No surprises

Chetty, Hendren, Kline and Saez are thinking about upward mobility of children;

In particular, areas with a smaller middle class had lower rates of  upward mobility. In contrast, a high concentration of income in the top 1% was not highly correlated with mobility patterns. Areas in which low income individuals were residentially segregated from middle income individuals were also particularly likely to have low rates of upward mobility. The quality of the K-12 school system also appears to be correlated with mobility: areas with higher test scores (controlling for income levels), lower dropout rates, and higher spending per student in schools had higher rates of upward mobility. Finally, some of the strongest predictors of upward mobility are correlates of social capital and family structure. For instance, high upward mobility areas tended to have higher fractions of religious individuals and fewer children raised by single parents. 

...some of the strongest predictors of upward mobility are correlates of social capital and family structure. 

[Thanks to Peter Gordon for the tip]