From the summary:
From an intergenerational perspective, the U.S. income distribution is sticky at both ends. Affluence and poverty are both partially inherited. Policy and research has focused on upward mobility, especially from the bottom. But relative intergenerational upward mobility is only possible with equivalent rates of downward mobility, where much less attention has been directed. Those born into more affluent families may be protected from falling by a “glass floor,” even if they are only modestly skilled.
In this paper we identify a group raised in higher-income households (top two-fifths of family income), who are predicted on the basis of their skills—both cognitive and non-cognitive—to fall down the ladder, but who remain in the higher-income bracket.