Do Black Children Benefit More From Small Classes? Multivariate Instrumental Variable Estimators With Ignorable Missing Data

Does reduced class size cause higher academic achievement for both Black and other students in reading, mathematics, listening, and word recognition skills? Do Black students benefit more than other students from reduced class size? Does the magnitude of the minority advantages vary significantly across schools? This article addresses the causal questions via analysis of experimental data from Tennessee’s Student/Teacher Achievement Ratio study where students and teachers are randomly assigned to small or regular class type. Causal inference is based on a three-level multivariate simultaneous equation model (SM) where the class type as an instrumental variable (IV) and class size as an endogenous regressor interact with a Black student indicator. The randomized IV causes class size to vary which, by hypothesis, influences academic achievement overall and moderates a disparity in academic achievement between Black and other students. Within each subpopulation characterized by the ethnicity, the effect of reduced class size on academic achievement is the average causal effect. The difference in the average causal effects between the race ethnic groups yields the causal disparity in academic achievement. The SM efficiently handles ignorable missing data with a general missing pattern and is estimated by maximum likelihood. This approach extends Rubin’s causal model to a three-level SM with cross-level causal interaction effects, requiring intact schools and no interference between classrooms as a modified Stable Unit Treatment Value Assumption. The results show that, for Black students, reduced class size causes higher academic achievement in the four domains each year from kindergarten to third grade, while for other students, it improves the four outcomes except for first-grade listening in kindergarten and first grade only. Evidence shows that Black students benefit more than others from reduced class size in first-, second-, and third-grade academic achievement. This article does not find evidence that the causal minority disparities are heterogeneous across schools in any given year.