The Causal Effect of Class Size on Academic Achievement: Multivariate Instrumental Variable Estimators With Data Missing at Random

This article addresses three questions: Does reduced class size cause higher academic achievement in reading, mathematics, listening, and word recognition skills? If it does, how large are these effects? Does the magnitude of such effects vary significantly across schools? The authors analyze data from Tennessee's Student/Teacher Achievement Ratio study (STAR) of 1985, where students and teachers are randomly assigned to a small or regular class. The authors propose a three-level multivariate simultaneous equation model with an instrumental variable (IV) and estimation via maximum likelihood (ML) to analyze the data under an assumption of data missing at random (MAR). The IV, random assignment of students to a small or regular class, reduces class size which, by hypothesis, improves academic achievement in these domains. The authors extend Rubin's Causal Model (RCM) by involving a modified Stable Unit Treatment Value Assumption (SUTVA), requiring no interference between classrooms and intact schools. The method accommodates data with a general missing pattern and extracts full information for analysis from the STAR data. The authors investigate both homogenous and heterogenous causal effects of class size on academic achievement scores across schools. The results show that reducing class size improves reading, mathematics, listening, and word recognition test scores from kindergarten to third grade, although the effects appear relatively small in second grade. The authors find no evidence that the causal effects vary across schools.