t have a good way to detect discrimination in promotion decisions, for example. Many of us suspect that it occurs, but unless you have a good measure of competence, you can’t really distinguish promotion discrimination from innate differences in talent. We don’t have a good method for testing that in a direct experiment, either, because unlike hiring, we can’t just use fake resumes with masculine or feminine names on them.