Every year on Equal Pay Day, while some Americans lament the fact that in 2014 women still earn around 20 percent less than men, others perform intellectual gymnastics to deny that a gender pay gap exists, or to blame women themselves — and the “choices” they make — for its persistence.

Today, Mark Perry and Andrew Biggs, two scholars at the American Enterprise Institute, got the assignment for The Wall Street Journal. After acknowledging that, yes, women working full-time earn about one-fifth less than what men take home, they write, “but every ‘full-time’ worker… is not the same.”

Men were almost twice as likely as women to work more than 40 hours a week, and women almost twice as likely to work only 35 to 39 hours per week. Once that is taken into consideration, the pay gap begins to shrink. Women who worked a 40-hour week earned 88% of male earnings. Then there is the issue of marriage and children. The BLS (US Bureau of Labor) reports that single women who have never married earned 96% of men’s earnings in 2012. The supposed pay gap appears when marriage and children enter the picture. Child care takes mothers out of the labor market, so when they return they have less work experience than similarly-aged males.

Let us first note that explaining why a phenomenon exists is not the same as demonstrating that it doesn’t exist. It’s not a “supposed pay gap” just because women pay an economic price for having kids.

Its here that the AEI fellows readily acknowledge a huge factor in the gender-gap: the biological reality is that women give birth, and the social reality is that women still bear a disproportionate share of the burden of caring for sick kids or elderly parents. When they take time off to do those things, they lose seniority and often end up looking for a new job after a period of time outside the labor force — neither of which is good for your paycheck.

In 2001, Karen Kornbluh estimated that women’s earnings drop by 7.5 percent with a first child and 8 percent with a second. It also explains why the wage-gap starts out small when men and women first hit the labor market and then grows significantly when they start having families.

So our economy punishes women for the biological reality that they bear children. The AEI guys are apparently fine with that — and want you to believe that it somehow renders the pay gap a “myth” — but it’s important to understand that it doesn’t need to be this way. The US is one of only three countries — along with Liberia and Papua New Guinea — that doesn’t require employers to offer maternity (or paternity) leave. When American women have a baby, their jobs often aren’t waiting for them to return; in most other developed countries, they are. This is a big reason why only four high-income countries in the Organization for Economic Cooperation and Development have larger gender pay gaps than the US.

Perry and Biggs go on to argue that women are paid less because they choose to pursue degrees that result in lower earnings and work in fields that pay less than those dominated by men.

There are two problems with that. First, as Bryce Covert pointed out in The Nation, men performing what have traditionally been seen as “women’s jobs” make more than women do, just as women make less than men for doing traditional “men’s work.”

Among the BLS’s thirteen industry categories, women make less than men in every single one. What this means is that even in “women’s fields,” men are going to rake in more. In fact, men have been entering traditionally female-dominated sectors during the recovery period, and as The New York Times noted, they’re meeting with great success—“men earn more than women even in female-dominated jobs.” Women can enter engineering all they want, but their pay still won’t catch up to men’s.

There’s also a chicken-and-egg issue here: do jobs seen as “women’s work” pay less because they’re inherently less valuable to society, or do they pay less because they’re dominated by women?

The gender pay gap is very real, and there are complex reasons for its stubborn persistence. But even accounting for all the differences in childrearing, career choices and education doesn’t explain away the entire difference in earnings. While it’s no longer socially acceptable, old-fashioned, Mad Men-style sexism is still around, and it still hits women in the wallet. Perry and Biggs use a paper — one often cited by conservatives — by two of their AEI colleagues to dismiss this reality, writing that when all other factors are accounted for, “labor market discrimination is unlikely to account for more than 5% [of the gap] but may not be present at all.”

That finding, however, is an outlier. As Pamela Coukos, a senior program advisor at the Department of Labor, wrote in 2012, “studies consistently conclude that discrimination is the best explanation of the remaining difference in pay.”

Economists generally attribute about 40% of the pay gap to discrimination – making about 60% explained by differences between workers or their jobs. However, even the “explained” differences between men and women might be more complicated. For example: If high school girls are discouraged from taking the math and science classes that lead to high-paying STEM jobs, shouldn’t we in some way count that as a lost equal earnings opportunity? As one commentator put it recently, “I don’t think that simply saying we have 9 cents of discrimination and then 14 cents of life choices is very satisfying.” In other words, no matter how you slice the data, pay discrimination is a real and persistent problem that continues to shortchange American women and their families.

Unfortunately, the “fact-checking” organizations, as they so often do, are seizing on statements that women earn less “for the same work” to conclude that the gender pay-gap is an “exaggeration.” Of the claim, made by Obama in a campaign ad, FactCheck.org states flatly that it’s “not true.” (They also say that he “implied” that “discrimination by employers is responsible for the difference,” but there’s nothing in the ad implying anything of the sort — they just inferred it.)

Their fact-check is “mostly false” — women working the exact same jobs are paid less than their male counterparts every day, for various and often complicated reasons, and those claiming it’s all a myth offer nothing to dispute that reality.