Here's a great find by Lisa Wade discussing Kathleen Gerson's book The Unfinished Revolution. She asks people what kind of family arrangements they'd like, and you see that both men and women say they want an egalitarian arrangement. But egalitarianism is hard in a society where expectations and institutions have been shaped around inegalitarian norms for hundreds of years. As Wade says, "many couples find that, once children arrive, it’s impossible for both to do both with equal gusto."
So what Gerson did is peer beneath what people say their ideal outcome would be to ask what they say their preferred fallback position is. And here you see a stark difference. Men say they want an egalitarian partnership, but if something has to give they want a traditional arrangement where they specialize in market labor and their wife specializes in childrearing and household tasks. Women say that they'd rather be single than be forced into a neotraditional arrangement.
I think this is very relevant to a lot of economic policy debates because the past 40 years have been marked by major changes in gender norms and family life that intersect with economic trends. There was a dispute last year between David Brooks and Paul Krugman—Brooks said that declining marriage rates were a key cause of economic stagnation, while Krugman said they were an effect of it. I said I thought that was backward, and declining marriage rates are more likely a consequence of women's economic empowerment.
I take this survey data to be evidence for my viewpoint. Marriage is an economically efficient arrangement, especially for the parents of young children. Exiting or avoiding it has always been costly in economic terms. If you make the price for women staying single prohibitively high, then very few will choose it, and women will simply have to give way to men's preferences. As women become more economically empowered, the price of staying single falls and more women will opt for it. In some sense, that's going to lead to reduced household incomes and lower material living standards, but that's a bit of an illusion.