In this paper we examine the importance of heterogeneity and self-selection into schoolingfor the study of inequality. Changes in inequality over time are a combination of price changes, selection bias and composition effects. To distinguish them, we estimate a semiparametric selection model for a sample of white males surveyed (during the 1990s) by the National Longitudinal Survey of Youth, but our results are applicable to broader analyses of inequality. In our data, as college enrollment increases in the economy, average college wages decrease and average high school wages increase, and therefore inequality between college and high school groups decreases. Moreover, selection bias causes us to understate the growth of different measures of the average return to schooling in our sample. It also leads us to understate the increase in wage dispersion at the top of the college wage distribution, and to overstate it at the bottom of the college wage distribution.