Women, lamented Hillary Clinton in an April 2014 tweet, make just 77 cents on the dollar to men. As a presidential candidate she has repeated that lament again and again, updating the numbers, in line with government statistics, to 78 cents in July 2015 and 79 cents this year.

This injustice, she says, must be remedied by government. “Last time I checked,” Clinton told an event sponsored by a salary site called Glassdoor, “there’s no discount for being a woman. Groceries don’t cost us less, rent doesn’t cost us less, so why should we be paid less?”

There is, as you might expect, a simple answer for that, which is that the 77 to 79 cents numbers are misleading. Women are being paid less than men almost entirely because, as my Washington Examiner colleague Ashe Schow writes, “The average working woman works in a lower-paying field and works fewer hours each week than the average working man.”

Don’t just take her word for it. Listen to Obama staffer Betsey Stevenson, a respected academic economist. “Seventy-seven cents captures the annual earnings of full-time, full-year women divided by the earnings of full-time, full-year men,” she said when pressed by questions from the White House press corps. “If I said 77 cents was equal pay for equal work, then I completely misspoke.”

It’s actually been illegal to pay women less than men for the same work since Congress passed a law to that effect in 1963 — 53 years ago. Any employer who does so is inviting a lawsuit, which most small businesses can’t afford, and courting a negative reputation, which any large business abhors.

Clinton’s use of statistics that are misleading (as Washington Post fact-checker Glenn Kessler concluded) is in service of an argument that as president she will break down barriers that are holding women back. That’s part of her strategy to reassemble Barack Obama’s 51 percent 2012 coalition by promising to break down barriers to upward mobility.

The argument is based on an assumption that every identifiable group would be equally represented in every stratum of society, absent the barriers erected by patriarchal white males. Such appeals have the political advantage of being always available. Beyond Lake Wobegon, some identifiable group will always have a tendency to rank lower than average in something.

The problem is that, if patriarchally erected barriers aren’t the reason for disparate data, it will be hard to deliver on promises that things will be different if they’re battered down. And policies that are supposed to do that may turn out to have the opposite of the intended effect.

Consider last week’s front page Wall Street Journal story headlined, “Women in elite jobs face stubborn wage gap,” and contain your outrage at injustices like the female M.D. who makes only $303,000 compared to her husband’s $364,000. The reporter’s suggested cure for this injustice? More men need to take paternity leave and do additional housework.

Which is to say, the gap results not from institutional barriers but from personal choices, which tend to be rooted in biology. Science — we all respect science, don’t we? — tells us men and women are different. Only women give birth and, it turns out, they’re more likely to take parental leave and choose work that requires limited and definite hours, and which, accordingly, pays less.

Note that these decisions are being made by people who grew up when most women worked outside the home and who attended female-majority colleges and graduate schools. Such women know they have choices, and they tend to choose to trade away income for family time. That’s a rational choice, even if it means never being CEO.

Hillary Clinton’s solutions for equalizing pay — “flexible scheduling, paid family leave and earned sick days” — tend to encourage women to take time off from work, which in turn tends toward lower lifetime earnings. That’s certainly been the effect in Scandinavia, where such policies have been carried farthest. The effect, Swedish scholar Nima Sanandaji writes, is that “many women work, but seldom in the private sector and seldom enough hours to reach the top.”

The fact is that the barriers Clinton thinks are holding women back mostly came down years ago. Her continuing battle against 1950s norms may inspire women of a certain age. But it doesn’t ring true for millennial women, who have been voting overwhelmingly against her in Democratic primaries. Misleading statistics, it turns out, don’t make good politics.

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