This study -- "Family scholarly culture and educational success: books and schooling in 27 nations" -- has lots of citations (here's a good example). This 20 year study of 27 nations (itself impressive) was authored by MDR Evans, Jonathan Kelley, Joanna Sikora and Donald J. Treiman, and it comes from a journal called Research in Social Stratification and Mobility 28 (2010) 171-197.
We should be doing a lot more with this. The "sticky" fact for me: if a child (between the ages of 0-5) of any socioeconomic level and despite the education attainment of the parents has 500 books in the home, it's as good as having two parents with Master's degrees.
How do people get 500 books in the home, especially if they don't have a lot of money? Can you spell "library?"