We also present new estimates that show that assortative mating was much stronger than previously estimated for the US.

From Family Trees and Falling Apples: Historical Intergenerational Mobility Estimates for Women and Men by Kasey Buckles, Joseph Price, Zachary Ward & Haley E.B. Wilbert.  From the Abstract.  

Efforts to document long-term trends in socioeconomic mobility in the United States have been hindered by the lack of large, representative datasets that include information linking parents to their adult children. This problem has been especially acute for women, who are more difficult to link because their surnames often change between childhood and adulthood. In this paper, we use a new dataset, the Census Tree, that overcomes these issues by building on information from an online genealogy platform. Users of the platform have private information that allows them to create links among the 1850 to 1940 decennial censuses; the Census Tree combines these links with others obtained using machine learning and traditional linking methods to produce a dataset with hundreds of millions of census-to-census links, nearly half of which are for women. With these data, we produce estimates of the intergenerational transmission of socioeconomic status from fathers to their sons and daughters. We find that for married men and women, the patterns of mobility over this period are remarkably similar. Single women, however, are less mobile than their male counterparts. We also present new estimates that show that assortative mating was much stronger than previously estimated for the US.