Since the 80s in the U.S., we show that there are more upward mobilities (i) in educational attainment, and (ii) in earnings. But, we also show that rank-rank correlation between children and parents earnings is stable across cohorts, thus suggesting that the rise in upward earning mobility is driven by a larger shift in inequalities within parents earnings than within children earnings. We also show that the impact of the income rank of parents with no college degree is very low on the earnings rank of their children, the income differences between parents with no college degree being not relevant in explaining the income positions of their children. For children of parents graduated from college, a high parental income allows them to insure against intergenerational income fall, thus generating a correlation between the income of the parents and that of their children.