77 cents, part II: What if secretaries became programmers?

When I was a kid in the 1960s, wage discrimination against women wasn’t something you had to ferret out with statistics.

My grade school was owned by the Lutheran church my family belonged to, and the congregation had to approve  the teachers’ salaries each year. So everyone knew that Male Teacher and Female Teacher were two different professions with different pay scales. If we hired a man and a woman straight out of the same Lutheran teachers’ college, we’d pay the man significantly more.

Everyone knew why: Male teachers (even if currently single) would need to support a family, while women (even if currently childless) taught either before or after their real profession, which was raising children.

That kind of thinking hung on longer in religious workplaces than elsewhere, but it wasn’t uncommon. Men made more than women, even if they were doing the same job. It was out in the open because nobody was ashamed of it.

Today, such overt separate-pay-scale discrimination is both illegal and socially unacceptable, so remaining wage discrimination (if any) must be hidden. That’s why we do statistics.

Last week I verified that at the grossest level, women still make less. In 2011, women working full time made 82 cents for every dollar made by men working full time. (The often-quoted 77 cents figure is a year older and figured slightly differently, which tells you something about the sensitivity of the calculations. In what follows I’ve been careful not to mix data from different sources. Everything comes from the Bureau of Labor Statistics table that leads to the 82-cent estimate.)

But why do women make less? Is it for reasons we can all live with, or is the pay gap an injustice that needs fixing? Several reasons are frequently offered, together with explanations why we can live with those reasons. (Never forget that those are two separate conversations. Even if the whole pay gap could be boiled down to something as simple as “Girls don’t like math”, we’d still need to discuss whether that’s a problem we can or should fix.)

For each proposed reason, there’s a study proving that it’s not the whole story. Today I want to look at one of the most popular explanations of the pay gap: Women choose lower-paying professions. In other words, the overall averages compare female special education teachers to male aerospace engineers. No surprise who makes more.

The Institute for Women’s Policy Research has a study “The Gender Wage Gap by Occupation” proving that occupational segregation (as they call it) is not the whole story. Using Bureau of Labor Statistics numbers from 2011 (the same ones in that 82-cent calculation), they list the 20 most popular occupations (out of around 400 listed by the BLS) for men and for women. Four occupations are on both lists, and six more are too segregated (i.e., construction worker, teacher assistant) to provide a reliable estimate of the minority gender’s earnings.

In the 30 remaining occupations, men make more in 28, and the other two are low-pay occupations where the female advantage is small: Female “stock clerks and order fillers” make $1.03 for every male dollar, and female “bookkeeping, accounting and auditing clerks” make $1.003. On the other pan of the scale, men have huge margins in high-pay occupations like “financial manager” (where women make 66 cents on the male dollar) and “chief executive” (69 cents).

So clearly, occupational segregation isn’t the whole story of the wage gap. But here’s the more interesting question: Granted that it isn’t the whole story, how big a part is it?

Maybe there’s a study that answers that question, but I didn’t find it. So I crunched some numbers myself. I started with the numbers in Table 1 and Table 2 of the IWPR report, restricting my attention to the 30 comparable occupations.

Eliminating the duplicate occupations and totaling up, we’ve got 18.4 million men making a total of $16.4 billion per week ($892 each) and 20.9 million women making $15.0 billion per week ($715 each), or about 80 cents on the dollar. So these 30 occupations are slightly better than average for both men ($832 overall) and women ($684), with women making almost the same relative wage (80 cents on the dollar) as in the total survey (82 cents).

To understand what I did next, imagine that there are only two occupations: male-dominated “software developers” and female-dominated “secretaries and administrative assistants”. (These are two of the 30 from the IWPR study.)

 occupation  # men  men $  # women  women $
 software  812  $1606  179  $1388
 office  84  $757  2059  $651
 Total/average  896  $1526  2238  $710

(The number of workers is in thousands.) So our miniature, two-occupation economy (call it “2-Job World”) employs 3,134,000 people (896,000 men and 2,238,000 women) and has a total weekly payroll of  $2.96 billion ($1.37 billion to men, $1.59 billion to women). Overall, its men average $1526 per week and its women $710. So the unfortunate women of 2-Job World make only 46 cents for every dollar a man makes, even though they make 86 cents on the dollar in each occupation. (That’s why I picked those two for my example.)

