Bounds on effects of class size reduction in project STAR

Beginning with the seminal work of Manski (1990), there has been a growing literature on estimation and inference on partially identifiable parameters, including the distribution and/or quantile functions of the heterogeneous treatment effect. This article applies and extends the bounding approaches that Williamson and Downs (1990) and Fan and Park (2010, 2012) to partially identify distribution of treatment effects of class size reduction (CSR). Empirical data I used are from the Project STAR. Conducted by Tennessee State Department of Education in 1985-1988, it was a large-scale, randomized experiment designed to investigate the effect of CSR on student performance. As an extension of the bounding approach that Fan and Park (2010) used, I proposed bounds for the conditional probability distribution function of treatment effects on pre-treatment outcomes. Although it was hard to find definitive properties of the conditional distribution due to the nature of bounding approach, I find the approach is insightful and has a potential.