Intraschool Variation in Class Size: Patterns and Implications

Economists attempting to explain the widening of the black-white wage gap in the late 1970's by differences in school quality have been faced the problem that recent data reveal virtually no gap in the quality of schools attended by blacks and whites using a variety of measures. In this paper, we re- examine racial differences in school quality. We begin by considering the effects of using the pupil- teacher ratio, rather than the school's average class size, in an education production function since the pupil-teacher ratio is a rough proxy, at best. Second, we consider the importance of using actual class size rather than school-level measures of class size. We find that while the pupil-teacher ratio and average class size are correlated, the pupil-teacher ratio is systematically less than or equal to the average class size. Mathematically, part of the difference is due to the intraschool allocation of teachers to classes. As a result, while the pupil-teacher ratio suggests no black-white differences in class size, measures of the school's average class size suggest that blacks are in larger classes. Further, the two measures result in differing estimates of the importance of class size in an education production function. We also conclude that school level measures may obscure important within-school variation in class size due to the small class sizes for compensatory education. Since black students are more likely to be assigned to compensatory education classes, a kind of aggregation bias results. We find that not only are blacks in schools with larger average class sizes, but they are also in larger classes within schools, conditional on class type. The intraschool class size patterns suggest that using within-school variation in education production functions is not a perfect solution to aggregation problems because of non-random assignment of students to classes of differing sizes. However, once the selection problem has been addressed, it appears that smaller classes at the eighth grade lead to larger test score gains from eighth to tenth grade and that differences in class size can explain approximately 15 percent of the black-white difference in educational achievement.