Amateur economists in 2-Job World — there are no professional economists, that would be a third job — could analyze their pay gap by constructing two counter-factual models. In each model, each occupation maintains the same the total number of jobs and the same total payroll, but women move towards equality in two different ways.

In 2-Job World Fantasy #1, the ratio of men and women in each profession equalizes. Overall, 29% of the workers are men. So in Fantasy #1, 29% of workers in each occupation are men. But the wage gap within each occupation stays the same: 86 cents on the dollar. That changes the table to look like this:

 occupation  # men  men $  # women  women $
 software  283  $1735  708  $1499
 office  613  $728  1530  $626
 Total/average  896  $1046  2238  $902

Basically, bringing lower-paid women into software allowed us to raise salaries in general, while bringing higher-paid men into the secretarial pool forced us to cut salaries there. But now we have an economy where there is no occupational segregation, and women make (surprise) 86 cents on the dollar.

In 2-Job World Fantasy #2, we leave everybody in their current job, but equalize pay within the occupations, so everybody makes the average salary for their occupation. That gives a table like this:

 occupation  # men  men $  # women  women $
 software  812  $1567  179  $1567
 office  84  $655  2059  $655
 Total/average  896  $1481  2238  $728

And here you wind up with women making 50 cents on the male dollar. You’ve only nudged the pay gap by 4 cents.

(I know what some of you are thinking: Where’s the extra 10 cents? Shouldn’t the 4 cents from equalizing pay and the 40 cents from equalizing occupational segregation add up to 2-Job World’s whole 54 cent pay gap? Congratulations, you have just discovered non-linearity. Equalizing pay in the already-desegregated world of Fantasy #1 would have a 14-cent effect, while it only has a 4-cent effect in the original 2-Job World.)

So 2-Job World looks like some people’s intuition about our whole economy: The big money is in getting women to become programmers instead of secretaries.

But when I applied the same two fantasies to the more representative 30-Job World, it came out exactly the other way. In 30-Job World (where women make 80 cents on the dollar), Fantasy #1 (desegregating the occupations) only gets us a 3-cent gain to 83 cents.

But Fantasy #2 (where both men and women make the average salary for their occupations) raises women’s relative pay to 92 cents. It gains women 12 cents rather than 3 cents.

So at least in 30-Job World, getting equal pay within each occupation turns out to be about four times more important than getting equal representation within the occupations.

Why? While programmers and secretaries are part of 30-Job World, the bigger effect comes from occupations that are already fairly well integrated, but men just make more, like retail sales supervisors: about 1.3 million men and 1.0 million women, but the women make 79 cents on the dollar.

Is that how things work in the overall economy (400+ Job World, if you use the BLS categories)? I’m not ready to say that yet. But until I see a better analysis, I’m going to be very skeptical of anybody who claims the wage gap is even largely due to women’s choice of professions. I’d be surprised if it ultimately explained more than a nickel of the gap.

Technical notes:

If you need to see for yourself, I’ve posted the larger tables: 30-Job World Actual, 30-Job World Fantasy #1, 30-Job World Fantasy #2.

I anticipate this objection: When I eliminated the 6 occupations where there wasn’t a large enough sample to get a good estimate of one gender’s wages, I disposed of exactly the occupations where desegregation would make a difference.

Strange things happen when you put those occupations back in, and they work backwards from what the objector might expect. Five of the six are male-dominated working-class jobs. When you lump them together, they pay less than even the female average in 30-Job World.

So the main effect is to pull the male average down, which gets the wage ratio in 36-Job World up to 83 cents. From there, Fantasy #2 gets you to 94 cents. Fantasy #1 is hard to apply (because you don’t know what to pay the minority gender). But if you equalize even further (just for those 6 occupations) by paying the minority gender the overall occupational average , you only get up to 84 cents — higher than in 30-Job World Fantasy #1, but showing a smaller improvement over 36-Job World Actual.

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