Here is the Chetty Paper. It's a big correlational study done across time in the US, looking at income mobility  comparing children's income at age 30 to that of their parents.
It's been floating around the blogosphere, and the results are surprising:

Income mobility has remained flat, in spite of the increase in inequality. This conflicts with the predictions made by Krueger et al ("The Rise and Consequences of Inequality in the United States.") and his "Great Gatsby curve". The results can be reconciled by noting that the Great Gatsby Curve applies to a single time, while the Chetty looks at changes over time. This suggests a two factor model 
inequality = A + B
butmobility = B
. Over time, factorA
has been increasing whileB
has remained constant. 
Parental resources explain very little about low mobility. Greg Mankiw does the math here. Conclusively, 91% of variance in child income is unexplained by parental income.

There is high regional variation. The southeast has low income mobility, the mountain states very high.

The complete lack of any long term change in mobility strongly suggests that various other factors commonly associated with income mobility are not that important overall. Single motherhood has increased significantly, the income share of the 1% has, immigration has gone way up, etc.

At any fixed time, many factors (most notably family structure  single parent families specifically) are negatively correlated with mobility. This suggests another twofactor model. Consider an underlying factor (intrinsic human capital?)
A
, and another temporally varying oneC
. Mobility scales likemobility = A
, but other correlated factors scale likesingle parenthood = A x C
.
My tentative conclusions:
mobility = B
inequality = A + B
single motherhood = A x C