The birth of sons or daughters, not having a sister and to some extent the pay-check of the husband are the key factors here:
Male CEOs typically pay their employees less and themselves more after having sons, but this trend doesn't hold with daughters. In fact, male CEOs with first-born daughters actually pay their employees more, giving female employees the biggest raises [1].
Men who have daughters also grow less attached to traditional gender roles: they become less likely to agree with the statement that “a woman’s place is in the home,” for instance, and more likely to agree that men should wash dishes and do other chores [2].
Having a sister, however, has the opposite effect, making men more supportive of traditional gender roles, more conservative politically, and less likely to perform housework [3].
Men with stay-at-home wives likewise favour a traditional division of labour. They tend to disapprove of women in the workplace, judge organizations with more female employees to be operating less smoothly, and show less interest in applying to companies led by female executives. They also more frequently deny promotions to qualified women [4].
Working with women, on the other hand, can encourage egalitarianism at home. Men take on more housework after switching from a male-dominated occupation, like construction or engineering, to a female-dominated one, like nursing or teaching, even after controlling for changes in income and hours [5].
But non-traditional career tracks don’t always mean non-traditional domestic roles: men whose wives out-earn them actually do a smaller share of housework than their breadwinner peers [6].
Evidently, the takeaway for women who want advancement at work and chore-sharing at home is this: work for a male CEO with lots of daughters, no sisters, and a working wife, and marry a man with plenty of female colleagues and a pay-check that’s bigger than yours.
References:
[1] Dahl et al., “Fatherhood and Managerial Style: How a Male CEO’s Children Affect the Wages of His Employees” (Administrative Science Quarterly, Dec. 2012)
[2] Shafer and Malhotra, “The Effect of a Child’s Sex on Support for Traditional Gender Roles” (Social Forces, Sept. 2011)
[3] Healy and Malhotra, “Childhood Socialization and Political Attitudes: Evidence From a Natural Experiment” (The Journal of Politics, Oct. 2013)
[4] Desai et al., “The Organizational Implications of a Traditional Marriage: Can a Domestic Traditionalist by Night Be an Organizational Egalitarian by Day?” (Kenan-Flagler Research Paper, March 2012)
[5] McClintock, “Gender-Atypical Occupations and Time Spent on Housework: Doing Gender or Doing Chores?” (presented at the annual meeting of the American Sociological Association,
Aug. 2013)
[6] Bertrand et al., “Gender Identity and Relative Income Within Households” (NBER Working Paper, May 2013)