Women’s Wages and the Back of My Envelope

Yesterday’s breathtakingly dishonest graph from the AFL-CIO touched off some discussion in comments about whether the male/female wage differential could plausibly be driven by employer discrimination.

The usual argument to the contrary runs like this: If the differential is driven by employer discrimination (as opposed to, say, the abilities and/or preferences of the workers), then non-discriminating employers (i.e. those who care only about making a buck, regardless of who they have to hire to do it) would draw only from the relatively cheap female labor pool. It wouldn’t take many of these non-discriminating employers to drive women’s wages up to the same level as men’s. We don’t see that happening, ergo the hypothesis of employer discrimination is refuted.

The problem with that argument is that it assumes employers won’t ignore a profit opportunity, whereas in fact employers ignore profit opportunities all the time — by keeping on their incompetent nephews, taking Wednesday afternoons off to play golf, or, yes, hiring people they like having around instead of people who could do a better job.

To rescue the argument, you need to make it quantitative. Here’s an ultra-quick back-of-the-envelope calculation. First, suppose half the work force is men and half women. (If you think that’s off, feel free to adjust this calculation as you see fit.) Then clearly the workforce at the average firm is half men and half women. If women earn 20% less than men — and if the difference is entirely driven by employer discrimination — then a non-discriminating employer could shave 10% off his/her wage bill by firing the male half of the work force and replacing it with women. (That’s because 10% is half of 20%.)

That 10% savings all goes into the pockets of the owners (in the case of a corporation, that’s the shareholders). According to the latest GDP numbers (from page 11 of the national income accounts), employee compensation is a bit more than three times the return to proprietors and shareholders. So a 10% reduction in the wage bill translates into a 30% increase in income for the owner, or, in the case of a corporation, a 30% increase in share price.

In other words: To believe that the gender gap in wages is driven by employer discrimination, you don’t just have to believe that everyone’s ignoring a profit opportunity — you have to believe that everyone’s ignoring an opportunity to kick their profits up by thirty percent. That number is large enough to strike me as wildly implausible. Might employers ignore a profit opportunity? Sure. Might they ignore a chance to kick up their profits by thirty percent overnight? Seems bloody unlikely.

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25 Responses to “Women’s Wages and the Back of My Envelope”


  1. 1 1 Bennett Haselton

    Steve — you have a link that’s not closed (after the words “national income accounts”).

  2. 2 2 Bennett Haselton

    And, maybe, an algebra error :) If employee compensation is three times the return to proprietors and shareholders, then a 10% reduction in wages means a percentage income increase for the owner of 3.33%, not 30%, doesn’t it?

  3. 3 3 Bennett Haselton

    Oh, wait, ignore the second post — you mean that if employee compensation is three times the return to shareholders, then the same fixed amount that represents a 10% reduction in wages, would represent a 30% increase in profits if expenses were reduced by that much. *smacks head*

    Oh well, I was still right about the un-closed link :)

  4. 4 4 Ryan

    This is funny – I never quantified the argument you’re making, but I’ve always assumed it to be logically true. I assumed that this perfectly demonstrates how much people thwart themselves when they engage in bigotry, and how much a single employer stands to gain by taking those employees that others refuse.

    I think this is visible in many segments of society, and not exclusively reserved to gender. Part of the reason guitarists insist that a “made in Mexico” guitar is inferior to a “made in the USA” guitar is racism, pure and simple. “They” can’t possibly make a guitar as well as “us.” Note that in this case, people will pay as much as 10 TIMES the price of a guitar in order to get the American model. Lucky for me, their racism means cheaper guitars for me – but it sure makes a lot of Mexican luthiers worse off.

  5. 5 5 Cos

    Actually, the biggest assumption you’re making here, but not stating, is that employers actually know what the value of their employees will be. I don’t know of any evidence for that assumption. Chances are they generally don’t.

  6. 6 6 Ryan

    Cos – For that matter, how will the employers “actually know what the value of their employees” is at any given point of time? Perhaps even the data they have staring them in the face is a function of the fact that the employee’s skills are over-/under- utilized.

    Every economic valuation is a best guess based on past experience and individual preference. The reason people can’t accurately assess “true value” of anything is because it’s subjective and wildly variable, depending on the circumstances of any given point in time. Equilibrium market prices give us a good starting point, but the nature of a market economy is that it is always trial-and-error, and the exogenous factors are constantly changing.

    …Which is a fancy/Austrian way of saying, “Nobody knows. It’s subjective.” But a best guess is a best guess.

