How much does sorting increase inequality?

Some commentators argue that increased sorting into internally homogeneous neighborhoods, schools, and marriages is radically polarizing society. Calibration of a formal model, however, suggests that the steady-state standard deviation of education would increase only 1.7 percent if the correlation between neighbors' education doubled, and would fall only 1.6 percent if educational sorting by neighborhood disappeared. The steady-state standard deviation of education would grow 1 percent if the correlation between spouses' education increased from 0.6 to 0.8. In fact, marital and neighborhood sorting have been stable, or even decreasing historically. Sorting has somewhat more significant effects on intergenerational mobility than on inequality.