Recent research exploits a variety of natural experiments that create exogenous variation in annual school days to estimate the average effect of formal schooling on students' academic achievement. However, the extant literature's focus on average effects masks potentially important variation in...

In this paper I demonstrate, both theoretically and empirically, that the interpretation of regression estimates of between-group differences in economic outcomes depends on the relative sizes of subpopulations under study. When the disadvantaged group is small, regression estimates are similar...