  7. 7 7 Dan Hill

    Cos – the assumption only matters if there is some systematic bias in the valuation of employees. Is there any reason to believe that the distribution of estimated value around the actual value is anything other than normal i.e. that employees over estimate as often and as much as the underestimate? And whatever the distribution, is there any reason to believe that it is different between men and women i.e. that employers misestimate the value of female employees in a different way than the misestimate the value of male employees? My working answer to both these questions would be “no”.

  8. 8 8 Seth

    “…or, yes, hiring people they like having around instead of people who could do a better job.” -SL

    This almost made coffee come up through my nose. How true.

    I see it often. I even see it with jobs that have relatively objective performance measures like head coaches in the NFL. Eventually performance does catch up, but I’m always amazed at the rationalization people go through to defend someone they have an affinity toward and at how effectively lackluster coaches can talk themselves, fans and owners into “one more year”.

    Part of that dynamic, however, is also fed by not having suitable replacement opportunities. You may be able to find someone who can do a better job, but that’s not always certain so you stick with what you have.

  9. 9 9 Silas Barta

    @Cos: You have to assume that regardless of what side you’re on. Or are you going to argue that employers don’t know the value of their employees, *but* that people outside do, and in what direction the misvaluation is?

    If this value is so hard to calculate in the first place, then on what basis do you even know someone’s getting underpaid?

  10. 10 10 Peter

    Yet another straw man knocked down with a simple numerical example.

    Suppose discrimination takes the following form. In 1984, employers believed women to be 32 percent less productive than men, even though they had no objective evidence that this was the case; in 2009, employers believe women to be 20 percent less productive than men, again even though they have no evidence. And suppose, because they are based on sexist attitudes, that these are dogmatic beliefs.

  11. 11 11 Harold

    Lets be realistic. Men and women *tend* to make different choices. A woman may take more time off when a couple has children. This will affect her years of work experience, and have an impact on her wages. If the child is sick, the mother may take more time off than the father. This will have an effect on her wages. The woman may put children as a higher priority than the man, this will affect the hours she wishes to work, and hence affect her wages. These could be said to be non-discriminatory differences, arising out of free choices, so for now I will put them aside, to return later.

    Now lets take a woman who makes the same choices as a man. She is less likely to get a job, less likely to get a promotion and is very likely to be paid less than a man for the same job. This is direct discrimination, and it does occur.

    Women are more likely to go into some professions / jobs than others. Take any female dominated job, it will be paid less than a male dominated job requiring similar level of skill and application. This is partly because the people supposed to represent the interests of women in the workplace, the unions, have done a terrible job of it. They have campaigned for higher mens’ wages, to the detriment of womens’. This is discrimination, and it does occur. (However, the gap is reducing.)

    So why don’t these women choose to be bus drivers instead of care-home workers? It is their choice, so they must prefer it that way. However, it seems our choices may not be quite as free as economists would like. We trap ourselves into narrowing our choices due to (amongst other things) decades of social pressures. We could ignore this, and say “any individual can make any choice they want!” But we know that this is not really the case. People are rewarded by society approval for making choices that society expects. That includes women not becoming engineers.

    But we also know that economic drivers exist, and they do change peoples behaviours. So today, women have been getting the message that pay is important, and they don’t want to work for less. They are choosing not to work in care-homes, not to stay home with the kids, and increasingly not to have children at all.

    Back to the woman who chooses to put effort into raising a family instead of work. It is essential that someone does this, or there is no future. In an equal world, it may be that men and women would share this duty. In the real world, this is not going to happen. If there are two parents, we know that it will mostly be women who will buckle first, and take the time off, even if they have the same status job as their partner. If there is only one parent, it is almost always the woman. So there is an externality here (I think). The men are getting the benefit of a society with children that are cared for, the women are paying for it in lower wages.

    So in conclusion, there is some direct discrimination against women. This does not explain all the “wage gap”. The rest is due to choices made by individual women which reduce their value in the workplace. These choices are of enormous benefit to the whole of society. These choices are affected by society pressure. There is some argument that these are not entirely “free” choices”.

  12. 12 12 Cos

    Dan Hill: “is there any reason to believe that it is different between men and women i.e. that employers misestimate the value of female employees in a different way than the misestimate the value of male employees?”

    Are you honestly asking that question? Because that is the very definition of the bias we’re talking about. Obviously the answer is a resounding yes, there’s plenty of reason to believe that, in spades. That’s the very point which several people here are assuming away, even though their logic suggests that this is exactly what real world data is telling us is true.

    Silas: I think the answer to your question is obvious enough that I conclude your underlying assumptions render you too blind for me to figure out how to answer you.

  13. 13 13 Steve Landsburg

    Cos:

    I think the answer to your question is obvious enough that I conclude your underlying assumptions render you too blind for me to figure out how to answer you.

