Why third generation immigrants earn less

It is well known that second generation immigrants fit better in the host country. This is particularly true with respect to human capital, with the first generation being either less educated than the second, or not being able to exploit fully its existing human capital. What happens to further generations? If the second generation has converged to the local population, there should nothing interesting to see, right?

Wrong, according to Vincenzo Caponi. He observes on Mexican immigrants to the US that the third generation has significantly lower wages than the second. The way I understand it is that there is selection in migration decisions: only those with higher than average abilities (not necessarily realized human capital) go. Their children inherit some of those traits, and thus have higher than average abilities and human capital. While the first generation was not able to fully exploit this, while the second does, wages go up. But abilities of the third generation continue regressing to the mean, and the selection effect erodes. This generation ends up with lower human capital than their parents and thus lower wages.