In this video, Christina Hoff Sommers recounts the standard result that after accounting for differences occupational choices, there isn't much of a gender gap left. She note that there are also plenty of omitted variables in the typical study to potentially account for most of the rest. 

Christina also emphasizes the market logic that could lead to such a result: if women are cheaper, a private equity firm could make a lot of money by taking over firms that are slowly losing money and make them profitable just by hiring cheaper women. They could cut wages and still get plenty of employees simply by being willing to hire mostly women. Somewhat harder, entrepreneurs willing to hire mostly women should often be successful against established businesses that are reluctant to hire women. I had a storify discussion about this: "The Argument that the Free Market Will Rectify Discrimination as a Guide to Business Opportunities." 

Let me say something about these two points in reverse order.

The logic that predicts the profit motive is enough to close the gender wage gap does not operate in areas where the profit motive is weak. This means that a good place to look for genuine gender wage gaps is in the nonprofit sector—for example, in nonprofit universities. Even there, cost-minimization in the hiring of lower staff is likely to suppress genuine gender wage gaps for lower-level staff. The genuine gender wage gaps are more likely to be concentrated among the professoriate. This does present a genuine opportunity for universities that hire more female professors. But it is not easy for private equity firms to take over a university and make it follow a policy of hiring more female professors. Nor is it easy to establish successful new universities that can compete at the top rank. So universities themselves need to decide to seize the opportunity if it is going to happen; it is not likely to be forced on them. (On this opportunity for Economics Departments specifically, see my post "When Women Don’t Get Any Credit for Coauthoring with Men.")

Turning to Christina's research summary suggesting their is very little in the way of a genuine gender wage gap, I am struck first by how many of the differences in occupational choices made by men and women to back to inequality within households headed by a male-female pair. In this list, let me use the terminology "husband" and "wife," with the understanding that similar issues applied to unmarried heterosexual couples:

1. Husbands are less willing to relocate to help out their wives' careers than wives are to help out their husband's careers. 
2. When there are children, more of the childcare duties typically fall on the wives than the husbands. In particular, being "on-call" for unpredictable child-related events such as a kid getting sick tends to fall more on wives than on husbands. Both regular childcare duties and being "on-call" for unpredictable child-related events make it more difficult to work long hours and more difficult to be "on-call" for an employer. 

Second, I am struck by the role of sometimes subtly, sometimes not-so-subtly hostile workplaces in discouraging women from pursuing many lucrative professions. For example, think of Christina's list of high-paying careers in which women are underrepresented:

• Petroleum Engineering
• Math and Computer Sciences
• Aerospace Engineering
• Chemical Engineering

I am willing to bet that women face ill-treatment in all of these fields. What I know best is that Silicon Valley has produced many stories of ill-treatment for women in the tech industry. In math, the discouragement of women begins early in telling them they are not good at math and sciences. On this, see "Calculus is Hard. Women Are More Likely to Think That Means They’re Not Smart Enough for Science, Technology, Engineering and Math" and "There's One Key Difference Between Kids Who Excel at Math and Those Who Don't." 

In addition to outright ill-treatment, a common type of discrimination against women comes from workplace cultures that amp up the need for highly "competitive" self-serving behaviors that our culture has more actively socialized women against doing than it has socialized men against doing. Men also take advantage of prosocial things that women have been socialized towards doing. 

The details differ by particular occupation. To see how this places out in a narrow neck of the woods, see "How Big is the Sexism Problem in Economics?

When men create hostile or unfair workplaces for women, there can be a tipping point where private equity firms and entrepreneurs swoop in and switch to workplaces with such a preponderance of women that the few men are unable to enforce a hostile workplace environment. But this can require a very discontinuous change. A few more women and a few less men won't do it. There are market opportunities here, but only for the bold.

Third, I do think that our culture bestows more approval on women who sacrifice salary for nonpecuniary benefits than on men who sacrifice salary for nonpecuniary benefits. Men who choose a low-paid meaningful job are more likely to face criticism than women are for not sucking it up and taking the alternative soul-deadening job in order to better support the family. Leaving anything related to child-rearing in another category (see above), here are some of the other nonpecuniary benefits women are given more social approval than men for choosing even at the cost of low pay:

• the knowledge that one is making the world a better place with one's job
• the knowledge that one is greatly helping particular individuals with one's job
• satisfying interpersonal interactions on the job with either coworkers or customers/clients
• an artistic element to a job
• physical safety

Looking at another, more complex dimension, both men and women are given more social approval for choosing jobs that seem gender appropriate. This cuts in all kinds of ways on the relative pay of men and women. For example, men may be too slow to leave the declining manufacturing sector for mid-level and low-level healthcare positions because a factory job seems more masculine. Here women are helped by the fact that nursing, which is a relative good career compared to factory work (given the way things are going), has been deemed gender-appropriate for women. On the other hand, women may be especially ready to go into elementary school teaching despite its low pay because even in 2018, this seems like an especially gender-appropriate career. 

Conclusion: The bottom line is this:

1. There are opportunities to do well by doing good in rectifying inequality in the workplace between men and women, but they may take insight and courage.
2. In addition to its direct harm, men behaving badly to women can be part of the source of pay differences. Better behavior is called for. It is great to see the dam break that guarded a cesspool of sexual assault and harrassment as the #MeToo moment continues with strength. Beyond that, there are a few words recommending better behavior in my post "On Being a Good Guy." 
3. The personal is economic. If husbands won't relocate for the sake of their wives' careers and won't take on tougher childcare duties, it puts women behind in the workplace.
4. Just because most employers aren't discriminating in the purest sense of discrimination doesn't mean that things are fair.  

Hat tip to Joseph Kimball for pointing me to this video.