Interviewed by Nick Schulz, he says,

In total, almost half of college graduates move out of their birth states by age 30. Only 27 percent of high school graduates and 17 percent of high school dropouts do so.

It is possible that mobility is the dependent variable, and that more education makes you more mobile. But consider the alternative possibility, which is that willingness to move is the independent variable, and that it happens to be highly correlated with education. Remember that one theory of how World War II ended the Depression is that it moved people out of their home towns, creating new patterns of specialization and trade.

UPDATE (lifted from the comments): Donald R. Davis and Jonathan I. Dingel propose a model in which people face different incentives to move, rather than different tastes for moving.