The most recent issue of the NBER Digest has a non-technical summary of an interesting paper published in 2015. Here’s the reference and a link to the full text of the piece:
Blau, Francine, “Immigrants and gender roles: assimilation vs. culture,” IZA Journal of Migration 4.1 (2015): 1-21.
Blau investigates the degree of assimilation in the US by focusing on the fertility and labor supply choices of female immigrants who come from countries with high fertility and low participation rates. She finds that assimilation does happen, albeit relatively slowly. Here’s a graph showing the rate of assimilation when it comes to female labor supply:
Interestingly, Blau also finds that assimilation rates may increase in the future. Specifically, “immigrant source countries may become more similar to the United States, thus reducing the effect of source country gender roles on the behavior of first- and second-generation immigrant women. This has already begun to happen with respect to fertility. The fertility of immigrant women relative to natives has been falling rapidly in the most recent immigrant cohorts.”