We estimate intergenerational mobility of children of immigrants in fifteen receiving countries. Children of immigrants have somewhat lower income than children of local-born parents. Around half of this gap can be explained by differences in parental income, with the remainder due to differences in mobility parameters. The daughters of immigrants enjoy higher absolute mobility than daughters of locals in most destinations. Absolute mobility of sons of immigrants is higher outside Europe and lower in Europe compared to sons of locals. Cross-country differences in absolute mobility are not driven by parental country-of-origin, but instead by destination labor markets and immigration policy.

Here is the paper, by Leah Boustan, et.al.  Via the excellent Samir Varma.