Good morning Hank, it's Tuesday. 
So a while back I said in a video, "In the United States women make seventy-seven cents for every dollar that men make in the workforce," and a lot of people pushed back in comments.  You know, "the wage gap is a lie", "that myth has been debunked", "your an idiot" with no apostrophe, etc.  Anyway now after a lot of reading I am going to attempt to share what I have learned about the gender pay gap hopefully without inciting a flame war in the comments. 
This whole question is fiendishly complex and people far smarter than I am have spent their whole careers devoted to it, but I want to begin with a broad observation.  There is a gender pay gap among full time workers around the world, but the size of the gender pay gap varies dramatically by country.  Like in New Zealand women working full time make on average ninety cents for every dollar that a man working full time makes; whereas, in South Korea that number is just sixty-two cents.  When it comes to calculating the pay gap in the United States, a lot depends on what exactly you are calculating.  Like by hourly wage the pay gap is about sixteen percent.  By weekly take-home pay it is between eighteen and nineteen percent.  By annual earnings it's around twenty-one percent.  The fuzziness here speaks to the complexity of what we're about to get into, but basically men on average work more hours than women on average.  Actually, nope, they don't, but men work more paid hours.  Right, but so this sixteen to twenty-one percent number just looks at all full-time workers.  It doesn't account for differences in education or skills or experience or occupation, and when you factor all that stuff in the pay gap shrinks to somewhere between four and eight percent depending on who is doing the math.  This is the so called 'unexplained' pay gap, that is there is no economic explanation for it, and most non-partisan analyses agree that this part of the pay gap is directly due to gender discrimination.  By the way you can find links to lots of sources in the doobly-doo.
But yeah, that four to eight percent number might sound low, but even on the extremely conservative end it would mean that women lose over two hundred forty-one million dollars of pay every year due to direct discrimination.  I should add here that there is also a wide racial pay gap in the United States, and as discussed in this Vlog Brothers video, there is overwhelming evidence that much of that gap is due to direct discrimination.  Because race and gender affect people long before they enter the workforce, it is difficult to disentangle causes here, but we do know that women of color are doubly disadvantaged when it comes to pay regardless of skill level, experience, or education.  
Right, so a portion of the gender wage gap is attributable to discrimination in the United States, but most of it is ostensibly about choice; choice of college majors or flexibility when it comes to hours or occupation, and this is what people generally mean when they talk about debunking the gender wage gap.  Women on average work fewer hours and tend to work in less lucrative professions from school teaching to care-giving; whereas, men are more likely to work in higher paying fields like engineering or anesthesiology.  And some of the pay gap can be found here like in one study in more than a hundred twenty professions, more women than men worked in nine of the ten lowest paying jobs, but of course that isn't only about choice.  It's also about the expectations of the social order.  Like why are there more female nurse anesthetist but more male anesthesiologists?  And then there is the fact that even within almost all of these professions the pay gap persists from computer programmers to teachers to lawyers.  Some of this is the aforementioned 'unexplained' pay gap but some of it is because men on average work more paid hours than women which brings us to the question of unpaid work.
The average adult American woman spends one hundred sixty-seven minutes per day on housework or care for household members.  For the average adult American male it's a hundred one minutes per day.  And that work, even though it's unpaid, is of course very real.  Now none of this is to criticize the many women and many men who work fewer hours or don't work in the labor force at all to focus on child care or housework.  It's only to say that women doing a disproportionate amount of the unpaid labor in the United States inevitably distorts the paid labor market.  We see this especially clearly in studies of what happens to workers after they have kids.  With each child a family has women see their average income relative to men go down.  It goes down about seven point five percent after the first child.  There have been a ton of studies exploring this, but I just want to highlight one.  In 2007 a Stanford professor sent out fictitious resumes to various firms and found that female applicant with children were less likely to be offered positions and when offered jobs were offered lower starting salaries.  Men meanwhile actually seemed to fair better after they have children in both employment opportunities and wages.  This may also be part of the reason that the pay gap gets worse over time.  It's near ten percent from young adulthood until about the age of thirty-five when it suddenly jumps up.  Like one study looking at business school graduates found that right out of school there was a relatively small gap but then eight years later it was much much larger.  And interestingly even in careers dominated by women, men disproportionately advanced to supervisory roles.  Like most librarians are women, but male librarians are disproportionately likely to become library directors.  And there are still large pay gaps within in careers that employ mostly women from nursing to librarianship.  In fact, unless you really cheery-pick the data, a real and consistent pay gap exists across almost all fields, at all education levels, at all ages, and at the current rate of change this wage gap won't close in the United States until 2058.  In short, Hank, there is a gender pay gap, but it is not as simple as women making seventy-seven or seventy-nine cents for every dollar men make.  Instead it's an extremely complicated web of interwoven factors.  Some of the pay gap is attributable to positive, empowered choice that individual women make to work less or to work in fields they find more fulfilling.  Much of it is due to direct discrimination against women especially mothers.  And much of it is also due to the way our social order constructs gender and our expectations of women, and that is something we can change together by, for instance, embracing the idea that there's no reason for the social order to saddle women with most of the world's unpaid work.  And we can also examine the real personal and systemic biases that are distorting the way that we look at women in the workplace and outside of it. 
So the gender pay gap is complicated, and it's integrated with many other socioeconomic phenomena, but make no mistake.  It is real. 
Hank, I'll see you on Friday.