California, Oregon and Washington, for instance, have among the lowest shares of women working, and some of the most expensive child care and shortest school days. North Dakota, South Dakota and Nebraska have higher shares of women in the work force, more affordable child care and longer school days.

Research has shown that in industrialized countries, subsidized child care and education had the single biggest effect on women’s employment. In Washington, D.C., public pre-K increased the labor force participation of women with young children by 10 percentage points. The lack of subsidized child care was a major reason the share of women working in the United States unexpectedly stalled in the 1990s. The economic benefits of good, affordable child care for low-income children extend for generations, research has shown, and some studies indicate spending on it more than pays for itself.

“As child care costs increase over the decade, what happens is we see mothers are spending more time in child care,” said Ms. Ruppanner, who conducted the study with Stephanie Moller at the University of North Carolina at Charlotte and Liana Sayer at the University of Maryland. “You’re boxing women out of the labor market.”

But in the United States, people have long had conflicted feelings about whether society and government should make it easier for mothers to work outside the home, and these are complicated by attitudes about race and poverty.

In the 19th century, people thought it was fitting for women to use child care and to work for pay only if their husbands were unable to support them because of death, disability, divorce or drunkenness, said Sonya Michel, professor emerita of history at the University of Maryland. A network of day nurseries started, mostly financed by philanthropy. By the turn of the century, though, they’d been replaced by so-called widows’ or mothers’ pensions. The idea was that if a woman didn’t have a husband to support her, it was still best that she stay home.

The expectation was different for black mothers, beginning with enslaved Africans. Later, poor black mothers were often denied the pensions that white mothers got. Today, most families receiving Temporary Assistance for Needy Families are required to work — and receive some government help with child care to do so.

“The country has been so traditional in the persistence of the idea that women did not belong in the work force,” Ms. Michel said, “but the idea that poor women, especially black women, should work has persisted.”