Over at the St. Louis Federal Reserve, economist George Levi-Gayle describes the research on this potentially important topic:
In a recent paper, my co-authors, Limor Golan and Mehmet Soytas, and I wrote that the structure of the family and the division of labor within the household were the main sources of the correlation of earnings across generations…Besides income, other factors need to be considered: how parents accumulate human capital in the labor market, the availability and returns to part-time jobs versus full-time jobs and the return to parental time invested in children.
In another study, we looked at the difference between blacks and whites in the intergenerational transmission of human capital. We focused on the roles of time and income spent in the early childhood years to see how they impacted educational outcomes, if at all. We found that the time that parents spend talking to and otherwise interacting with their children is the major reason for the disparity in educational outcomes between black and white children. For example, for black and white parents who spent the same amount of time interacting with their children, there is no black-white attainment gap.
Check out his research here.