Children of affluent parents get more schooling than children of poor parents, which seems to imply that reducing income inequality would reduce inequality in schooling. Similarly, one of the best predictors of an individual's income is his educational attainment, which seems to imply that reducing inequality in schooling will reduce income inequality. Economic theory predicts that all else being equal an increase in income inequality will lead to an increase in inequality of educational attainment. Empirical estimates suggest that when income inequality increased in the United States so did inequality in educational attainment. But changes in government education policies reduced the impact of the increase in income inequality on inequality in schooling. Economic theory also predicts that all else being equal an increase in inequality of educational attainment will result in greater inequality of earnings. But unequal schooling does not account for much of the variance in income, so equalizing schooling will do little to reduce the overall variation in economic success among adults. (Contains 2 tables and 18 notes.)