"Based on all of these measures, we find that children entering the labor market today have the same chances of moving up in the income distribution (relative to their parents) as children born in the 1970s.
"Although these rank-based measures of mobility have remained stable, income inequality increased over time in our sample, consistent with prior work. Hence, the consequences of the "birth lottery"---the parents to whom a child is born---are larger today than in the past. A useful visual analogy is to envision the income distribution as a ladder, with each percentile representing a different rung. The rungs of the ladder have grown further apart (inequality has increased), but children’s chances of climbing from lower to higher rungs have not changed (rank-based mobility has remained stable).
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"Together, these two facts can be used to construct various measures of mobility. For example, if one defines mobility based on relative positions in the income distribution---e.g., a child’s prospects of rising from the bottom to the top quintile---then intergenerational mobility has remained unchanged in recent decades. If instead one defines mobility based on the probability that a child from a low-income family (e.g., the bottom 20 percent) reaches a fixed upper-income threshold (e.g., $100,000), then mobility has increased because of the increase in inequality. However, the increase in inequality has also magnified the difference in expected incomes between children born to low- (e.g., bottom-quintile) versus high- (top-quintile) income families. In this sense, mobility has fallen because a child’s income depends more heavily on her parents’ position in the income distribution today than in the past."