    Funny, I was about to say the same thing about you.

    Your model presumes not just that *some* employers are blind to an opportunity to raise profit by 30%, but that the *great majority* are.

    I’ve spent enough time on hiring committees, in both academia and the private sector, to know how much effort goes into identifying and recruiting the very best candidates. It’s nuts to think that an opportunity of the sort you’re envisioning could be systematically overlooked by just about everyone.

    But of course, as others have asked — if you’re willing to assume that nearly everyone else is that blind, why are you not willing to assume the same of yourself? If nobody else has the slightest idea of the true productivity difference between men and women, then why should you?

  14. 14 14 Al V.

    The thing that is always unclear to me on this topic, is whether the wage gap is controlled for the actual job and experience. If it’s not controlled for job, then the gap could be explained by supply and demand: women may apply for jobs that have a larger pool of qualified candidates (than jobs that men apply for), and thus they have to take less to get the job.

    Harold has already discussed the need to control for experience.

    Another factor may be the marital state of the employee. Married men in single-earner households tend to work more hours than single men or women, or men or women in dual-earner households, and this makes them more attractive to employers.

  15. 15 15 Pete

    Can a desire for diversity mitigate some of the potential gains? You started from the assumption that everyone employs 50% of each gender. For a company to fully realize the potential savings on labor, they’d have to employ all women. Could it be that companies have factored in the value of having males for the sake of diversity, maybe for more consistency since they don’t leave for maternity, or maybe a preferance for the company of men.

    I think that even factoring all of these, most would still prefer the cheaper female employees, but maybe it would balance out at a 60-40 split or something else other than 50-50 or 100% women.

  16. 16 16 Raymond Rundelli

    I haven’t read through all of the comments today and yesterday, so someone may have made this point already, but I will paraphrase Napoleon and say it is best to attribute the misleading nature of the graph to incompetence rather than to malice. Could it be that graphically the chart is actually helpful in that it shows that the wage gap is FALLING over time? Having the gap curve trend upward would have been more what we were accustomed to seeing given the other information on the graph but having it trend downward makes the conclusion to be drawn (though admittedly probably not the one intended) more graphically, does it not?

  17. 17 17 Patrick

    Steven, I don’t think we should be quite so hard on Cos. His point about being careful not to assume away key independent variables is well taken. Just a few days ago you berated the “Python misinterpreter” for baking in a constant for people’s willingness to engage in a risky behavior – whereas a key part of your argument was that people can adjust their behavior based on the perceived level of risk. In the present case, you can say that EITHER a) almost all employers are bigoted, and willing to forgo a 30% increase in profits to stay true to their prejudice; or b) most employers are not bigoted, but other differences, such as experience, willingness to make personal sacrifices, etc. account for the observed wage differential. Your own experience indicates that (a) is extremely unlikely, and I agree. But so far you haven’t strictly mathematically disproved it – just shown it to be highly unlikely.

    Related thought: I think it is in theory possible for this type of behavior to exist even if employers are not bigoted. As an analogy, think of the case of the famous lunch counter at Wolworth’s. The classical libertarian argument here is that the government should have let Wolworth’s treat their customers however they wanted, because if enough people in the community shunned this company for its racist practices, it would soon either go out of business or be forced to end the discrimination. But imagine that the manager is not a racist – he just wants to maximize his earnings. Imagine that the policy of allowing black customers will, for example, result in 5 black customers per day, but because many of the white customers are racists, 20 of them will not show up. In this case, the racist company policy continues, the manager maximizes the store’s earnings, and we need not assume that he shares his customers’ bigoted views.

    The same could be true for employers. Imagine that the managers just want to make as much money as possible. They will hire men, women, aliens, whatever, as long as they get the job done. But imagine that the other workers are a little biased. A woman will distract them from their work. The possibility of intra-office romances (or harassment suits) will reduce productivity. And so on. You don’t need to assume that the manager is biased to achieve the result that the profit-maximizing labor mix consists of more men than women. If this is true across many companies, the demand for female workers will be lower, and their wages will be correspondingly lower. I could especially imagine this being the case in an industry like investment banking, where upper management is mostly male as a relic from our less enlightened recent past, and barriers to entry (huge regulatory costs, capital requirements, “goodwill” with large customers) prevent enterprising young CEOs from starting new all-female competitors.

    In any case, I hope this might at least provide the framework for an argument that even though management is not inherently biased, and even though they care only about maximizing the company’s profits, a wage gap could exist even where a skill or experience gap does not.

  18. 18 18 Seth
  19. 19 19 Harold

    “If the differential is driven by employer discrimination (as opposed to, say, the abilities and/or preferences of the workers),”

    Here is the rub. Some is driven by employer discrimination. Anyone who disputes this is deliberately ignoring the evidence.

    Some of the rest is driven by abilities and / or preferences of the workers.

    BUT those abilities / preferences are partly driven by discrimination. This is where it gets too complex for backs of the envelope. The discrimination starts from before birth.

  20. 20 20 Harold

    Quick example for illustration. Patrick said “b) most employers are not bigoted, but other differences, such as experience, willingness to make personal sacrifices, etc. account for the observed wage differential”

    It is not willingness to make personal sacrifices, it is willingness to spend more time at the job. The woman makes a much bigger personal sacrifice by caring for the children and damaging her career. It is typical that the man’s choice is seen as heroic, and the woman’s ignored.

    (I have interpreted the statement to mean that the choice of someone to spend more time at work is what Patrick meant by sacrifice. He may have meant it a different way, but it remains typical of the sort of statements one often hears).

  21. 21 21 Tal F

    I agree with the overall gist of the original post, but I do not think that it conclusively “proves” that women are not underpaid. Rather, if one truly wishes to prove that they _are_ underpaid, Steve’s post suggests a much better avenue for doing so than the misguided and misguiding statistics posted by unions. One could look at the proportion of women in different companies in the same industry, and if women are indeed underpaid, one would expect to find the high women companies to be more profitable than the low women companies. Has anybody ever actually tried to measure this?

    Of course, failure to reject would not lead one to accept the null (of no discrimination).

  22. 22 22 Tal F

    Patrick’s comment actually gives a great example of why one might fail to reject the null even though the null is false. Perhaps there is no way to conclusively answer this question (at least using economics and statistics). If men are more willing to work with men, whether due to discrimination or romantic interest or fear of lawsuits, hiring more men may be profit maximizing. In many industries, the performance of a large group of employees may be driven by a few of the very best, and if these best happen to be more comfortable around other men, it may be worthwhile to suffer the higher wages of their coworkers in order to increase their productivity.

  23. 23 23 Patrick

    Harold:

    I would view willingness to work late hours, rather than spend time with your friends, family, or whatever, as a personal sacrifice. I agree that taking time away from your job to start a family is also a type of personal sacrifice. It was not my intention to imply that one is more noble or heroic than the other. I agree that “willingness to spend more time at work” would have been a more neutral, and more accurate, way to express my idea. Thanks.

  24. 24 24 Tracy W

    Harold: People are rewarded by society approval for making choices that society expects. That includes women not becoming engineers.

    Then how did women ever become engineers? (asks she with an engineering degree.) How did women start having babies out of wedlock and raising them? How did the suffrage movement begin?

    (And, while we are at it, why do electrical engineering schools, which I did, run about 90% male students, while chemical and civil about 60% male, and medicine now over 50% female? It seems hard to explain that differential on what society expects.)

    The men are getting the benefit of a society with children that are cared for, the women are paying for it in lower wages.

    But the men are paying for it by lower consumption than if they didn’t have kids, or longer working hours, or both. This may not be a trade-off for non-materialistic workaholics, but for most men it is a tradeoff.

    What’s more, one of my friends is working while her husband stays at home with the kids. And part of the reason they did this was that one of his male friends was already doing that (and they’re not university-educated liberals, but tradesmen living in a small town, where I would expect the social forces you discuss to be stronger).

    There is some argument that these are not entirely “free” choices”.

    Yeah, but the relevant question is whether these social forces are so much as to justify reducing other people’s freedoms by producing political forces. Given the social shifts we’ve seen happpening already, as I’ve outlined, it’s much more difficult to argue that second case.

    Harold: It is typical that the man’s choice is seen as heroic, and the woman’s ignored.

    Actually no, it’s not. Take for example your earlier argument. You totally ignored the sacrifice most men make in terms of lower consumption and/or longer working hours in order to support a family, all you thought about was the sacrifice the woman makes. Nothing odd there, and probably in a different context you’d've thought about the sacrifice that fathers make for their kids, I’m certainly not accusing you of sexism, but this sort of admiration of women, but not of men, is about as typical as the opposite way around.

  25. 25 25 certified accountants

    Can a desire for diversity mitigate some of the potential gains? You started from the assumption that everyone employs 50% of each gender. For a company to fully realize the potential savings on labor, they’d have to employ all women. Could it be that companies have factored in the value of having males for the sake of diversity, maybe for more consistency since they don’t leave for maternity, or maybe a preferance for the company of men.

    I think that even factoring all of these, most would still prefer the cheaper female employees, but maybe it would balance out at a 60-40 split or something else other than 50-50 or 100% women.

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